Download MAT-074 Section D,C Solved problems 3P 1. Place the correct symbol

MAT-074 Section D,C Solved problems 3P
1. Place the correct symbol (< or >) between the numbers: − 43 < − 78 2. Evaluate the expression:
(a) (−200)(2)(3) = −1200
(b)
(c)
3
− 56
8
9
− 20
24
24
−11
24
8
− 29 ÷ 15
− 29 · 15
8
− 2·15
9·8
30
− 72
5
− 12
(d) 24 + 18 ÷ 3
24 + 6
30
3. Evaluate the expression for x = −2 and y = 3
(a) −3x − (2y)2
−3(−2) − (2(3))2
6 − (6)2
6 − 36 = −30
(b) 4y − x3
4(3) − (−2)3
12 − (−8)
12 + 8 = 20
4. Write in exponential form 2 · 2 · (x + y) · 2 · (x + y)
23 (x + y)2
5. Use the distributive property to expand −2x(x − 5).
−2x2 + 10x
6. Identify the property of real numbers illustrated (x + 2)(x + 3) = (x + 3)(x + 2)
The commutative property of multiplication
7. Simplify the expression:
(a) (3t2 )(2t4 )
6t4
(b) 2x2 − 3x + 5x2 − (2 + 3x)
7x2 − 3x − 2 − 3x
7x2 − 6x − 2
(c) 3(x2 + x) − 2(2x − x2 )
3x2 + 3x − 4x + 2x2
5x2 − x
8. Solve the equation and check the solution
(a) 12x − 3 = 7x + 27
5x − 3 = 27
5x = 30
x=6
5x
(b) 2x −
= 13
4
8x − 5x = 52
3x = 52
x = 52
3
(c) 2(x − 3) + 3 = 12 − x
2x − 6 + 3 = 12 − x
2x − 3 = 12 − x
3x − 3 = 12
3x = 15
x=5
9. Solve and graph the inequality 12 − 3x ≤ −15
−3x ≤ −15
−3x ≤ −15 − 12
−3x ≤ −27
x≥
−27
−3
x ≥ 9, and graph.
10. Your pay is nine dollars and fifty cents per hour plus sixty cents for each part you
assemble. How many parts must you assemble in an hour to earn fifteen dollars and
fifty cents?
15.50 = 9.50 + 0.60x
6.00 = 0.60x
6.00
06.0x
=
0.60
0.60
x = 10
11. A store uses a markup rate of 62% on all items. A CD player costs the store $48. For
how much do they sell the CD player?
p = 48.00 + (0.62)(48.00)
p = $77.76
12. Solve the proportion
x+4
2x
=
3
5
(2x)(5) = (3)(x + 4)
10x = 3x + 12
7x = 12
x=
12
7
13. Write the fraction
3
8
as a percent and as a decimal.
37.5%; 0.375
14. You traveled 264 miles in 5.5 hours. What was your average speed?
d = rt
d
r=
t
264
r=
5.5
r = 48 hours
15. A bank advertises four percent simple interest on savings accounts. How much must
you deposit to earn two hundred dollars per year in interest?
I = P rt
200.00 = P (0.04)(1)
200.00
=P
(0.04)(1)
P = $5000.00
16. 90 is what percent of 250?
x
90 =
(250)
100
90
x = 100 ·
250
x = 36%
17. You can paint a room in three hours. Your friend can paint the same room in four
hours. How long will it take both of you working together to paint the room?
t
t
+ =1
3 4
t
t
4 · 3( + ) = 4 · 3(1)
3 4
4t + 3t = 12
7t = 12
t=
12
7
18. Solve for t in the formula d = rt.
d
t=
r