Algebra

1. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
5x – 2y = -1
x + 4y = 35

2. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-4x + 9y = 20
-2x – 2y = 10

3. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
The sum of two numbers is 54, and their difference is nine more than the smaller number. Find the numbers.

4. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $135.00 for 3 days and 300 miles, while Mary was charged $250.00 for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

5. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
An orchard operator must dilute 11 quarts of a 60%-insecticide solution by adding water. How many quarts of water should be added to get a mixture that is 2% insecticide?

6. Given the pair of linear equations in two variables:
? Find the x- and y-intercepts (if any) for each line. Show your work.
? Plot those intercepts, and graph the two lines on the same chart.
? Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.
x + 8y = 8
9x – 5y = -5

7. Given the pair of linear equations in two variables:
? Find the x- and y-intercepts (if any) for each line. Show your work.
? Plot those intercepts, and graph the two lines on the same chart.
? Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.
-5x + 4y = 8
15x – 12y = 24

Algebra

See the attached file.

Solve each proportion:
34) b = -3
3 4

40) c + 3 = c + 2
c – 1 c – 3

Solve each equation:

8) y – 1 = 3
X + 3 4

18) 1 = E__
R + r

For R.

Algebra

1. Solve using the five-step problem solving process. Show all steps necessary to arrive at your solution. Express the answer in scientific notation to three decimal places.

If the distance from the earth to the sun were 92,900,000 miles, how long would it take a rocket, traveling at 2.8×10^3 miles per hour, to reach the sun? (Round to three decimal places)

2. Solve using the five-step problem solving process. Show all steps necessary to arrive at your solution.

A semicircular window of radius 14 inches is to be laminated with a sun block coating that costs $0.70 per square inch to apply. What is the total cost of coating the window, to the nearest cent?

3. Solve using the five-step problem solving process. Show all steps necessary to arrive at your solution.

A square light-switch plate is made which measures 6 inches on each side. A square hole measuring 1 inch on each side is left in the center. If the cost to construct the plate is $3.50 per square inch, what is the construction cost?

Algebra

Please see the attached file for the fully formatted problems.

Problem #6
Write the following geometric expression using the given symbol.
times pi times the cube of the radius (r)

Problem #7
Do you think multiplication is distributive over subtraction?
½ (16 – 10) and ½ x 16 – ½ x 10

Problem #8
Determine the range for the following set.
-7, -2, 1, 8, 11

Algebra

Problem-1:
Find the gas mileage of a dream car or any car of your choice. Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer.

Problem-2:
An application of a rational function is T = (AB)/(A+B), which gives the time, T, it takes for two workers to complete a particular task where A & B represent the time it would take for each individual worker to complete the identical task.

Estimate how long it takes you to complete a task of your choice (house cleaning, mowing, etc.) in a given week. Suppose that Jermyn is slower than you at the given task and takes three times as long as you do. If you work together, how long would it take you to complete the task?

Include the type of job, the time it takes you and Jermyn individually to complete the job, and the calculations needed to show how long it would take to complete the job if you worked together. Include units with your answer.

Algebra

2. Write in lowest terms

3. Express compound fraction in lowest terms

4. Write as a single rational expression

5. Add and simplify

6. Reduce to lowest terms

7. Reduce rational expression to lowest terms

8. Solve for z

9. Solve all values of w

10. Find all values of w

11. Solve for u

12. Rewrite in simplified radical form

13. Simplify

14.Rewrite in simplified radical form

15. Simplify

16. Write in simplified radical form by rationalizing denominator

17. An aquarium tank can hold 7700 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 44 minutes. The second pipe can fill the tank in 77 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
18. Solve for y

19. Solve for u

20. Write without exponents

21. Write the following in simplified radical form

22. Simplify. Write without using negatives.

23. Perform complex number multiplication and write in standard form

24. Karl drove 376 miles using 18 gallons of gas. At the same rate, how many gallons of gas does he need for a trip of 282 miles?
25. Simplify complex number as much as possible

Algebra

1. The mass of Earth is about 6 x 10^21 metric tons. The mass of the sun is about 1.998 x 10^27 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.

2. The perimeter P of a square of side x is given by the polynomial equation: P=4x. A baseball diamond is a square 90 ft on a side. Find the perimeter of a baseball diamond.

3. Hadley Electronics is marketing a new kind of plasma TV. The firm determines that when it sells x TVs, its total revenue R (the total amount of money taken in) will be R = 280x – 0.4x^2 dollars. What is the total revenue from the sale of 75 TVs?

4. The polynomial equation C = 0.041h – 0.018A – 2.69 can be used to estimate the lung capacity C, in liters, of a female of height h, in centimeters, and age A, in years. Find the lung capacity of a 20-year-old woman who is 165 cm tall.

5. A researcher wants to investigate the potential spread of germs by contact. She knows that the number of possible handshakes within a group of x people, assuming each person shakes every other person’s hand only once, is given by the following formula.

Use this formula for the following exercises. N = (1/2)(x^2 – x).

a. There are 100 people at a party. How many handshakes are possible?

b. Everyone at a meeting shook hands with each other. There were 300 handshakes in all. How many people were at the meeting?

Algebra

Please assist with the given algebra problems.

See the attached file.

Algebra

Various Algebra Questions. See attached file for full problem description.

1. Simplify: . Show work.

2. Simplify: Show work. Give the exact answer (including a radical).

3. (a) Is the graph of a circle a graph of a function? (Yes or no)

(b) Find the center and the radius of the circle represented by the equation
x2 + y2 + 10x – 4y – 7 = 0

4. Let .

(a) Find g(-1)

(b) Find g(t + 1) and simplify.

(c) Find the domain of the function

5. Acme Electric Company’s monthly bill includes a basic customer charge of $12.00, and a usage charge of $0.07 for each kilowatt hour of electricity supplied.
(a) Write an equation that can be used to determine the monthly bill, given the number of kilowatt hours h supplied.

(b) Determine the electric bill if 1850 kilowatt hours of electricity are supplied.

Algebra

When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -10t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in meters/sec and “k” is the initial height in meters (as if you were on top of a tower or building).

Make up a scenario where a ball is thrown, shot, etc. into the air. You can choose any initial velocity (in meters/sec) and any initial height (in meters) of the ball, but include them in your written scenario. The ball can leave your hand, the top of a building, etc. so you can use many different values for the initial height.

Insert the chosen values for “v” and “k” into the formula listed above.
Use the formula to find the height of the ball at any two values of time, t, in seconds that you want. Show your calculations and put units on your final answer!
Provide a written summary of your results explaining them in the context of the original problem.

