Basic Algebra

1. Write the interval notation for the graph up through 10.
-¥Ü-20____-10___0___10___)20_______30______?

2. Write in interval notation the real numbers between 0 and 1.

3. Write in interval notation the set of real numbers between -2 and 2, inclusive.

4. Write the real value of |-4|.

5. Which is the smaller number, |-5| or -4?

6. Find the sum ¾ + 1/6.

7. 1/15 divided by 1/3=

8. 10 + (-30) =

9. -12.34/-3 =

10. Simplify a-(b-c-a)

basic algebra

See attachment and please show your work.

1. Add
(7x^3 – 6x^2 + 8x) + (6x^3 + 8x^2 -13)

2. Subtract. (2v^5 + 7v) – (-8v^5 – 6v + 7)
3. Subtract. (8x^4 + 4x^3 – 1) – (9 x^2 – 3x + 8)
4. Find the hole using the percent equation.
35 patients is 50% of what number of patients?

5. Use the product rule to simplify the expression. (-4x^6)(4x^6)
6. Simplify (3x^2y^2z)^2* (x^3y)^4
7. Find the product of the monomial and the polynomial -5y(4y + 7)
8. Find the product (3x – 4)(x^2-2x + 1)
9. Use the FOIL method to find the product (w + 4)(w-2)
10. Sharon needs 64-credits to graduate from her community college. So far she has earned 56 credits. What percent of the required credits does she have?
11. Multiply. (2t^2 – t – 9)(2t^2 + 2t – 1)
12. Square the binomial (3x – 7)^2
13. Find the value of the expression. 41 + 21 /3 * 3
14. Evaluate the expression. 4^(-2)
15. Simplify the expression. (7^2)^2
16. Use the exponent rule to simplify the expression. (m^4n)^-3/m^-7n^6
17. Simplify the expression and tell whether the statement is true or false.
7 * 5 + 7 * 7 >=0
18. Divide. 64y^6 / 8y^2
19. Divide and check
20. Write the word statement in symbols. Six is less than ten minus one.
21. Convert the number to scientific notation. 1,554,000,000
22. Convert the number to scientific notation. 0.0000000006
23. Multiply and write the answer without exponents
24. Multiply (5a +4d)(5a – 4d).

Basic Algebra

Please see the attached file for the fully formatted problems.

Name: __________________________ Date: _____________

1. Write in simplest form.

2. Simplify.

3. Multiply.

4. Solve.

5. Add. Express your answer in simplest form.

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

7. Solve.

8. A car uses 10 gallons of gasoline on a trip of 130 miles. At that rate, how much gasoline will a trip of 234 miles require?

9. Write in simplest form.

10. Divide.

11. Subtract. Express your answer in simplest form.

12. Subtract. Write your answer in simplest form.

13. Solve. – = 1

14. Solve.

15. Solve.

16. One number is 5 times another. If the sum of their reciprocals is , find the two numbers.

17. Simplify.

18. Divide.

24.

48.

56.

72.

6. Number problem. If one-half of one integer is subtracted from three-fifths of the
next consecutive integer, the difference is 3. What are the two integers?

18. Science and medicine. A passenger train can travel 325 mi in the same time a
freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi/h
faster than the speed of the freight train, find the speed of each.

22. Science and medicine. Ariana took 2 h longer to drive 360 mi on the first day of
a trip than she took to drive 270 mi on the second day. If her speed was the same
on both days, what was the driving time each day?

26. Science and medicine. A plane flies 720 mi against a steady 30-mi/h headwind
and then returns to the same point with the wind. If the entire trip takes 10 h, what
is the plane’s speed in still air?

34. Business and finance. Kevin earned $165 interest for 1 year on an investment of
$1500. At the same rate, what amount of interest would be earned by an investment
of $2500?

10.

28. Science and medicine. Fungicides account for 1/10 of the pesticides used in the
United States. Insecticides account for 1/4 of all the pesticides used in the United
States. The ratio of fungicides to insecticides used in the United States can be written 1/10 1/4
. Write this ratio in simplest form.

