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Math Problems
Algebra 1
Compare linear and exponential growth
(
v
+
1
5
)
2
−
9
=
0
\left(v+\frac{1}{5}\right)^{2}-9=0
(
v
+
5
1
)
2
−
9
=
0
\newline
What is the sum of the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
5
-\frac{3}{5}
−
5
3
\newline
(B)
−
2
5
-\frac{2}{5}
−
5
2
\newline
(C)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(D)
0
0
0
Get tutor help
(
x
+
3
)
2
−
4
=
0
(x+3)^{2}-4=0
(
x
+
3
)
2
−
4
=
0
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
1
,
x
=
5
x=1, x=5
x
=
1
,
x
=
5
\newline
(B)
x
=
1
,
x
=
−
5
x=1, x=-5
x
=
1
,
x
=
−
5
\newline
(C)
x
=
−
1
,
x
=
5
x=-1, x=5
x
=
−
1
,
x
=
5
\newline
(D)
x
=
−
1
,
x
=
−
5
x=-1, x=-5
x
=
−
1
,
x
=
−
5
Get tutor help
x
2
−
13
x
+
30
=
0
x^{2}-13 x+30=0
x
2
−
13
x
+
30
=
0
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
−
15
x=-15
x
=
−
15
and
x
=
2
x=2
x
=
2
\newline
(B)
x
=
−
10
x=-10
x
=
−
10
and
x
=
−
3
x=-3
x
=
−
3
\newline
(C)
x
=
3
x=3
x
=
3
and
x
=
10
x=10
x
=
10
\newline
(D)
x
=
−
2
x=-2
x
=
−
2
and
x
=
15
x=15
x
=
15
Get tutor help
(
x
−
3
)
2
(x-3)^{2}
(
x
−
3
)
2
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
2
+
6
x
+
9
x^{2}+6 x+9
x
2
+
6
x
+
9
\newline
(B)
x
2
−
6
x^{2}-6
x
2
−
6
\newline
(C)
2
x
2
+
9
2 x^{2}+9
2
x
2
+
9
\newline
(D)
x
2
−
6
x
+
9
x^{2}-6 x+9
x
2
−
6
x
+
9
Get tutor help
f
=
12
g
h
+
15
g
f=12 g h+15 g
f
=
12
g
h
+
15
g
\newline
The equation gives the quantity
f
f
f
in terms of the quantities
g
g
g
and
h
h
h
. Which of the following equations correctly expresses
g
g
g
in terms of
f
f
f
and
h
h
h
?
\newline
Choose
1
1
1
answer:
\newline
(A)
g
=
f
12
h
+
15
g=\frac{f}{12 h+15}
g
=
12
h
+
15
f
\newline
(B)
g
=
f
12
h
−
15
g=\frac{f}{12 h-15}
g
=
12
h
−
15
f
\newline
(C)
g
=
f
−
15
12
h
g=\frac{f-15}{12 h}
g
=
12
h
f
−
15
\newline
(D)
g
=
f
27
h
g=\frac{f}{27 h}
g
=
27
h
f
Get tutor help
j
=
m
c
⋅
78
j=\frac{m}{c} \cdot 78
j
=
c
m
⋅
78
\newline
Which of the following equations correctly expresses
c
c
c
in terms of
j
j
j
and
m
m
m
?
\newline
Choose
1
1
1
answer:
\newline
(A)
c
=
m
j
⋅
78
c=\frac{m}{j} \cdot 78
c
=
j
m
⋅
78
\newline
(B)
c
=
m
78
⋅
j
c=\frac{m}{78 \cdot j}
c
=
78
⋅
j
m
\newline
(C)
c
=
j
m
⋅
78
c=\frac{j}{m} \cdot 78
c
=
m
j
⋅
78
\newline
(D)
c
=
j
78
⋅
m
c=\frac{j}{78 \cdot m}
c
=
78
⋅
m
j
Get tutor help
A
=
1
2
(
b
1
+
b
2
)
h
A=\frac{1}{2}\left(b_{1}+b_{2}\right) h
A
=
2
1
(
b
1
+
b
2
)
h
\newline
The area,
A
A
A
, of a trapezoid that has a height,
h
h
h
, and bases,
b
1
b_{1}
b
1
and
b
2
b_{2}
b
2
, can be found by using the given equation. Which of the following correctly shows the trapezoid's height in terms of its area and
2
2
2
bases?
\newline
Choose
1
1
1
answer:
\newline
(A)
h
=
A
2
(
b
1
+
b
2
)
h=\frac{A}{2}\left(b_{1}+b_{2}\right)
h
=
2
A
(
b
1
+
b
2
)
\newline
(B)
h
=
2
A
(
b
1
+
b
2
)
h=\frac{2}{A\left(b_{1}+b_{2}\right)}
h
=
A
(
b
1
+
b
2
)
2
\newline
(C)
h
=
A
2
(
b
1
+
b
2
)
h=\frac{A}{2\left(b_{1}+b_{2}\right)}
h
=
2
(
b
1
+
b
2
)
A
\newline
(D)
h
=
2
A
(
b
1
+
b
2
)
h=\frac{2 A}{\left(b_{1}+b_{2}\right)}
h
=
(
b
1
+
b
2
)
2
A
Get tutor help
l
=
125
m
+
50
n
l=\frac{125}{m}+50 n
l
=
m
125
+
50
n
\newline
The equation gives the quantity
l
l
l
in terms of the quantities
m
m
m
and
n
n
n
. Which of the following equations correctly expresses
n
n
n
in terms of
l
l
l
and
m
m
m
?