Algebra

1. Multiply. (10×9)(-5×8)

2. Write using positive exponents only. b-19

3. Write 0.0000073 in scientific notation.

4. Add 10y2 + 9y – 2 and 10y2 + 6y – 7.

5. Multiply. (2x – 5y)(3x – y)

6. Multiply. (2m – n)2

7. Divide.

8. The distance from a star to a planet is 5.1  1018 m. How long does it take light, traveling at 1016 m/year, to travel from the star to the planet?

9. Divide.

10. Subtract 2x – 3×2 + 5×3 from 5×3 + 4x – x2.

11. Find the greatest common factor. 21b2, 35b3, 70b10

12. Use the ac test to determine if the following trinomial can be factored. If it can be factored, find the values of m and n.
3×2 + 11x – 4

13. Factor. 12x4y3 + 16x3y3 – 20x3y4

14. If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?

15. Factor. x(x – 1) + 9(x – 1)

16. Factor. 9x(x + 6y) – 4(x + 6y)

17. Factor completely. 5×2 + 39x + 28

18. Rewrite the middle term as the sum of two terms and then factor by grouping.
x2 + 11x + 10

19. Rewrite the middle term as the sum of two terms and then factor by grouping.
x2 – 2x – 15

20. Solve. x2 + 8x + 15 = 0

21. If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number.

22. Simplify.

23. Add. Express your answer in simplest form.

24. A 6-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 18 feet?

25. One number is 3 times another. If the sum of their reciprocals is , find the two numbers.

26. Write in simplest form.

27. Add. Express your answer in simplest form.

28. Subtract. Write your answer in simplest form.

29. Solve.

30. What values for x must be excluded in the following fraction?

31. Evaluate , if possible.

32. Find the length x. Express your answer in simplified radical form.

33. Which two expressions are equivalent?

34. Find the distance between (19, -8) and (7, -3).

35. Evaluate , if possible.

36. Simplify. Assume x represents a positive number.

37. Simplify.

38. Use a calculator to approximate to the nearest hundredth.

39. Graph the quadratic equation after completing the given table of values. y = x2 – 1

x y
-2
-1
0
1
2

40. The length of a rectangle is 3 cm more than 2 times its width. If the area of the rectangle is 89 cm2, find the dimensions of the rectangle to the nearest thousandth.

41. Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).

y = x2 – 4x

42. Find the x-intercepts.
y = x2 + x – 5

43. Find the x-intercepts.
y = x2 – 4x + 4

44. Graph the quadratic equation after completing the given table of values. y = -x2 – 2x

x y
-3
-2
-1
0
1

45. Find the axis of symmetry.
y = -x2 – 8x + 5

46. The height h in feet of an object after t seconds is given by the function
h = -16t2 + 60t + 9.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

algebra

These problems are labeled as Natural numbers, Prime numbers, Integers, Rational numbers, Irrational numbers, Groups Felds and Real numbers, Discrete Mathematics,and Crytography.

p.188 #26 Classify as an example of the commutative property, the associative property, or both: (3+5)+(2+4)=(3+4)+(5+2)

p.188 #30 Think of three nonassociative word triples (i.e., (word1 word2) word3 has a different meaning than word1 (word2 word3), e.g., (man eating) tiger and man (eating tiger).

p.190 #59 (Solve two different ways) Put the appropriate plus or minus signs between the numbers, in the correct places, so that the sum total will equal 1.
0 1 2 3 4 5 6 7 8 9 = 1

p.203 #18 Write the prime factorizations for each of the numbers. If the number is prime, so state.
a. 108 b. 740 c. 699 d. 123

p.203 #20 Write the prime factorizations for each of the numbers. If the number is prime, so state.
a. 490 b. 4,752 c. 143 d. 51

p.203 #32 Find the canonical representation of the number 111.

p.203 #46 Two movie theatres, UAI and UAII, start their movies at 7:00 PM. The movie at UAI takes 75 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start at the same time?

p.203 #50 Pairs of consecutive odd numbers that are primes are called prime twins. For example, 3 and 5, 11 and 13, and 41 and 43 are prime twins. Can you find any others?

p.212 #20 Simplify the expressions:
a. -5(8-12) b. [-5(8)]-12

p. 212 #30 Simplify the expressions:
a. -14-21 b. -9+16+(-11)

p. 212 #32 Simplify the expressions:
a. -46-(-46) b. |7-(-3)|

p. 212 #46 Simplify the expressions:
a. [-54(-9)] 3 b. -54[(-9)3]

p.220 #26 Perform the indicated operations:
a. 1/2 + 1/3 + 1/5 b. 2-1 + 3-1 + 5-1

p. 220 #32 Perform the indicated operations:
a. 1/10 * (-2)/5 b. -5/18 * 9/25

p. 220 #36 Perform the indicated operations:
a. 2/3 – 7/12 b. -7/24 + (-13/16)

p. 220 #38 Perform the indicated operations:

Algebra

See the attached file.

Solve by completing the square
________________________________________________________________________
The width of a rectangle is 1ft less than the length. The area is find the length and width.

The width is __________ft

The Length is _________ft

A farmer decides to enclose a rectangular garden, using the side of a bard as one side of the rectangle. What is the maximum area that the farmer can enclose with 100ft of fence. What should the dimensions of the garden be to give this area?

The maximum area that the farmer can enclose with 100ft of Fence is ______sq ft

The dimensions of the garden to give this area is 50 ft by ______ft

Find the x-intercepts and y -intercepts for

The x intercept(s) is (are) __________
The y intercept(s) is (are) __________

(type an ordered pair. Type an integer or a decimal. Round to the nearest tenth. Use commas to separate answers as needed. Type N if there is no intercept.

Write a quadriatic equation in the variable x having the given numbers as solutions. Type the equation in standard form, .

Solution: 3, only solution

The equation is ____________=0

Determine the nature of the solutions of the equation.

a. 2 real soluions
b. 1 real solutions
c. 2 imaginary solutions

Find the x intercepts of:
What are the x intercepts___________________
(type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. use a comma to separate answers as needed)

A. Solve
B. Find the x-intercepts of

a) what are the solutions?
X=________________
(type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. use a comma to separate answers as needed)

b) What are the x intercepts?
_______________________
(type an ordered pair, type an exact answer using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. use a comma to separate answers as needed. Type N if there is no x intercepts)

A student opens a mathematics book to two facing pages. The product of the page numbers is 110. Find the page numbers.

The first page is_____
The second page is _________.

Algebra

1. Express and evaluate the distance between the numbers 84 and -34 using absolute value.
2. -6 (2x-9) -4x+5
3. (x ) -3
4.
5. 2+6 given x = 4
6. ( 8-7w + 2y)
7. 8x+7 given x = -3
8. Simplify 7 completely.
9.
10.
11.
12.
13. Determine whether 15>16 is true or false.
14. 6 + 3
15. Given x = 1 and y = 3

Algebra

See attached file for full problem description.