32. Science and medicine. The combined resistance of two resistors R1 and R2 in a
parallel circuit is given by the formula
RT = 1
———–
1/R1+1/R2

Simplify the formula.

Basic Algebra

Section 5.1

#22 Write fraction in simplest form. (-10a^3b^2c^3)/(15ab^4)

*I got the answer -(2a^2c^2)/(3 b^2), is this correct?

#48 Write the expression in simplest form. (ab-3a+5b-15)/(15+3a^2-5b-a^2b)

*I got the answer of -(a+b)(5+a^2), is this correct?

Section 5.2

#14 Multiply the fractions. (x^2-3x-10)/5x times (15x^2)/(3x-15)

*I got 5x^2+10x or 5x(x+2), which is correct?

#36 Divide the following fractions: 16x/(4x^2-16) divided by (4x-24)/(x^2-4x-12)

*I got x/x-2, is this correct?

#48. Perform the indicated operations. (14x-7)/(x^2+3x-4) times (x^2+6x+8)/(2x^2+5x-3) divided by (x^2+2x)/(x^2+2x-3)

*I got 7/x, is this correct?

Section 5.3

#22 Subtract. Express the results in simplest form. 5a/a-3 minus 15/a-3

#42 Add. Express results in simplest form. -12/(x^2+x-12) plus x^2/(x+3)*(x+4) plus x/(x^2+x-12)

Section 5.4

#56 Add. Express results in simplest form. 2/(3b-6)plus 3/(4b+8)

#72 Number problem. One number is two less than another. Use a rational expression to represent the sum of the reciprocals of the two numbers.

Section 5.5

#10 What values for x, if any, must be excluded in the following algebraic function: x-1/x-5

#32 Solve and check the following equations for x: 3/x = 5/3 minus 7/x

#54 Solve and check the following equations for x. 2/(x+2) = 3/(x+6) plus 9/(x^2+8x+12)

#70 Solve for x. x/10 = 9/30

Section 5.6

#8 Number problem. One number is 3 times another. If the sum of their reciprocals is 1/6, find the two numbers.

#16 Science and medicine. Tina can run 12 mi in the same time it takes her to bicycle 72 mi. If her bicycling rate is 20mi/h faster than her running rate, find each rate.

Section 5.7

#8 Simplify the comples fraction: 6/(x^2)/9/(x^3)

#28 Science and medicine. Fungicides account for 1/10 of the pesticides used in the US. Insecticides are 1/4 of all persticides used in the US. The ratio of fungicides to insecticides in the US can be written as 1/10 divided by 1/4. Write this ratio in simplest form.

#30 The area of a rectangle is 2(3x-2)/x-1. One of the long sides of the rectangle is (3x-2)/x-2. Find the width of the rectangle.

Basic Algebra

Complete and please show the work.
Please see attached file for full problem description.

1. Express 775% as a decimal.

A) 775 B) 77,500 C) 77.5 D) 7.75

2. Evaluate. | -7 | + | 13 |

A) 20 B) -20 C) 6 D) -6

3. Evaluate. 81 ÷ 9 – 16 ÷ 8

A) 7 B) 9 C) 6 D) 8

4. Express 9.41 as a percent.

A) 94.1% B) 941.0% C) 0.0941% D) 9.41%

5. Find the GCF for 14 and 21.

A) 7 B) 1 C) 42 D) 6

6. Subtract. 12.537 – 9.21

A) 3.327 B) 3.516 C) 1.1616 D) 11.616

7. Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.
3(6 + 7)

A) 16 B) 39 C) 126 D) 25

8. Evaluate if m = -2, n = 4, and p = -1.

A) 16 B) -24 C) 24 D) -16

9. Multiply.
2y3  5y6

A) 10y18 B) 7y9 C) 10y9 D) 7y18

10. Use your calculator to evaluate the following expression if x = -3.07, and y = 8.77, and z = -6.66. Round your answer to the nearest tenth.
x – yz

