Solve the problem.
164)
A quantity, 2
3 of it, 1
2 of it, and 1
7 of it, added together, equals 22. What is the quantity?
164)
A)
97
42
B)
42
97
C)
2134
42
D)
924
97
165)
Martha can rake the leaves in her yard in 8 hr. Her brother can do the job in 7 hr. How long will it
take them to do the job working together?
165)
A)
56 hr
B)
1
15 hr
C)
311
15 hr
D)
1
56 hr
Simplify the expression, using only positive exponents in your answer.
166)
x–2
x–2– y–2
166)
A)
y
y2– x2
B)
y2– x2
y2
C)
y2
y2+ x2
D)
y2
y2– x2
Solve the formula for the specified variable.
167)
S =a
1 – r for r
167)
A)
r =a
S– 1
B)
r =a
S
C)
r = S – a
D)
r =S – a
S
Add or subtract. Write the answer in lowest terms.
168)
m2– 10m
m – 4 +24
m – 4
168)
A)
m – 6
B)
m2– 10m + 24
m – 4
C)
m – 4
D)
m + 6
Find the LCD for the fractions in the list.
169)
–4
n –5 , 8
5– n
169)
A)
n2+ 25
B)
5– n
C)
n2– 25
D)
n + 5
B
Find all values that make the expression undefined.
170)
m– 3
4
170)
A)
Never undefined
B)
–3
C)
0
D)
3
A
Solve the equation.
171)
m +6
m2+ 10 m + 25
–6
m2+ 10 m + 25
=m –6
m2+ 10 m + 25
171)
A)
{5}
B)
{–30}
C)
{–5}
D)
{30}
C
A
Solve the formula for the specified variable.
172)
1
a+1
b= c for b
172)
A)
b=a
ac – 1
B)
b=1
ac
C)
b=1
c– a
D)
b=ac –1
a
Provide an appropriate response.
173)
If one form of the correct answer of a difference of two rational expressions is 11
k –5, what would
be an alternate form of the answer if the denominator is 5– k?
173)
A)
11
k –5
B)
–11
5– k
C)
11
k +5
D)
–11
k +5
Find the least common denominator for the fractions in the list.
174)
4
x2– 3x – 4 , 8
x2– 2x – 3
174)
A)
(x – 4)(x + 1)(x – 3)
B)
(x + 1)(x – 3)
C)
(x + 4)(x – 1)(x – 3)
D)
(x – 4)(x + 1)
Write the rational expression in lowest terms.
175)
y2+ 3y – 28
y2– 2y – 63
175)
A)
3y – 28
–2y – 63
B)
3y – 4
–2y – 9
C)
y – 4
y – 9
D)
–y2+ 3y – 28
y2– 2y – 63
Rewrite the rational expression with the given denominator.
176)
x
x + 5 =?
3x + 15
176)
A)
3
3x + 15
B)
3x
3x + 15
C)
x
3x + 15
D)
5x
3x + 15
Add or subtract. Write the answer in lowest terms.
177)
6
z2–9
z
177)
A)
3(3z – 2)
z
B)
3(2 + 3z)
z2
C)
3(2z + 3)
z2
D)
3(2 – 3z)
z2
Solve the equation.
178)
2
t=t
–2t + 6
178)
A)
{0, 36}
B)
{2, –6}
C)
{0, –6}
D)
Identify as an equation or an expression.
179)
2
7x +3–5
6x –8
179)
A)
Equation
B)
Expression
Provide an appropriate response.
180)
If the rational expression 3 x9y6
7 p9q represents the area of a rectangle and 7 x8y4
p8 represents the
length of the rectangle, what rational expression represents the width?
180)
A)
3xy2
49 pq
B)
3 x17y8
49p9q
C)
3 xy2
14 pq
D)
3 x17y8
p9q
Solve the problem.
181)
Mara can type 2080 words in 2
3 hr (40 minutes). How many words per minute can she type?
181)
A)
1387 words per min
B)
52 words per min
C)
78 words per min
D)
35 words per min
182)
A boat can go 99 mph in still water. It takes as long to go 250 mi upstream as it does to go
downstream 300 mi. How fast is the current?
182)
A)
5 mph
B)
8 mph
C)
1 mph
D)
9 mph
Solve the equation.
183)
3x
2+ x =5
183)
A)
2
B)
10
3
C)
3
D)
15
2
Find the numerical value of the rational expression for the given value of x.
184)
9 x2+ 3 x
–6 x , x = 3
184)
A)
5
B)
4
C)
– 4
D)
– 5
Multiply or divide as indicated. Write the answer in lowest terms.