Algebra

1. Solve using the five-step problem-solving process. Don’t forget to include the fifth check equation step of the problem- solving process in your answer.
The difference between two positive integers is 36. One integer is three times as great as the other. Find the integers.

2. Use an inequality and the five step problem-solving process. Don’t forget to include the fifth check equation step of the problem- solving process in your answer.
The color guard is making new triangular flags that must have a base of 18 inches to fit on their flagpoles. What is the maximum length of the triangular flags, if they want to use a maximum of 180 in^2 of cloth?

Algebra

Lets say Costco price club claims that they sell a 6 pack of Coors Beer at the wholesale price plus an additional 5% off. But with Costco, you also have to pay a yearly membership fee of $60 just to have the privilege of shopping there. The wholesale price of Coors at Costco is $3.50 a six pack. The 5% discount is taken at the register when you pay.

My local grocery is currently running a special on Coors Beer 6 packs where the price is discounted by 10% of the regular price. The regular price is $5.00 a six pack.

Here is the question (After all that you say!): What is the minimum number of 6 packs of Coors per month would I have to buy at Costco to make the membership worthwhile as compared to just getting the 10% at my neighborhood grocery store?

Algebra

1. Express in terms of i:
-sqrt(-297)

2. Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero.
8-1/3ax-7/8z^8

3. Simplify. Assume that no radicals were formed by raising negative numbers to even powers.
sqrt(20)k^7q^8

4. Simplify:
(-3a^2)^3

5. Simplify. Do not use negative exponents in your answer.

(2xy)^(-3)

6. Add.
3x^8 + 8x^7 + 6x^6 – 4
5x^8 + 2x^7 + 6x^6 – 8

7. Find the degree of the given polynomial.
-4y^8 – 3x^7z + 4xz^7

8. Multiply.
(m^3n – 9)(m^3n – 5)

9. Perform the indicated operation.
(42k^3 + 12k^2 + 18k) ÷ (6k)

10. Solve the problem. If necessary, round to the nearest tenth.
A car dealer advertised a big sale by stretching a string of banners from the top of the building to the edge of the driveway. If the building is 26 m high and the driveway is 43 m from the building, how long is the string of banners?

11. Factor the expression into a product of two binomials.
5x(3x – 5) + 2(3x – 5)

12. Factor completely. If the polynomial is prime, state this.
75x^2 – 3

13. Factor completely. If the polynomial is prime, state this.
48x^2 + 40xy – 48y^2

14. Factor by grouping, if possible.
x^3 + 3x^2 + 8x + 24

Algebra

1. Factor the following expression completely
36×3 – 16x

2. Andrew factored the expression 28x^3-6x^2-10x as 2x(14x^3-3x^2-5x). But when Melissa applied the distributive law and multiplied out 2x(14x^3-3x^2-5x), she got 28x^4-6x^3-10x^2 ; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

3. The area of a rectangular athletic field is represented by the expression 36y^2-81z^2 square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution.

Algebra

Please demonstrate. Please see the attached file.

Algebra

2-3 paragraphs

Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch). Compute the volume of your solid and include units with your answer. You do not need to use fractions in your computations; their decimal equivalents are fine. Include the type of object, the measurements, and show how you obtained the volume. Please summarize your results in a brief sentence using the correct units of measure for volume.

Part 2: The equation C=mx+b can be used to model the monthly cost, C, of a cell phone plan where b is the flat monthly cost, m represents the cost in dollars per minute and x is the number of minutes used in the month. Choose a flat monthly rate and cost per minute and insert the values you have chosen for m and b into the equation. Then use this equation to find the total monthly cost, C, if 67 minutes are used (or as if there were 67 minutes of overage).

Be sure to reference your sources using APA style.

Algebra

Please show work for each!

54. Find the polynomial function of degree 3 with real coefficients that satisfies the given conditions.

Zero of 4 having multiplicity 2 and zero of 2 having multiplicity 1; f(1) = -18

48. Use the intermediate value theorem for polynomials. 1 and 2

58. Show that the real zeros of each polynomial function satisfy the given conditions.
no real zero is greater than 1

14. Solve each variation problem.

If m varies jointly as z and p, and m = 10 when z = 2 and p =7.5, find m when z = 5 and p = 7.

28. The current in a simple electrical circuit varies inversely as the resistance. If the current is 50amps when the resistance is 10 Ohms, find the current if the resistance is 5ohms.

40. The number the long distance phone calls between two cities in a certain time period varies directly as the populations p1 and p2 of the cities, and inversely as the distance between them. If 10,000 calls are made between two cities 500 mi apart, having populations of 50,000 and 125,000, find the number of calls between two cities 800mi apart, having populations of 20,000 and 80,000.

52. Concept check, Work each problem.

What happens to y if y is inversely proportional to x, and x is tripled?

Algebra

The picture is just of a square 3/4 of the square is shaded if I can get help with that information thank you you will not be able to see the picture of the square.
1. Area of a square. Find a polynomial A(x) that represents
the area of the shaded region in the accompanying figure.

——————X——————–
3 THE SAME GOING DOWN 3 AND X

ONE THIRD OF THE SQUARE IS SHADED

2. Compounded semiannually. P dollars is invested at annual
interest rate r for 1 year. If the interest is compounded
semiannually, then the polynomial P(1+R/2)2
represents the
value of the investment after 1 year. Rewrite this expression
without parentheses. Evaluate the polynomial if
P = $200 and r = 10%

Algebra

Solve the algebra equation.

Algebra

Sue is offered a new job selling furniture where she makes a base pay of $1500 a month plus commission. According to a current employee, she should be able to earn $30,000 in sales monthly. To maintain her standard of living she must make $3000 total monthly. What commission rate must she earn to maintain her standard of living?

4.5%
5%
5.5%
6%

Given that a line passes through two points (4, 5) and (6, 9), answer the following questions:

a. What is the slope of the line?

b. What is the equation of the line in slope intercept form?

c. What is the equation of the line in point slope form?

d. What is the equation of the line in standard form?

Write the equation of the linear function passing through the points (2, 3) and

(4, 5) in slope intercept form.

A y=x-5

B y=x+5

C y=x+4

D y=x+1

Write the equation of the linear function passing through the points (6,3) and

(7,8) in standard form.

A -5x + y = -27
B -x – 5y = 3
C y – 5x = 27
D y = 5x +27

Determine the linear function that models the directly proportional data in the following chart.

R S
42.0 294.00
54.5 381.50
66.0 462.00

A S=5R
B R=5S
C R=7S
D S=7R

In order for the function shown in the table to be linear, what must be the value of b?