A) 55.3 B) 54.0 C) 53.9 D) 56.4

11. Which property of the real numbers is illustrated by the following statement?
7 + 8 = 8 + 7

A) Distributive property C) Associative property of addition
B) Commutative property of addition

12. Add. -5.4 + 9.7

A) -15.1 B) 4.3 C) 15.1 D) -4.3

13. Solve. -8x + 8 + 10x = 2x + 1

A) No solution B) Identity C) 0 D) 1

14. Identify the base in the statement “20% of 500 is 100.”

A) 500 B) 100 C) 20%

15. A principal of $5000 was invested in a savings account for 4 years. If the interest earned for the period was $400, what was the interest rate?

A) 2.5% B) 2% C) 1% D) 1.5%

16. Solve. -7x = -14

A) -98 B) 98 C) 2 D) -2

17. Convert 0.32 to a percent.

A) 32% B) 3.2% C) 0.32% D) 0.0032%

18. A television is marked down from $350 to $308. What is the discount rate?

A) 12% B) 87% C) 11% D) 13%

19. Which of the ordered pairs is a solution for the equation 5x – 4y = 20?

A) (-4, -5) B) (0, 5) C) (0, -5) D) (-4, 0)

20. Find the slope of the graphed line.

A) 1 B) -2 C) Undefined D) 0

21. Find the slope of the graphed line.

A) B) 4 C) -4 D)

22. Give the coordinates of the point graphed below.

A) (-2, 3) B) (3, -2) C) (-3, 2) D) (2, -3)

23. Find the slope of the graphed line.

A) -2 B) – C) 2 D)

24. Rewrite the equation 4x – 10y = 11 as a function of x.

A) B) C) D)

25. Write the equation of the line that passes through point (1, -8) with a slope of 0.

A) x = -8 B) y = 1 C) y = -8 D) x = 1

26. One day, the temperature at 9:00 A.M. was 42°F, and by 2:00 P.M. the temperature was 57°F. What was the hourly rate of temperature change?

A) 3°F/h B) 4°F/h C) 5°F/h D) 2°F/h

27. Given f(x) = 5×2 – 3x + 1, find f(-2).

A) 15 B) 27 C) -13 D) -25

28. Write the equation of the line passing through (-6, -3) and (-6, 1).

A) y = 4x B) y = x – 6 C) x = -6 D) y = -6

29. The length of a rectangle is 1 in. more than twice its width. If the perimeter of the rectangle is 26 in., find the width of the rectangle.

A) 4 in. B) 5 in. C) 6 in. D) 3 in.

30. Solve the following system of linear inequalities by graphing.
x – 2y  4
x  4

A)
B)
C)
D)

31. One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.

A) 7 B) 17 C) 34 D) 5

32. Solve the following system of linear inequalities by graphing.
x + 2y  3
2x – 3y  6

A) C)
B) D)

33. Janet invested $25,000, part at 5% and part at 2%. If the total interest at the end of the year is $980, how much did she invest at 5%?

A) $16,000 B) $9,000 C) $15,000 D) $17,000

Basic Algebra

1. What is the square root of -9?
2. What is the cube root of -64?
3. What is 27^(2/3)?
4. Express in simplest form: sqrt(27x^5)
5. Express in simplest form: sqrt(4/49)
6. Express in simplest form: 3*sqrt(25)/sqrt(2)
7. Solve for X: sqrt(X-1) = 5
8. Solve for P: 7 – sqrt(P+3) = 5
9. A rectangle had a length of 12 feet and a diagonal of 13 feet. What was its width?
10. A triangular flower bed had a width of 33 feet, a length of 56 feet and a hypotenuse of 65 feet. Was it a right triangle? Explain.

