Written Practice

Lesson 21

1. For every 4 feet a ladder rises, the base of the ladder should be placed 1 foot away from the bottom of a building. If the base of the ladder is 7 feet from the bottom of a building, find the height the ladder rises up the building.

7 ft

x

2.

What is a term of an algebraic expression?

3.

Explain how to use the inverse operations to solve . 8

3

2x

4. In physics equations, a change in a quantity is represented by the delta symbol, Δ. A change in velocity, Δ v is calculated using the equation Δv = vf – vi where vi is the initial velocity and vf is the final velocity. If a cart has an initial velocity of 5 miles per second and experiences a change in velocity of 2 miles per second, what is the final velocity of the cart?

5.

Graph the ordered pair (-2, 6) on a coordinate plane.

6.The length of a rectangular picture frame is 3 times the width.

a. Draw a picture of the picture frame and label the dimensions.

b. Write an expression for the area of a frame.

7. Complete the table for y = 2x+7

x -5 1 4

y

8. Solve

53

x

9. Which step can you use first to solve

a. Multiply both sides by b. Multiply both sides by -9c. Divide both sides by -52d. Divide both sides by 52

529

x

9

1

10. Alan makes $1 for each snow cone he sells. Alan calculates his profit by subtracting the daily cost of $195 to run the stand from the amount he makes on the snow cones that he sells each day. How many snow cones does Alan need to sell to make a profit of $200 a day?

11. Explain which terms in

3z2y + 2yz – 4y2z – z2y + 8yz

can be combined.

12. The relative weight of an object on the surface of Jupiter can be found using 2.364w, where w, is the weight of the object on Earth. The space shuttle weighs about 4,500,000 pounds on earth. What would be the weight of the space shuttle on Jupiter?

13. The length of a frame is 8 inches. Let w be the width of the frame. The formula A= 8w calculates the area of backing needed for a framed picture. Complete the table and graph the solutions.

w A

2

4

6

8

14. Simplify

- 4 - 3 + 2 - 4 - 3 - 8

15. Simplify

a. 9 – 3pb. 3p-9c. 13p + 5d. 13p - 9

2875 pp

16. Evaluate using two different methods. Verify the solution of each method.

4

34

3

2

17. A letter of the alphabet is randomly chosen. What is the probability that the letter is a vowel?

18. The area of a square is 100 square feet. What is the length of each side?

19. A picture framer calculates the amount of materials needed using 2l + 2w. If the framer used 2w + 2l, would the results be the same? Explain.

20. Alda’s school is 1200 yards from her house. She walks 150 yards per minute. The equation y=1200-150x represents how far she will be from the school after x minutes.

a. Complete the table and graph the solutions.

b. What does it mean to say that after 8 minutes, she is 0 yards from the school?

x y

1

4

6

8

21. A students says that to solve you should divide each side by . Another student says that to solve the equation you should multiply each side by . Will both methods result in the correct solution? Explain.

124

3 x

4

3

3

4

22. Determine whether .

a. Simplify the expressions 43 and .

b. Write an expression for the multiplication of 43 and without using exponents. Then check to see if the product of the expressions is 1.

14

14

33

3

4

1

3

4

1

23. Will dividing two integers ever produce an irrational number? Explain.

24. If a student is converting from 225 square units to 22,500 square units, what units of measure is he or she most likely converting?

25. A round of golf takes 4.5 hours and each hole takes 0.25 hours. In the equation y = 4.5 – 0.25x, x is the number of holes played and y is the remaining time to finish the round. Make a table for 4, 8, 12, and 16 holes and then graph the ordered pairs in your table.

26. Simplify

-|15 – 5|

27. One fruit stand has s strawberries and k kiwis to sell. Another stand has twice as many strawberries and four times as many kiwis to sell.

a. Write expressions representing the number of strawberries and kiwis each stand has to sell.

b. Write an expression for the total number of pieces of fruit.

28. Sketch a graph to represent the following situation: A tomato plant grows at a slow rate, and then grows rapidly with more sun and water.

29. Write an algebraic expression for “0.21 of what number is 7.98?”

30. Two students solve x – 5 = 11. Which student is correct? Explain.

Student A Student B

x – 5 = 11 +5 = +5x = 16

x – 5 = 11 -5 = - 5x = 6