40 72
45 84
50 96
55 b
60 120

A 132
B 110
C 84
D 108

Algebra

1) Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x)=-2x(squared) + 8X – 1

2) An equation of a quadratic function is given — f(x)= -2X(squared) – 12X + 3
– Determine without graphing, whether the function has a minimum value or a maximum value.
– Find the minimum or maximum value and determine where it occurs.
– Identify the function’s domain and it’s range.

3) Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible, what is the maximum product?

Algebra

Please tell whether the statement is true or false. Please justify answers.

1. (11, 9) = (9,11)
2. (2-12,7-9) = (-10, -2)
3.(10 + 13, 2 + 13) = (10,2)

Find the cartesian product
4. A= {0}
B={11, 21, 31}
Find B x A

Find the indicated cardinal number. Show work.
5. Find n (G), given that n (D x G)=20 and D ={7, 8,9, 10}

6. Find n(B)giventhat n(AxB)=15 and n(A)=5

7. Find n (A x B)given that n(A)=29 and n(B)=5.

Algebra

The Sugar Sweet Company is going to transport its sugar to market. It will cost $3125 to rent trucks, and it will cost an additional $125 for each ton of sugar transported.

Let c represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating to C , and then graph your equation using the axes below.

C
4500

4000

3500

3000

2500
-1 1 2 3 4 5 6

Algebra

Liza kept the following records of her utility bills for 12 months.
find the mena of he folliwng set of numbers. …
[See the attached Question File.]

Algebra

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2015. Solve the problem using the method similar to that used to solve number 65 on page 422 of the e-book. Show your detailed, worked out solution for full credit. Write a paragraph about how you might use this information in a role as a politician, government administrator or business owner/operator. What will it mean to the country, its economy, resources or the business? Be sure to reference all sources using APA style. Do not use any part of the sample below in your post; do not use India, China or the United states as your country. Type (1.014)^7 for (1.014) to the seventh power.

Note that this sample would not receive full credit because there is no detailed work shown, nor does it have the discussion asked for in the prompt.

Sample Post: The population of India in 2005 was 1,080,264,388 (there is more recent data available, so use the most recent you can find). The growth rate is 1.4%. Note that in this instance, the percent must be converted to its decimal equivalent before it can be used to make computations with the formula.

In 2006, the approximate population is 1,095,388,089. P = 1,080,264,388 * (1.014)^1
In 2007, the approximate population is 1,110,723,523. P = 1,080,264,388 * (1.014)^2
In 2008, the approximate population is 1,126,273,652. P = 1,080,264,388 * (1.014)^3

In 2012, the approximate population is 1,190,681,880. P = 1,080,264,388 * (1.014)^7

In your example, you should carry this out to 2015, as instructed.

Cite your sources using APA style.

Algebra

Find the slope of the line that goes through a pair of points

22. (5,1), (8,9)

26. (-1,3),(3,5)

30. (-1,3), 5,-2)

34. (-3,6),(8,6)

38. (-0.1,0.2)

Algebra

Part 1:

Using the Library, web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer.

Cite your sources using APA style.

Part 2:

The equation

D=sqrt(2h)
, also typed as D=sqrt(2h), can be used to approximate the distance, D, in miles that a person can see to the horizon from a height, h, in feet. Suppose that you are in an airplane. By choosing any height, find the corresponding distance that you should be able to see to the horizon. Include the height and the calculations needed to find the distance. Include units with your answer, and show all work for full credit.

Algebra

1. The Population of the town is 7,000 people. …
2. Suppose that the mayor of the town you have chosen has built a new factory in hopes of drawing as many new people to the town as possible. …
3. Population Decline Modeled by a Rational Equation …

For noninteger answers, please write your answer as a fraction rather
than a decimal.
To show your work, you will need to include
the algebra used to compute the solution to any equations.
the formula with substituted values.
the final calculated answer with units.

[See the attached Question File.]

Algebra

Below are examples expressions for a variable. I need to explain my problem and answer just like the examples below, please give me a few problems to explain just like the samples below thanks…

A mathematical expression is similar to a phrase or fragment of a sentence. An expression has no subject and no verb or relation symbol such as ‘=’ (is equal to) or ‘<‘ (is less than) or ‘>’ (is greater than)

Examples:

Four smaller than a number … n – 4
Five times a number … 5n = 5 ? n = 5 (n) = (5) (n)

We cannot solve an expression for a variable. If we are given a value to substitute for the variable, we can simplify or evaluate the expression.

Examples:

Substitute 13 for ‘n’ and simplify or evaluate the expressions.

n – 4 = 13 – 4 = 9

5n = 5 g 13 = 65

An equation is similar to a complete sentence. It has a subject and verb, and is a complete idea. Mathematical sentences or statements are called equations (=) and inequalities (<, £, >, ³). The relation symbols are the verbs of the sentences.

Examples:

Ten is six less than a number … 10 = n – 6

Seven times a number is equal to twenty-eight … 7n = 28

We can solve an equation for a variable … finding the numerical value that makes the sentence or equation a true statement.

Example:

Solve for n: 10 = n – 6

10 = n – 6 … We always write the original problem when we start
n = 10 + 6
n = 16 … This means that n = 16 makes the original equation a true statement

Check:

10 = n – 6
10 = 16 – 6
10 = 10 … True Statement

Example:

Solve for n: 7n = 28

7n = 28
n = 28 ¸ 7
n = 4 … This means that n = 4 makes the original equation a true statement

Check:

7n = 28
7 g 4 = 28
28 = 28 … True Statement

Algebra

Solve the following:
secx = -5

find sin 2x

find cos 2x

tan 2x

if tan x = 1/2
find sin x/2

cos x/2.

Algebra

1. y = 2x + 3 and y = -x – 4

2. 2y + 3x = 7 and 8y + 12x = 28

3. 5x + 6y = 1 and x + 7y = 2

Algebra

The basic income generated by my main product is $10 a unit, but this increases by $1 for every unit I make.
If I have to cover fixed costs of $100, how many units must i sell to cover all my costs.

Algebra

Review examples 2, 3, and 4 in section 8.4 of the text. How
does the author determine what the first equation should be? What about the second equation?
How are these examples similar? How are they different? Find a problem in the text that is similar
to examples 2, 3, and 4.

EXAMPLE 2 Blending Flower Seeds. Tara’s website, Garden Edibles, specializes
in the sale of herbs and flowers for colorful meals and garnishes. Tara
sells packets of nasturtium seeds for $0.95 each and packets of Johnny-jumpup
seeds for $1.43 each. She decides to offer a 16-packet spring-garden combination,
combining packets of both types of seeds at $1.10 per packet. How
many packets of each type of seed should be put in her garden mix?