Basic Algebra

1.) 2(a-4)+4=5(9-a)

2.) t-5x=4x

3.) Fill in the table using the given formula (solve for Y)

y=-5x+10

__X__Y_

-1
0
1
2
3

4.) Even Integers. Find two consecuitive integers that have a sum of 450.

5.) Determine whether the given number is a solution to the inequality following it.

0,4x+9 is greater than or equal to 5(x-3)

6.) word problem

Alana makes 5.80 per hr working in the library. To keep her job she must make at least 116.00 per week; but to keep her scholarship she must not earn more than 145.00 per week.what is the range of the number of hours per week that she may work?

Basic Algebra

Practice skills- 16 Problems
Each correct answer is worth 6-1/4 points

1. Write in simplest form.

A) -2r3s2t
B)

C)

D)

2. Write in simplest form.

A)

B)

C) 4a4b
D)

3. Multiply.

A)

B)

C)

D)

4. Multiply.

A)

B)

C) -n2 + n
D) 3

5. Divide.

6. Divide.

A)

B)

C)

D)

7. Add. Express your result in simplest form.

A)

B)

C)

D)

8. Subtract. Express your result in simplest form.

A)

B)

C)

D)

9. Add. Express your answer in simplest form.

A)

B)

C)

D)

10. Subtract. Express your answer in simplest form.

A)

B)

C)

D)

11. Add. Express your answer in simplest form.

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

A)

B)

C) , 3

D) , 3

13. Solve.

14. Solve.

15. A plane took 1 hour longer to travel 560 miles on the first portion of a flight than it took to fly 480 miles on the second portion. If the speed was the same for each portion, what was the flying time for the second part of the trip?
A) 5 hours
B) 6 hours
C) 7 hours
D) 8 hours

16. Simplify.

Basic Algebra

Place each of the following sets in ascending order.

Evaluate.
Note: These are absolute sign problems!

SECTION 9.2

Add and subtract using the proper rules.

Evaluate each of the following absolute value expression.

Label each of the following statements as true or false.

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?

SECTION 9.3

Subtract.

Watch those signs!

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? Look at your thermometer and put the numbers on that scale.

SECTION 9.4

Perform the indicated operations.

Remember the order of operations.

Section 9.5

Perform the indicated operations.

Basic Algebra

Please see the attached file for the fully formatted problems.
Find all real or imaginary solutions to each equation. Use the method of your choice.

#94. 7x + 29 = x + 3

#62. (x – 10)(x – 2) = – 20

#64. z = 7z – 4
12(z – 1)

#88. Open-top box. Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?

Solve each rational inequality. State and graph the solution set.

# 34. x + 3 ≤ – 2
X

Graph each quadratic function and state its domain and range.

#32. h(x) = – 3×2

Basic Algebra.

1. Write the ratio 5 to 9 as a fraction.

2. Are the following two lines parallel, perpendicular, or neither?

A) Parallel
B) Perpendicular
C) Neither

3. Complete the following statement.

8,000 lb = ________ tons
A) 3
B) 4
C) 5
D) 6

4. Write the ratio of to 6 in simplest form.

5. Complete the following statement.

16 gal = ________ qt
A) 32
B) 128
C) 4
D) 64

6. A caterer made 150 sandwiches for 120 people. How many sandwiches are there for each person?

7. Write as a percent.

A) 37.5%
B) 3.75%
C) 375%
D) 0.375%

8. Write 58% as a fraction or a mixed number.
A)

B)

C)

D)

9. Find the unit price for the item: $35.80 for 4 caps.

10. Rewrite the statement, using percent notation.

13 out of 25 college students work at part-time jobs.
A) 13%
B) 52%
C) 26%
D) 25%