185)
k2+ 9k + 18
k2+ 12k + 27
·k2+ 9k
k2– 2k – 48
185)
A)
k2+ 9k
k – 8
B)
k
k2+ 12k + 27
C)
k
k – 8
D)
1
k – 8
Write the rational expression in lowest terms.
186)
(y + 6)(y – 8)
(y – 8)(y + 9)
186)
A)
y + 6
y + 9
B)
2y – 8
2y + 1
C)
y – 6
y – 9
D)
y + 8
y + 1
Simplify the complex fraction.
187)
4
3r – 1 –4
4
3r – 1 +4
187)
A)
2 +3 r
3 r
B)
3 r
2 –3 r
C)
2 – r
r
D)
2 –3 r
3 r
Solve the formula for the specified variable.
188)
3
x–4
y+10
z= 1 for x
188)
A)
x =3xyz
yz + 4z –10y
B)
y =4xz
3xz + 10x – xz
C)
z =10xy
xy – 2y + 4x
D)
x =3yz
yz + 4z –10y
Simplify the complex fraction.
189)
x7
4y5
x2
y2
189)
A)
x9
4y7
B)
x5
y3
C)
x5
4y7
D)
x5
4y3
Add or subtract. Write the answer in lowest terms.
190)
13
12x–6
12x
190)
A)
7
B)
7
24x
C)
12x
7
D)
7
12x
Write the rational expression in lowest terms.
191)
xy –5x +2y –10
xy +3x +2y +6
191)
A)
y –5
y +3
B)
y –3
y +5
C)
xy –5x +2y –10
xy +3x +2y +6
D)
y +5
y –3
192)
pq –2p +7q –28
qr +4q –2r –8
192)
A)
pq –2p +7q –28
qr +4q –2r –8
B)
p –7
r +4
C)
p +7
q –4
D)
p +7
r +4
193)
x3–8
x2+2x +4
193)
A)
x +4
B)
x –4
C)
x –2
D)
x +2
Identify as an equation or an expression.
194)
4x –6
x +5–x
3+5
194)
A)
Expression
B)
Equation
Provide an appropriate response.
195)
Which of the following complex fractions is equivalent to
–6–9
5
7–3
2
?
195)
A)
6–9
5
–7–3
2
B)
6+9
5
–7+3
2
C)
–6+9
5
7+3
2
D)
6+9
5
7–3
2
Rewrite the rational expression with the indicated denominator.
196)
x
x + 4 =?
5x + 20
196)
A)
5
5x + 20
B)
5x
5x + 20
C)
x
5x + 20
D)
4x
5x + 20
197)
7
9= ?
54
197)
A)
42
54
B)
7
54
C)
9
54
D)
6
54
Simplify the complex fraction.
198)
x–2+5y–2
x–1–y–1
198)
A)
y2+5x2
y – x
B)
5y2+x2
5xy(y – x)
C)
y2+5x2
xy(y – x)
D)
5y2+x2
5(y – x)
Rewrite the rational expression with the indicated denominator.
199)
–14
x2+ 2x
= ?
x(x + 2)(x – 7)
199)
A)
–14(x – 7)
x(x + 2)(x – 7)
B)
–14
x(x + 2)(x – 7)
C)
–14(x + 7)
x(x + 2)(x – 7)
D)
–14(x + 2)
x(x + 2)(x – 7)
Solve the formula for the specified variable.
200)
I =kE
R for R
200)
A)
R =I
kE
B)
R = kE – I
C)
R =kE
I
D)
R = kEI
Write the rational expression in lowest terms.
201)
4x + 3
20x2+ 23x + 6
201)
A)
1
5x + 2
B)
4x + 5
5x + 23
C)
4x
5x + 2
D)
4x + 3
20x2+ 23x + 6
Solve the problem.
202)
The sum of the reciprocals of two consecutive integers is 11
30 . Find the integers.
202)
A)
11 and 12
B)
5 and 6
C)
6 and 7
D)
4 and 5
Simplify the complex fraction.
203)
1
a+ 1
1
a– 1
203)
A)
1 + a
1 – a
B)
1 – a2
C)
1
D)
a
1 – a2
Identify as an equation or an expression.
204)
3x +7
4=5 x
2–5
204)
A)
Equation
B)
Expression
Multiply or divide as indicated. Write the answer in lowest terms.
205)
x2–4x –12
6x ·x2–6x
x2–12x +36
÷x +2
x +6
205)
A)
x +2
x
B)
x +6
2
C)
x –6
x
D)
x +6
6
Solve the problem.
206)
The speed of a stream is 5 mph. If a boat travels 60 mi downstream in the same time that it takes to
travel 30 mi upstream, what is the speed of the boat in still water?
206)
A)
17 mph
B)
10 mph
C)
18 mph
D)
15 mph