EXAMPLE 3 Student Loans. Jed’s student loans totaled $16,200. Part was
a Perkins loan made at 5% interest and the rest was a Stafford loan made at 4%
interest. After one year, Jed’s loans accumulated $715 in interest. What was the
amount of each loan?

EXAMPLE 4 Mixing Fertilizers. Yardbird Gardening carries two kinds of
fertilizer containing nitrogen and water. “Gently Green” is 5% nitrogen and
“Sun Saver” is 15% nitrogen. Yardbird Gardening needs to combine the two
types of solution to make 90 L of a solution that is 12% nitrogen. How much
of each brand should be used?

Algebra

Factoring a sum or difference of two cubes
Factor completely:

27t^3-125

Algebra

Part 1: Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , where p is the number of new homes built in the first year recorded. If you were a homebuilder looking for work, would you prefer that the value of a to be between 0 and 1 or larger than 1? Explain your reasoning.

Typing hint: Type formula above as H = p * a^t

Part 2: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents.

Find the pH factor of a substance of your choice. Is this substance acidic or basic? Why?

Using this pH, show how to find the hydrogen ion content of the substance using the formula. Round to 10 decimal places or write your answer using scientific notation. Include units on your answer.

Typing hint: 2.3 * 10^4 is an example of a number typed in scientific notation. Note that it is inappropriate to use decimals in the exponents of numbers written in scientific notation.

Be sure to reference all sources using APA style.

Algebra

Good morning – my son has chapter test tomorrow and on linear equations. I would love to be able to help him study, unfortunately is been a while since I’ve done linear equations and my knowledge is sketchy at best.

Attached is a study guide that he will be using to study from. Can you please solve the equations and provide a brief description of how you solved the equation (note the explanation is very important part of the exercise so that I will be able to explain it to him what needs to be done).

Algebra

All boulders and rocks (large enough not to be buffeted by air current) appear to take the same time to hit bottom. My conjecture, observes Galileo, leader of the team, is that there is a universal gravitational constant which affects all objects, large or small. Knowing, as he does, that if such a constant exists, call it g for gravity, it can be plugged into our quadratic equation

x(t) = -½gt2 + v(t=0)t + x(t=0)

where v(t = 0) is our initial velocity (which is 0 if the object is dropped, rather than thrown, off of the leaning tower) and x(t = 0) is the distance that we are standing above ground level (the height at that level of the leaning tower). Well, what we know, and what Galileo is about to find out, is that our gravitational constant g = 32 ft / sec / sec. Let us say, then, that we begin by dropping rocks and boulders of various sizes off of the leaning tower. Just dropping our object, our v(t = 0) term would be 0, so that our equation becomes

x(t) = -½gt2 + x(t=0)

We have, as we know, g = 32 ft / sec / sec and the following data
storey 1 height = 39.37 ft. Consequently, our equation for storey 1 is
-16t2 + 39.37 = 0

Well, we trudge up to a height of 77.7 ft. At this point, Galileo is exhausted. Consequently, in frustration on the third storey, he throws an object toward the earth (rather than just dropping it) at a rate of 20 ft / sec. Thus, on storey 3, at a height of 77.7 ft, our object has an initial velocity of 20 ft / sec. downward.
Formulate the quadratic equation, giving height as a function of time, for our object thrown from the 3rd storey of the Leaning Tower. Again, determine the solutions for this equation and interpret the solutions. How long does it take for our object, thrown off of storey 3, to hit bottom?

Algebra

1. At the kickoff of a football game, the receiver catches the ball at the left side of the goal line and runs for touchdown diagonally across the field. How many yards would he run? (football field is 100 yards long and 160 feet wide)

2. At a large size U.S company, the profit, y is related to the number of Vice Presidents, x according to the equation y=-25 +300x. What number of Vice presidents will maximize the company profit? What is the maximum possible profit in millions?

3. At the denver Broncos game the number of tickets sold decreases with increasing price, but the total revenue generated for the broncos team does not necessary decrease. Use the formula R=p(48000-400p) to determine the revenue when the price p of each ticket is 20dollars and when the price p is 25 dollars. What price would produce revenue of 1.28 million dollars? Use the graph to find the price that determines the maximum revenue for his Broncos football team.

4. Ken has just got a job offer and been commuting 60 miles each way to and from work. Returning home one evening he increased his average speed 9 miles per hour above the rate on the way to work. This increase in miles per hour reduced his return time by 20 minutes. What was his average speed going to work and returning home.

(solving rational inequality) State and graph solution set

9. vertex and intercept -sketch graph and state domain and range

Algebra

1. Why is it necessary to study the order of operations and the laws of operations before you start solving equations?
2. Of the three laws, commutative, associative, and distributive, which one is most frequently used in algebra? Why?
3. How does a term differ from a factor?
4. When adding or subtracting expressions, how do you identify like terms. Show an example.

Algebra

Graph the slope -1 passing through (5,5).

Algebra

Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 25 degrees Celsius. They also find that the temperature decreases by 3 degrees Celsius for each kilometer you go up from the surface.
Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). Write an equation relating T to H and then graph your equation.

Algebra

The table below shows where people over 65 in the US live. A total of 23% of elderly men live either alone or with relatives. The sum of double the percent of men who live alone and triple the percent who live with relatives exceeds the percent of US women over 65 who live with their spouse by 13%. What percent of elderly men live alone and what percent live with relatives?

Males who Live with Spouse 74%
Females who Live with Spouse 40%

Females who Live Alone 42%

Females who Live with Relatives 16%

Males who Live with Non-relatives 3%
Females who Live with Non-relatives 2%

Algebra

1) Find the quotient,q(x), and the remainder,r(x), when 3x^3+9x^2-16x-51 is divided by x^2+5x+7.

q(x)=
r(x)=

2) Solve: x^3-1/2x^2+4/3=11/3x^2-2/3x+4/3

The smallest zero is ________

The largest zero is _________

3) Given that 3x-2 is a factor of 3x^3-2x^2-15x+10, select all of the following that are real solutions of the equation 3x^3-2x^2-15x+10=0.

a)x=2
b)x=sqrt(5)
c)x=-2/3
d)x=1
e)x=-sqrt(5)
d)x=2/3
e)x=5

Algebra

46. Draw line h through (0,3) with slope 1 and line h through (0,0) with slope 1.

48. Draw h through (-2,11) with slope 2/3 and draw h through (-2,1) with slope -3/2.

58. In each case determine weather the lines h and h are parallel , perpendicular or neither

a) Line h goes through (-1,4) and (4,6). Line h goes through -7,0) and (3,4).

60. Line h goes through (1,2) and (1,-1). Line h goes through (4,4) and (3,3)

62. Line h goes through (-3,7) and (4,7). Line h goes through (-5,1) and (-3,1)

Algebra

Concept Exercise 5

Problem: The level of a prescription drug in the human body over time can be found using the formula
L = D
1-( )
Where D is the amount taken every n hours and H is the drugs half-life in hours.

