Name ______________________________ Period ________ Date ________________
Simplify the following. Leave answers in exponential form. 1. y0
2.
5. (4c 2 d 3 ) 5
6.
510 55
49 x14 y 12 7 x18 y 5
3. (7 3 ) 2
4.
7. x 8
8. (2x5y2)(4x6y-9)
9. Write in scientific notation. a. 137,000,000,000
b. 0.000000295
10. Write in standard notation. a.
b.
11. Use what you know about the rules of exponents and scientific notation to solve the following. Express your answer in scientific notation. a. (3.0 10 6 )(2.5 1014 )
b. (9.3 1013 ) (3.1 109 )
c. (7.6 x 109) + (5.6 x 109)
d. (7.62 x 107) – (8.9 x 106)
12. Sam fills a water balloon with 7.8 x 10-3 ft3 of water. If he fills 48 water balloons, how much water will he need? Write your answer in scientific notation.
13. Determine if the following triangles are similar. Explain why or why not.
40˚
110˚ 30˚
30˚
14. In the figure below the angles are formed by a transversal and two parallel lines. Identify the appropriate angle. A. alternate interior to C B. alternate exterior to H B
A
C. vertical to E
G
F
C
E
D
D. corresponding to B
15. Identify the angle relationship and solve for x. 8x + 16
10x - 18
16. Classify the numbers as rational or irrational. Explain. a. 7.28
b. 6.8
c.√14
d. 3/14
H
17. Solve for the missing angles. a.
b. 127
85 – 5y
10y +70
155
D. 90
64 x+5
5y
18. Find the volume. a.
125
b.
12in
8in
6.5 ft
3.8 ft
8in
5in
11in
3.8 ft
8in
19. Solve each equation. SHOW ALL WORK! a.
4r – 5 = 14r + 10
b.
6m – 4(m +1) = 14
20. Three tables are given below. Decide if the table shows a linear relationship, or a nonlinear relationship. Then explain how you know. Table A x
y
Table B
-2 0.25
x
y
-2
-3
-1
0.5
-1
-1
0
1
1
2
0 1
1 3
2
4
2
5
3
8
3
7
Table C x
y
-2
2
-1
0
0 1
2 2
2
6
3
12
21. The cost of a school banquet is $95 plus $15 for each person attending. There is a linear relationship between the number of people attending and the total cost of the banquet. Some sample values are given in the following table. Number Attending (n) Cost (c)
0
10
20
30
40
95
245
395
545
695
Use the given data to identify the y-intercept, calculate the slope, and write and equation showing how cost, c, depends on the number attending, n. y-intercept =
slope =
equation =
Explain what the number value of the slope and y-intercept mean. (Relating the number attending to the cost of the banquet) 22. Write if the following table is a function or not a function and explain why. A.
B.
23. Adam and Bianca are competing to see who can save the most money in one month. Adam made a graph of his savings and Bianca made a table of hers. Use the information to answer the following questions. a. Who had more money in their account to start with?
b. Who saves more money per week?
c. At the end of the month who will have more money? (30 days)
24. Write an expression that is equivalent to: a.
8(-3 – 6x) + 12x
b.
3y – 4(9 – 9y)
25. Identify the transformation that occurred.
26. Two points (-5, 2) and (2,-4) are graphed on a coordinate plane. What is the shortest distance between the two points?
27. A square table has an area of 289in2. What is the approximate length of a side of the table?
28. Solve the following systems of linear equations using substitution. Show all of your work. Remember to write your answer as an ordered pair. x = 13 – y 3y + x = 35
29. The Stellar International Cellular long-distance company charges $13.95 per month plus $0.39 per minute of calling time. The Call Anytime Company charges no monthly service fee but charges $0.95 per minute. a. Represent each charge plan with an equation.
b. For what number of minutes are the costs for the two plans equal?
c. When is it best to use the Call Anytime Company? Be specific!
(7.62 x 107) â (8.9 x 106). 12. Sam fills a water balloon with 7.8 x 10-3 ft3 of water. ... 6m â 4(m +1) = 14. 20. Three tables are given below. Decide if the table ...
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