# Cumulative Problems SECTION 3.1 34) SECTION 3.2 60) Science

```Cumulative Problems
SECTION 3.1
 X 5Y 2
34) 
4
 Z



3
SECTION 3.2
60) Science and medicine. Archimedes estimated the universe to be 2.3 _ 1019
millimeters (mm) in diameter. If this number were written in standard or decimal
form, how many 0s would follow
SECTION 3.3
28)
9a 2  5a from 11a 2  10a
SECTION 3.4
32) s  12s  8
SECTION 3.5
40) 3 x x  2 
2
SECTION 3.6
 2 x 4 y 4 z 4  3x 3 y 3 z 3  xy 2 z 3 

20) 
xy 2 z 3


SECTION 4.1
18) 18 x 3 y 2 z 3 , 27 x 4 y 2 z 3 , 81x y 2 z
SECTION 4.2
32) t 2  4t  60
SECTION 4.3
56)
2 y3  y 2  3y
SECTION 4.4
52) x 2  8 x  16
SECTION 4.5
18) 2 p 4  3 p 3 q  2 p 3 q  3 p 2 q 2
SECTION 4.6
38) x 2  11x  24
SECTION 4.7
34) 12x  1  17x  1  6
2
SECTION 4.8
50) Business and finance. The relationship between the number of calculators x that
a company can sell per month and the price of each calculator p is given by
x _ 1700 _ 100p. Find the price at which a calculator should be sold to produce a
monthly revenue of \$7000. (Hint: Revenue _ xp.)
SECTION 5.1
14 x 2 y
20)
 21xy 4
SECTION 5.2
24)
3 x  15 4 x

x 2  3x 5  x
SECTION 5.3
18)
11
4

x7 x7
SECTION 5.4
52)
7a
4

a  a  12 a  4
2
SECTION 5.5
26)
x 3 x 1
 
6 4
4
SECTION 5.6
28) Science and medicine. How many centiliters (cL) of pure acid must be added to
200 cL of a 40% acid solution to produce a 50% solution?
SECTION 5.7
a
2
b
16) 2
a
4
b2
SECTION 9.1
256
25
14)
SECTION 9.2
7a 2
16)
SECTION 9.3
20
2

5
5
34)
SECTION 9.4
38)

a 4

a 4

SECTION 9.5
18) 2 x  3x  2  8
SECTION 9.6
10) Geometry. Find the length of a rectangle whose diagonal is 9 in. and whose width
is 6 in.
SECTION 10.1
20) 16 x 2  3
SECTION 10.2
24) x 2  2 x  1
SECTION 10.3
12) x 2  5 x  2  0
SECTION 10.4
32) y  x 2  5x  4
SECTION 10.5
16) Geometry. The sum of the lengths of one side of a right triangle and the hypotenuse
is 20 cm. The other leg is 5 cm shorter than the hypotenuse. Find the
length of each side.
```