11. Find 60% of 3,200.
A) 192
B) 1,920
C) 1,280
D) 128

12. Complete the statement.

3, 500 cm3 = ________ L
A) 3,500
B) 350
C) 35
D) 3.5

13. Give an appropriate name for the indicated angle.

A) ABC
B) BCA
C) CAB
D) CBA

14. Subtract.

A) 6 gal 3 qt
B) 6 gal 1 qt
C) 5 gal 3 qt
D) 5 gal 2 qt

15. Find the rate:

A) 49

B) 0.02

C) 294

D) 94

16. Write 40% as a decimal.
A) 0.4
B) 1.4
C) 4
D) 40

17. Solve for the unknown:

18. Is the rate equivalent to the rate ?

19. Write 0.21 as a percent.
A) 0.21%
B) 2.1%
C) 210%
D) 21%

20. On the blueprint of Lauren’s new office building, the scale is 3 in. equals 8 ft. What will be the actual length of Lauren’s office if it measures 6 in. long on the blueprint?

Basic Algebra

28 Algebra Problems
Please see the attached file for the fully formatted problems.
1. Write in simplest form. 6x^7
____
24x^3

2. Write in simplest form. 5r^3st^2
_______
-10r^6s^t

Basic Algebra

1. Find the value of c ( formula ) C = P/9 if p = 144.

2. Find the perimeter of a triangular postage stamp with sides 2.7, 2.7, and 1.7 centimeters long.Choose from the following.

3. Choose “<“, “=”, or “>” symbol to make a true statement.
|-5| ….. – (-19)

4. Evaluate the expression.
(9 + 8 . 5)^3

5. Find the area of a triangle with a base of 5.75 centimeters (cm) and a height of 1.5 cm.Choose the correct answer from the following.

6. Remove the parentheses.

– 6(t – 9)

7. Is the statement below true or false?

12^2 + 8(13X – X^2) + 3X = 4X^2 + 107X

8. Solve the formula D = 1/10 bw for the variable b and choose the correct answer from the following.

9. The carpenter in the figure below saws a board into two pieces. He wants one piece to be 4 feet longer than twice the length of the shorter piece. Find the length of each piece if y = 28.

10. Find the midpoint of the line segment PQ.
P(2, 7), Q(5, 11)

11. True or False:
The points (3, 7), (0, 6), and (3, 5) lie on the following line:

y = 1/3x + 6

12. Tell whether the line that passes through the two given points is parallel or perpendicular (or neither) to a line with a slope of -2. Match the points in the left column with the appropriate phrase in the right column. Which one is Parallel, neither parallel nor perpendicular, or perpendicular.

(5,9), (7,5)
(5,9), (7,10)
(5,9), (7,-9)

13. Use point-slope form to determine the equation of the line passing through the two given points. Then write the equation in slope-intercept form.

(6,1), (7,7)

14. Determine the equation of the line that passes through the point (1,2) and is parallel to the line 6 y – 24 x = 5. Select the correct answer in slope-intercept form:

15. Simplify the expression.

(3x^7 n ^-3)^2

16. Evaluate the polynomial function.

f (x) = 4 x 2 – 4 x + 5 for x = 2

17. Do the subtraction.

(7 x 2 y 5 + 5 x y – 7 y 4 ) – (2 x 2 y 5 – 9 xy + 3 y 4 )

18. Find the product.

(3 x – 3)(-5 x + 4)

Basic Algebra

25 Algebra problems.
1. Which number is prime?

A) 4 B) 43 C) 39 D) 121

2. Find the GCF for 14 and 21.

A) 1 B) 6 C) 7 D) 42

3. Find the LCM for 13 and 78.

A) 1 B) 13 C) 78 D) 1014

4. Convert to a fraction.

A) B) C) D)

5. Convert 0.4 to a fraction and write the result in lowest terms.

A) B) C) D)

6. Multiply. 5.34 ? 3.17

A) 15.9378 B) 16.6478 C) 15.6478 D) 16.9278

7. Write the following phrase using symbols. ” The quotient of p minus q, divided by 5″

A) B) C) D)