1) If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours then to what level does the drug build up over time?
2) If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?
3) What is the difference between taking 2.5 milligrams of Lorazepam every 12 hours and taking 5 milligrams every 24 hours?

Concept Exercise: Given the above problem, provide written responses to address the following points as precisely and thoroughly as possible.

1) Explain the problem in your own words.
2) What mathematical concepts learned in this module apply to this problem?
3) Explain the steps you must take to solve the problem.
4) What is the most difficult aspect of solving this problem?
5) Explain exactly what the answer means from a mathematical perspective.

[See the attached questions file.]

Algebra

Should algebra be taught to everyone? Who should study algebra? The statements below serve as possible answers to these questions and are only ‘food for thought.’ I welcome your constructive ideas and comments on one or several of them.

Whether you agree or do not agree, the study of algebra is good for the brain. The brain is a muscle, and you must use it to keep it strong.
Learning algebra does not have to be agonizing … the process of learning algebra is easier if students are introduced to algebraic reasoning early in life.
Students who learn algebra at the elementary level have a stronger foundation for higher-level mathematics.
Algebra helps to pave the way for college.
Algebra is very conceptual, but there are ways to teach it to make it concrete, to give specific examples that are relevant to students of any age.
While a force of mathematical specialists is needed for society, most individuals do not need algebra.
Students should be encouraged to study algebra to increase their career opportunities … algebra is a gatekeeper to countless educational and economic prospects.
Several students ‘fear’ algebra … it is only an extension of arithmetic.

Algebra

The line passes through the point(x,y) = (-7,6) and has a slope of 3; write an equation for this line.

Algebra

Please solve as follows:
• o For noninteger answers, please write your answer as a fraction rather than a decimal.
• To show your work, you will need to include
o the algebra used to compute the solution to any equations.
o the formula with substituted values.
o the final calculated answer with units.

1. Solve . You must show all work to receive full credit.

Show work here: First I simplify:
2(x + -4) = 2[x + -3(x + -1) + 2]

Then reorder:
2(-4 + x) = 2[x + -3(x + -1) + 2]
(-4 * 2 + x * 2) = 2[x + -3(x + -1) + 2]
(-8 + 2x) = 2[x + -3(x + -1) + 2]

-8 + 2x = 2[x + -3(-1 + x) + 2]
-8 + 2x = 2[x + (-1 * -3 + x * -3) + 2]
-8 + 2x = 2[x + (3 + -3x) + 2]

Reorder the terms:
-8 + 2x = 2[3 + 2 + x + -3x]

Combining like terms:
3 + 2 = 5
-8 + 2x = 2[5 + x + -3x]

Combining like terms:
x + -3x = -2x
-8 + 2x = 2[5 + -2x]
-8 + 2x = [5 * 2 + -2x * 2]
-8 + 2x = [10 + -4x]

Solving for X
-8 + 2x = 10 + -4x

First I move all terms X to left and the rest to the right:

Add ‘4x’ to each side of the equation.
-8 + 2x + 4x = 10 + -4x + 4x

Combine like terms: 2x + 4x = 6x
-8 + 6x = 10 + -4x + 4x

Combine like terms: -4x + 4x = 0
-8 + 6x = 10 + 0
-8 + 6x = 10

Add ‘8’ to each side of the equation.
-8 + 8 + 6x = 10 + 8

Combine like terms: -8 + 8 = 0
0 + 6x = 10 + 8
6x = 10 + 8

Combine like terms: 10 + 8 = 18
6x = 18

Divide each side by ‘6’.
x = 3
Final Answer: X=3

2. Solve . You must show all work to receive full credit.

Show work here:

Final Answer:

3. The cell phone service for the CEO of a small company is $39.99 a month plus $0.10
per minute for long distance. In a month when the company’s phone bill was $75.19,
how many minutes of long distance did the CEO use? Set up an equation and solve.
Show all work to receive full credit.

Equation:

Show work here:

Final Answer:

4. The equation represents the formula for total distance traveled. The distance
traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use this
formula to help solve the following problem.

Two runners, Jay and Ben, start at the same time from opposite ends of an 8-mile jogging trail and begin running toward each other. Jay is running at the rate of 5 mph, and Ben is running at a rate of 7 mph. How long, in minutes, after they start will Jay and Ben meet?

A. Who will have traveled the longer distance?
Answer:

B. When they meet, what is the combined distance Jay and Ben will have traveled?
Answer:

C. What equation represents this situation?
Answer:

D. Solve the equation; show work your here:
Answer:

E. How long, in minutes, did it take for Jay and Ben to meet?
Answer:

5. Solve the following two equations separately: and

Show work for solving here:

Show work for solving here:

Explain the difference between the two solutions; it must be detailed to receive full credit:
Answer:

6. A clothing store may reduce the regular price of a product because the clothes are damaged, odd sizes, or discontinued items. The discount, or markdown, is the amount by which the store reduces the regular price of a product. The percent discounted is called the discount rate and is usually expressed as a percent of the original selling price. Taking the regular price and subtracting the discount calculates the sale price. The formula can be used to help find the sale price. The sale price, S, is equal to the regular price, R, minus the discount rate, r, multiplied by the regular price, R (Aufmann, Vernon, & Lockwood, 2006).

Using the aforementioned information, solve the following problems.

A. A pair of shoes that are currently selling for a price of $89.99 are going to be marked down 20% for the spring sale. Use the sale price formula to find the new
price of the shoes. Round to the nearest cent.

Set up equation:

Show work here:

Sale price of shoes:

B. A suit coat that is marked down 35% has a sale price of $292.50. Use the sale price
formula to find the regular price of the suit coat. Round to the nearest cent.

Set up equation:

Show work here:

Regular price of the suit coat:

C. Using the formula , find another formula that represents the discount
rate. (Hint: Solve for r.)

Discount rate formula:

D. A prom dress with a regular price of $395 is on sale for $280. Find the discount rate;
round to the nearest tenth of a percent.

Show work here:

Discount rate:

2

1. The following table shows the number of hours five car salespeople worked and the number of cars they sold. Using Excel, plot each point on the same graph where the first coordinate is the number of hours and the second coordinate is the number of cars sold (hours, cars). After plotting each point, explain if there is a linear relationship between the number of hours worked and the number of cars sold.

Sales Hours Worked Cars
Sold
Tim 40 3
Bob 26 5
Brandi 10 1
Kurt 60 1
Kelly 30 7

Graph:

Explanation of linear relationship:

2. Graph the following equations.

A.

Graph:

B.

