Expert: Lynn Houston - 10/24/2008

Question
QUESTION: 11. simplify: -2 (5 - 8)^3

which choice?:

a.)18     b.)54

c.)-29    d.)-18


12. Simplify: 4(3-m) - (2m+1)

a.)6m - 11  b.)11 + 6m

c.)11 - 6m  d.)-6m - 11


13. Solve: 2 > y + 2 ≥ 0

a.) 4 > y and y ≥ -2  b.) 0 > y and y ≥ 2

c.)0 ≥ y and y > -2   d.) 0 > y and y ≥ -2


14. Solve: -1 ≤ 3z + 2 ≤ 8

a.)-1 ≤ z and z ≤ 2     b.)0 ≤ z and z ≤ 3

c.) -1 ≥ z and z ≤ 2    d.)0 ≥ z and z ≥ 3


15. Solve: 3k + 7 < 1 or 2k - 3 >1

a.)k < 2 or k > -2  b.)k < -2 or k > 2

c.) k > -2 or k > 4    d.)k > -2 or k < 4


16. Solve: 2x + 3 > 1 or 5x - 9 ≤ 6

a.) x < -1 or x ≤ 3    b.)ø

c.) x ≥ -1 or x < 3    d.)x > -1 or x ≤ 3


17. The usual toll charge to use the Bingham tunnel is 50 cents.  If you purchase a special sticker for $5.50, the toll is only 35 cents.  At least how many trips through the tunnel are needed before the sticker costs less than paying for each trip separately?

a.)37    b.) 27

c.) 43   d.) 11


18. The lengths of the legs of an isosceles triangle are integers.  The base is half as long as each leg.  What are the possible lengths of the legs if the perimeter is between 6 units and 16 units?

a.)3, 6, 8, or 9   b.)6, 7, 8, or 9

c.) 2, 3, 4, or 5  d.)3, 4, 5, or 6


19. Find three consecutive multiples of 15 such that twice their sum is 360.

a.)45, 60, 75      b.)30, 45, 60
 
c.)many solutions  d.)15, 30, 45


20. The second of three numbers is 4 times the first number.  The third number is 12 less than the first.  Find the three numbers given that their sum is 42.

a.)10, 14, 18  b.) -4, 6, 40

c.) 9, 36, -3  d.) -10, 4, 48



ANSWER: I'll do a couple of these, but I'm not going to do your entire homework assignment...

11. simplify: -2 (5 - 8)^3
-2(-3)^3
-2(-27) = 54

12. Simplify: 4(3-m) - (2m+1)
12 - 4m - 2m - 1
11-6m

14. Solve: -1 ≤ 3z + 2 ≤ 8
-3 ≤ 3z ≤ 6
-1 ≤ z ≤ 2  (-1 ≤ z and z ≤ 2)

16. Solve: 2x + 3 > 1 or 5x - 9 ≤ 6
2x > -2 or 5x ≤ 15
x > -1 or x ≤ 3  

17. The usual toll charge to use the Bingham tunnel is 50 cents.  If you purchase a special sticker for $5.50, the toll is only 35 cents.  At least how many trips through the tunnel are needed before the sticker costs less than paying for each trip separately?
.35x + 5.5 < .50x
5.5 < .15x
36.66 < x, so if you take 37 trips or more, the special sticker is a better deal.


19. Find three consecutive multiples of 15 such that twice their sum is 360.

2[15x + 15(x+1) + 15(x+2)] = 360
15x + 15(x+1) + 15(x+2) = 180
15x + 15x+15 + 15x+30 = 180
45x + 45 = 180
45x = 135
x=3, therefore the numbers are 45, 60 and 75


---------- FOLLOW-UP ----------

QUESTION: no it is not a homework assignment i wanted to check my work
before i turn it in

ANSWER: Well, in that case
11. b.)54
12. c.)11 - 6m
13. d.) 0 > y and y ≥ -2
14. a.)-1 ≤ z and z ≤ 2
15. b.)k < -2 or k > 2
16. d.)x > -1 or x ≤ 3
17. a.)37
18. d.)3, 4, 5, or 6
19. a.)45, 60, 75
20. c.) 9, 36, -3  



---------- FOLLOW-UP ----------

QUESTION: i got the past ones right thanks!
what about these?
i had a little problem with these

1. The second of three numbers is 4 times the first number.  The third number is 12 less than the first.  Find the three numbers given that their sum is 42.

a.)10, 14, 18  b.) -4, 6, 40

c.) 9, 36, -3  d.) -10, 4, 48


2. There are three consecutive even integers such that the sum of the second and third integers is 30 more than the first integer.  Find these three even integers.

a.)26, 28, 30  b.)24, 26, 28

c.)22, 24, 26  d.)20, 22, 24


3. Find all sets of three consecutive even integers whose sum is between 25 and 45.

a.)12, 14, 16 OR 14, 16, 18 OR 16, 18, 20  

b.)8, 10, 12 OR 10, 12, 14 OR 12, 14, 16

c.)6, 8, 10 OR 8, 10, 12  OR 10, 12, 14  

d.)6, 10, 14 OR 8, 12, 16 OR 10, 14, 18


4. Jim's second test score was 8 points higher than his first test score.  His third score was 88.  He had a B average (between 80 and 89, inclusive) for the three tests.  What can you conclude about his first test score?  

a.)It was between: 75 and 88.5    b.)72 and 85.5

c.)80 and 82.5          c.)74 and 86


5. The three sides of an equilateral triangle are increased by 20 cm, 30 cm, and 40 cm, respectively.  The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle.  What can you conclude about the length of a side of the original triangle?  

a.)It is between: 10 cm and 30 cm   b.)7.5 cm and 10 cm

c.)15 cm and 30 cm          d.)15 cm and 45 cm  

Answer
With multiple choice, it very easy to just "test" the answers to figure out which one is correct. That's all I did to give you the answers.  However, if you want to learn how to solve them, I'll do a couple so you can do others when it's NOT a multiple choice test.


1. c.) 9, 36, -3
2. b.)24, 26, 28
3. b.)8, 10, 12 OR 10, 12, 14 OR 12, 14, 16
4. a.)It was between: 72 and 85.5    
5. c.)15 cm and 30 cm

4. Jim's second test score was 8 points higher than his first test score.  His third score was 88.  He had a B average (between 80 and 89, inclusive) for the three tests.  What can you conclude about his first test score?  

(x+x+8+88)/3=80...2x+96=240...2x=144...x=72
(x+x+8+88)/3=89...2x+96=267...2x=171...x=85.5