8. Which of the following is not an expression?

A) y(z + 10) B) y – ÷ z C) z?y – 8 D) z + y + 4

9. Which property of the real numbers is illustrated by the following statement?
(2 + 16) + 3 = 2 + (16 + 3)

A) Commutative property of addition C) Distributive property
B) Associative property of addition D) Identity Property

10. Find the median.
13, 17, 40, 46, 54, 26, 52, 31

A) 35.5 B) 13 C) 31 D) 40

11. Evaluate. 8 + 2 ? 5 – 24 ÷ 6 ? 2

A) 16 B) 10 C) 48 D) 42

12. Evaluate if m = -2, n = 4, and p = -1.

A) -24 B) 24 C) -16 D) 16

13. Solve. 2x + 4 = -8

A) -8 B) 0 C) -6 D) -2

14. Solve. – 6 = 12

A) 36 B) C) D) 45

15. Tickets for a play at the community theater cost $16 for an adult and $10 for a child. If 270 tickets were sold and the total receipts were $3420, how many of each type of ticket were sold?

A) 100 adult tickets, 120 child tickets B) 140 adult tickets, 200 child tickets
C) 80 adult tickets, 110 child tickets D) 120 adult tickets, 150 child tickets.

16. A furniture store marks up items 20% (based on cost). If the furniture store buys a couch for $350, what will the selling price be?

A) $410 B) $420 C) $430 D) $440

17. A bracelet was marked up $175 from cost, which amounts to a 50% increase. Find the original cost of the bracelet.

A) $365 B) $360 C) $360 D) $350

18. Solve and graph the solution set. 3x &#8805; 7x + 20

A)
-5 0
B)
-5 0
C)
0 5
D)
0 5

19. Give the coordinates of the point graphed below.

A) (0, 4) B) (4, 0) C) (0, -4) D) (-4, 0)

20. Find the slope of the line passing through the points (-5, 5) and (-3, 5).

A) 0 B) 1 C) 2 D) Undefined

21. Use the following tabe to answer the question.
Population of Europe by Age Groups
Population (in thousands)
1950 1970 1995
Age 0-14 143,175 166,367 139,464
Age 15-64 359,162 421,432 487,110
Age 65+ 44,981 68,642 101,338
Age 75+ 14,553 22,762 38,139
Total 547,318 656,441 727,912
Source: European Rural Development (ERD) Project.

What percentage of Europe’s population was in the age 75+ group in 1970?

: A) 6.0% B) 4.5% C) 5.0% D) 3.5%

22. Write the equation of the line with slope -5 and y-intercept (0, 5).

A) y = 5x – 5 B) 5x – 5y = 0 C) y = -5x + 5 D) -5y = 5

23. Match the graph with one of the equations.

A) B) C) y = 2x – 1 D)

24. Determine which two equations represent parallel lines.
(a) y = -5x + 2 (b) y = 5x + 2 (c) y = x + 2
(d) y = -5x + 5

A) (a) and (b) B) (b) and (c) C) (a) and (c) D) (a) and (d)

25. Solve the system by addition.
-4x – 7y = -11
x – 2y = -1

A) (3, -2) B) (-1, 1) C) (3, 2) D) (1, 1)

Basic Algebra

The quotient when 3 more than a number is divided by 3 less than that same number

Science and medicine-It is estimated that the earth is losing 4000 species of plants and animals every year. If S represents the number living last year, how many species are on Earth this year?

Science and medicine-The kinetic energy of a particle of mass m is found by taking one-half of the product of the mass (m) and the square of the velocity (v). Write an expression for the kinetic energy of a particle.

Business and Finance-Ramon owes $780 on his VISA account. He returns three items costing $43.10, $36.80, and $125.00 and receives credit on his account. Next, he makes a payment of $400. He then makes a purchase of $82.75. How much does Ramon still owe?

Geometry-A triangle has sides 3x + 7,4x – 9, and 5x + 6. Find the expression that represents its perimeter.

Please see the attached file for the fully formatted problems.

Basic Algebra

Please see the attached file for the fully formatted problems.