Graph:

3. Answer the following questions pertaining to the following graph.

A. Give a brief explanation describing the graph in terms of its x-axis and y-axis.

B. In what year was the number of sales the highest?

C. Find the slope of the line. Show all work to receive full credit.

D. Write a sentence that explains the meaning of the slope within the context of this problem.

E. Find the equation of the line that represents the number of book sales. Show all work
to receive full credit.

F. Interpret the y-intercept of this equation.

4. For a 2-day rental, a rental car agency charges a $40 fee per day plus $0.35 per mile.
The equation represents this model, where C symbolizes the total cost of
the rental, and x stands for the number of miles driven.

A. Find the y-intercept of this graph and explain what it means in the context of the problem. Show all work to receive full credit.

B. Explain the slope of the line within the context of this problem.

C. Graph the equation.

5. The director of a summer day camp estimates that 120 children will join if the camp
fee is $250, but for each $25 decrease in the fee, five more children will enroll.

A. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the line. Show all work to receive full credit.

B. Graph the linear equation that represents the number of children who will enroll at a given fee.

C. Approximately how many students will enroll if the camp fee is $190? Round to the nearest child. Show all work to receive full credit.

D. Approximately how many students will enroll if the camp is free? Round to the nearest child. Show all work to receive full credit.

The number of arrests y of a city over a period of time x is graphed on a rectangular coordinate system. Write a paragraph describing your interpretation when the slope is positive, zero, and negative. If you were buying a home in this particular city, which slope would be most attractive to you and why?

3

From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material.

1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The numbers represent the number of hats and T-shirts sold.

A. How much of each item had the teams sold by the end of the second week. Use matrices to solve the problem. Final answer must be given in matrix form. Show all work to receive full credit.

B. Which team had sold the most items at the end of the second week, and how many total items did they sell?

C. By the end of the third week, the totals were as follows:

D. Which baseball team won the contest, and what was their total sales?

2. Use augmented matrices to solve the following systems of equations. Show all work to receive full credit. Final answer must be given in matrix form.

A.

Answer:

B.

Answer:

3. A company’s employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 22 carbohydrates and 14 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work to receive full credit.

Carbohydrates Protein
Peanut Butter 2 4
Oats 8 1

A. Write an equation for the total amount of carbohydrates.

B. Write an equation for the total amount of protein.

C. Determine the augmented matrix that represents the previous two equations.

D. Solve for the previous matrix. Show all work to receive full credit.

E. How many tablespoons of each will there need to be for the new energy bar?

4. A total of 700 tickets were sold for a musical. Senior citizen tickets sold for $15, children tickets sold for $20, and adult tickets sold for $25; the total earnings from ticket sales was $15,750. Five times more children tickets were sold than senior citizen tickets. How many tickets of each type were sold? Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.

A. What are the three unknowns?

B. Write a separate equation representing each of the first three sentences of the word problem.

C. Determine the augmented matrix that represents the three equations.

D. Solve for the matrix. Show all work to receive full credit.

E. How many of each type of ticket were sold?

4

1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .)

A. By looking at the picture, do you think is an acute, obtuse, right, or a straight angle?

B. What can you say about the relationship between and ?

C. If , what is the measurement for ? Show all work as to how you received your final answer.

2. The two parallel lines a and b are cut by a transversal c. Find the missing angles, and give a brief explanation as to how you found each one.

3. A rectangle is a parallelogram with four right angles. A rectangle has a width of 15 feet and a diagonal of a length 22 feet; how long is the rectangle? What is the perimeter of the rectangle? Round to the nearest foot. Show all work to receive full credit.

Length of rectangle:

Perimeter of the rectangle:

4. The following picture shows a high school gymnasium. The art class is planning to create a circular design for the center of the floor, and the students know the diameter of the circle must be 16 feet. They have a budget of $100 and want to make sure they have enough money to buy paint to cover the full circle.

A. What is the area of the circle that needs to be painted?

B. If a pint of paint covers 60 ft2, how many pints of paint are needed to complete the job? Round up to the nearest pint.

C. If each pint costs $6.95, find the cost of the paint needed.

D. Will the art class be able to make its budget?

5. Judy and Pete are building a new house and want to carpet their living room, except for the entranceway and the semicircle in front of the fireplace that they want to tile (Alexander & Koeberlein, 2003).

A. How many whole square yards of carpeting are needed? (Hint: There are 9 square feet in one square yard.) Only whole square yards of carpet are sold. Show all work to receive full credit.

A. How many square feet are to be tiled? Show all work to receive full credit.

6. An observatory has the shape of a right circular cylinder topped by a hemisphere. The radius of the cylinder is 10 ft and its altitude measures 24 ft (Alexander & Koeberlein, 2003).

A. What is the approximate surface area of the observatory? Round to the nearest foot.
Show all work to receive full credit. (Hint: Remember the top and bottom of the cylinder will not be painted, so do not include them in your surface area. However, note that the hemispherical dome will be painted.)

B. If 1 gallon of paint covers 300 ft2, how many gallons are needed to paint the surface if it requires three coats? Round up to the nearest gallon. Show all work to receive full credit.

7. Two angles are supplementary of each other. Twice one angle is equal to the other
angle minus the product of six and eight.

A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.)

B. Graph each of the equations on one rectangular coordinate system. (Hint: You must get y by itself before graphing.) Scale the graph accordingly; you will need your x-axis and y-axis to go to at least 200.

C. What do you notice about the intersection of the two lines?

D. Solve the system of equations in part A to determine the degrees of each angle by using Gaussian elimination.

5

1. The following chart shows some common angles with their degrees and radian measures. Fill in the missing blanks by using the conversions between radians and degrees to find your solutions. Show all work to receive full credit.

Work shown here:

2. An A-frame lake house is 21 feet wide. If the roof of the home makes a angle with the base of the home, what is the length of the house from ground level to the peak of the roof? Round final answer to the nearest foot.

3. Use common trigonometric identities for the functions given to find the indicated trigonometric functions. (Hint: Remember the reciprocal properties of sine, cosine, and tangent.) Show all work to receive full credit. Give answers in exact form – no decimals.

A. If and , what are the values of

a) =

b) =

c) =

B. If and , what are the values of

a) =

b) =

c) =

4. Solve the following application problem. Show all work to receive full credit.

A. A man at ground level measures the angle of elevation to the top of a building to be . If, at this point, he is 15 feet from the building, what is the height of the building?

Draw a picture, show all work, and find the solution. Round to the nearest hundredths.

B. The same man now stands atop a building. He measures the angle of elevation to the building across the street to be and the angle of depression (to the base of the building) to be . If the two buildings are 50 feet apart, how tall is the taller building? See the following figure. Round to the nearest hundredths.

