ALLIED MAT110 MODULE 7 CHECK YOUR UNDERSTANDINGS

Simplify .
a. 54
b.
c.
d.
1
2. State
whether is rational or irrational.
a. Rational
b. Irrational
1
3.
Perform the indicated division. Rationalize the denominator,
if necessary. Then, simplify.

a. 9 +
b. 9 +
c. 9 +
d. 27 +
1
4.
A manufacturer has two machines that produce dog toys. On
Wednesday, machine A operates for 4 hours and machine B operates for 5 hours
and 175 dog toys are produced. On Thursday, machine A operates for 6 hours and
machine B operates for 5 hours and 225 dog toys are produced. Use the following
system:

4x + 5y = 175
6x + 5y = 225

where x is the number of dog toys produced by machine A in
an hour and y is the number of dog toys produced by machine B in an hour. Solve
the system graphically.

a. A: 25 per hour,
B: 15 per hour
b. A: 15 per hour,
B: 25 per hour
c. A: 5 per hour, B:
15 per hour
d. A: 15 per hour,
B: 5 per hour
5. State
whether is rational or irrational.
a. Rational
b. Irrational
1
6. Adult
tickets for a play cost $17 and child tickets cost $12. If there were 32 people
at a performance and the theater collected $474 from ticket sales, how many
children attended the play?
a. 13 children
b. 14 children
c. 15 children
d. 18 children
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7.
The forces (in pounds) on the arm of an industrial lift
provide the equations.

1.4x + 1.8y = 50
2.7x – 1.2y = 10

Use the addition method to solve this system. Round your
results to the nearest hundredth.

a. x = 13.54 lb, y =
21.01 lb
b. x = 21.01 lb, y =
13.54 lb
c. x = 18.50 lb, y =
11.93 lb
d. x = 11.93 lb, y =
18.50 lb
1
8. A 82-ft
rope is cut into two pieces so that one piece is 8 ft longer than the other.
How long is each piece?
a. 29 ft, 53 ft
b. 37 ft, 45 ft
c. 8 ft, 74 ft
d. 41 ft, 41 ft
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9. The base
of a ladder is 4 feet away from the wall. The top of the ladder is 5 feet from
the floor. Find the length of the ladder to the nearest thousandth.
a. 6.403 feet
b. 4.271 feet
c. 8.704 feet
d. 5.382 feet
10.
Solve the following system by adding.

-0.3x + 0.9y = -6.6
0.6x + 0.4y = -22

a. (–26, –16)
b. (–260, –160)
c. (–16, –26)
d. (–160, –260)
0
11. Simplify.
Assume x represents a positive real number.

a.
b.
c.
d.
1
12. Solve.
a. 1
b. 0
c. -1
d. No solution
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13. Simplify.
Assume all variables represent positive real numbers.
a.
b.
c.
d.
.
1
14. Perform
the indicated multiplication. Then simplify the radical expression.
a. w + 4
b. w + 4 + 4
c. 9 +
d. 27 +
1
15. One number
is 12 more than another. The sum of the smaller number and twice the larger
number is 39. Find the larger number.
a. 5
b. 7
c. 17
d. 34
16. Simplify
by combining like terms.
a.
b.
c.
d. Cannot be
simplified
17.
Solve the following system by adding.

a. (–1, –8)
b. (–8, –1)
c. (1, 8)
d. (8, 1)
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18. A chemist
has a 35% and a 15% acid solution. How much of each solution should be used to
form 50 mL of a 31% solution?
a. 8 mL of the 35%
solution, 42 mL of the 15% solution
b. 42 mL of the 35%
solution, 8 mL of the 15% solution
c. 40 mL of the 35%
solution, 10 mL of the 15% solution
d. 10 mL of the 35%
solution, 40 mL of the 15% solution
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19.
Decide whether the following is already written in simplest
form. If it is not, explain what needs to be done.

a. Simplest form
b. Remove perfect
square factors from radical
20.
The area is given in square feet. Find the length of a side
of the square. Round your answer to the nearest hundredth of a foot.

a. 4.12 ft
b. 4.47 ft
c. 2.24 ft
d. 5.10 ft