5. A weather balloon B lies directly over a 1500-meter airstrip extending from A to C.
The angle of elevation from A to B is and from C to B is (Larson, Hostetler, Edwards, 2005).

Find the distances from A to B and from C to B. Show all work to receive full credit. Round to the nearest hundredths.

Algebra

Evaluate the expression using a =1 and c= -3

(a + c)(a -c)
Determine whether the given number is a solution to the
equation following it.
5,3x-7=2x+1

Algebra

Write one or two paragraphs comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by providing appropriate examples.

Algebra

Please have a look to the attached word document with several algebra exercises.

Section 7.1
Exercise 76 – Page 451
Write a system of two equations in two unknowns for each problem. Solve each system by substitution. See Examples 7 and 8.

76. Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?

Exercise 82 – Page 452
Write a system of two equations in two unknowns for each problem. Solve each system by substitution. See Examples 7 and 8.

82. Ticket sales. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?

Exercise 87 – Page 452
Write a system of two equations in two unknowns for each problem. Solve each system by substitution. See Examples 7 and 8.

87. Textbook case. The accompanying graph shows the cost of producing textbooks and the revenue from the sale of those textbooks.
a) What is the cost of producing 10,000 textbooks?
b) What is the revenue when 10,000 textbooks are sold?
c) For what number of textbooks is the cost equal to the revenue?
d) The cost of producing zero textbooks is called the fixed cost. Find the fixed cost.

Exercise 88 – Page 453
Write a system of two equations in two unknowns for each problem. Solve each system by substitution. See Examples 7 and 8.

88. Free market. The function S = 5000 + 200x and D = 9500 – 100x express the supply S and the demand D, respectively, for a popular compact disc brand as a function of its price x (in dollars).
a) Graph the functions on the same coordinate system.
b) What happens to the supply as the price increases?
c) What happens to the demand as the price increases?
d) The price at which supply and demand are equal is called the equilibrium price. What is the equilibrium price?

Section 7.2
Exercise 50- Page 461
Solve each system by substitution or addition, whichever is easier.

Exercise 64- Page 461
Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice. See Examples 7 and 8.

64. Books and magazines. At Gwen’s garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?

Exercise 70- Page 462
Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice. See Examples 7 and 8.

70. Low-fat yogurt. Ziggy’s Famous Yogurt blends regular yogurt that is 3% fat with its no-fat yogurt to obtain lowfat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt?

Exercise 74- Page 462
Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice. See Examples 7 and 8.

74. Super Bowl contender. The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do not play is 1. What is the probability that San Francisco plays in the next Super Bowl?

Algebra

Simplify the expressions:( 54b4 x4 1/3)
( ___________), (6ax4)2 (2x)-2, 5y 4b
16bx2 ___ + ____
axy2 bx2y ,

express as a polynomial: X(X+2)+3(3X-5), (X-4)(2X+3), (5X+3)2

express 13 2
__ – __
10 15

Algebra

Solve for x

Simplify your answer as much as possible.
1/5x + 6= 4/5x +7/2

algebra

Find an equation for the line (2,8), (3,-8).

Algebra

Solve for x .

Simplify your answer as much as possible
1/5x – 1 = 3/2x – 1/5

Algebra

Part 1:

Find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 50 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer.

Cite your sources using APA style.

Part 2:
The equation,
D=/1.30h

, also typed as D=sqrt(1.30h), can be used to approximate the distance, D, in nautical miles that a person can see to the horizon from a height, h, in feet. This equation includes a correction for the refraction of light. Suppose that you are in an airplane. By choosing any height, find the corresponding distance that you should be able to see to the horizon. Include the height and the calculations needed to find the distance. Include units with your answer, and show all work for full credit.

Algebra

What is the number of x- and y intercepts that quadratic functions may have?

algebra

Suppose that a households monthly water bill (in dollars) is a linear function of the amount of water the house hold uses(in hundreds of cubic feet, HCF)When graphed, the function gives a line with a slope of 1.65. if the monthly bill for 15 HCF is $26.37 what is the monthly bill for 10 HCF?

Algebra

Write equations for the vertical and the horizontal lines passing through the point (-1,0) in the (x,y) coordinates.

Algebra

Sec. 9.1
Place each of the following sets in ascending order.
16. 3/7, – 6/7, 1/7, -1/2, 2/7
————————————————————————–
Evaluate
32. [4] + [-3]
44. [-9]-[-4]
Sec. 9.2
Add.
40. 7+(-9) +(-5) +6
48. 1/3 + (-5/6) + (-1/2)
Evaluate each of the following expressions.
58. [-27 + 14]
Label each of the following statements as true or false
66. [-8] + [3] = [-8 + 3]
72. Business and finance. Jean deposited a check for $625, wrote two for $68.74 and
$29.95 and used her debit card to pay for a purchase of $57.65. How has her
account balance changed?
Sec 9.3
Subtract
44. -1/2 -(-5/8)
48. -3.4 -(7.6)
54. Statistics. The lowest temperature ever recorded in the state of Oregon was -54 F ( in Seneca, on February 10, 1933. The State’s record high temperature occurred in Pendleton on August 10,1898, when it reached 119 F, What is the historical temperature range in the State of Oregon?

Algebra

For the following functions, find (a) (f+g)(x), (b) (f-g)(x), (c) (f+g)(2), and (d) (f-g)(-1).
f(x)=3x+4, g(x)=1-2x

f(x)=

Algebra

Part 1:
Using web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 50 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer.
Cite your sources using APA style.
Part 2:
The equation,

, also typed as D=sqrt(1.30h), can be used to approximate the distance, D, in nautical miles that a person can see to the horizon from a height, h, in feet. This equation includes a correction for the refraction of light. Suppose that you are in an airplane. By choosing any height, find the corresponding distance that you should be able to see to the horizon. Include the height and the calculations needed to find the distance. Include units with your answer, and show all work for full credit.

[See the attached questions file.]

Algebra

Find the corresponding y values for x= -4,-3,-2,-1,0,1,2 if Y=x^2+2x-3

Algebra

1a. (2 x 10)(4 x10)=
1b. (3.5 x 10)(2 x 10)=
1c. 200(5 x 10)(1 x 10)= ?

Algebra

1. Kathy bicycles 5 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Kathy can bicycle 72 km. How fast does each bicyclist travel?

2. The office jet printer can copy Lisa’s dissertation in 8 min. The laser jet printer can copy the same document in 10 min. If the two machines work together, how long would they take to copy the dissertation.

Algebra

Solve -5z-9=6.

Algebra

Please help me with the attached algebra problems.

Algebra

Find two numbers whose sum is 58 and whose difference is 4. ( we will call the two numbers x and y).

Algebra

Please answer the attached questions and show work Thanks!