\newline
Choose
1
1
1
answer:
\newline
(A)
n
=
l
−
125
50
m
n=\frac{l-125}{50 m}
n
=
50
m
l
−
125
\newline
(B)
n
=
l
50
−
125
m
n=\frac{l}{50}-\frac{125}{m}
n
=
50
l
−
m
125
\newline
(C)
n
=
l
50
−
5
2
m
n=\frac{l}{50}-\frac{5}{2 m}
n
=
50
l
−
2
m
5
\newline
(D)
n
=
5
2
m
−
l
50
n=\frac{5}{2 m}-\frac{l}{50}
n
=
2
m
5
−
50
l
Get tutor help
A circle graphed in the
x
y
x y
x
y
-plane has its center at
(
0
,
15
)
(0,15)
(
0
,
15
)
. If the point
(
3
,
2
)
(3,2)
(
3
,
2
)
lies on the circle, which of the following is an equation of the circle?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
x
−
15
)
2
+
y
2
=
178
(x-15)^{2}+y^{2}=178
(
x
−
15
)
2
+
y
2
=
178
\newline
(B)
(
x
−
15
)
2
+
y
2
=
178
(x-15)^{2}+y^{2}=\sqrt{178}
(
x
−
15
)
2
+
y
2
=
178
\newline
(C)
x
2
+
(
y
−
15
)
2
=
178
x^{2}+(y-15)^{2}=178
x
2
+
(
y
−
15
)
2
=
178
\newline
(D)
x
2
+
(
y
−
15
)
2
=
178
x^{2}+(y-15)^{2}=\sqrt{178}
x
2
+
(
y
−
15
)
2
=
178
Get tutor help
What is the value of
sin
(
6
0
∘
)
?
\sin \left(60^{\circ}\right) ?
sin
(
6
0
∘
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
2
-\frac{\sqrt{3}}{2}
−
2
3
\newline
(B)
−
1
2
-\frac{1}{2}
−
2
1
\newline
(C)
1
2
\frac{1}{2}
2
1
\newline
(D)
3
2
\frac{\sqrt{3}}{2}
2
3
Get tutor help
If
y
=
(
x
2
−
1
)
(
x
+
4
)
−
9
y=\left(x^{2}-1\right)(x+4)-9
y
=
(
x
2
−
1
)
(
x
+
4
)
−
9
, what is the value of
y
y
y
when
x
=
1
x=1
x
=
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
9
-9
−
9
\newline
(B)
−
5
-5
−
5
\newline
(C)
−
4
-4
−
4
\newline
(D)
0
0
0
Get tutor help
f
(
x
)
=
x
3
−
4
x
2
+
3
x
−
12
f(x)=x^{3}-4 x^{2}+3 x-12
f
(
x
)
=
x
3
−
4
x
2
+
3
x
−
12
\newline
The function
f
f
f
is shown. If
x
−
4
x-4
x
−
4
is a factor of
f
f
f
, what is the value of
f
(
4
)
?
f(4) ?
f
(
4
)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
12
-12
−
12
\newline
(B)
0
0
0
\newline
(C)
12
12
12
\newline
(D)
64
64
64
Get tutor help
f
(
x
)
=
2
x
3
−
2
x
2
+
18
x
−
18
f(x)=2 x^{3}-2 x^{2}+18 x-18
f
(
x
)
=
2
x
3
−
2
x
2
+
18
x
−
18
\newline
The function
f
f
f
is shown. If
x
−
1
x-1
x
−
1
is a factor of
f
f
f
, what is the value of
f
(
1
)
f(1)
f
(
1
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
40
-40
−
40
\newline
(B)
−
18
-18
−
18
\newline
(C)
0
0
0
\newline
(D)
1
1
1
Get tutor help
If
f
(
x
)
=
3
x
3
−
7
x
2
+
9
x
−
4
f(x)=3 x^{3}-7 x^{2}+9 x-4
f
(
x
)
=
3
x
3
−
7
x
2
+
9
x
−
4
, what is the value of
f
(
0
)
f(0)
f
(
0
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
4
-4
−
4
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D)
3
3
3
Get tutor help
−
20
x
2
+
25
x
2
y
−
40
x
=
−
5
x
(
4
-20 x^{2}+25 x^{2} y-40 x=-5 x(4
−
20
x
2
+
25
x
2
y
−
40
x
=
−
5
x
(
4
\newline
In the given equation,
c
c
c
is a positive constant. What is the value of
c
c
c
?
Get tutor help
[
(
9
f
+
9
)
+
(
9
f
+
9
+
1
)
]
⋅
f
[(9 f+9)+(9 f+9+1)] \cdot f
[(
9
f
+
9
)
+
(
9
f
+
9
+
1
)]
⋅
f
\newline
Which of the following expressions is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
18
(
f
2
+
f
)
18\left(f^{2}+f\right)
18
(
f
2
+
f
)
\newline
(B)
18
f
2
+
18
f
+
1
18 f^{2}+18 f+1
18
f
2
+
18
f
+
1
\newline
(C)
18
(
f
2
+
f
+
1
)
18\left(f^{2}+f+1\right)
18
(
f
2
+
f
+
1
)
\newline
(D)
18
f
2
+
19
f
18 f^{2}+19 f
18
f
2
+
19
f
Get tutor help
−
y
2
(
6
x
−
y
)
-y^{2}(6 x-y)
−
y
2
(
6
x
−
y
)
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
x
3
+
x
2
y
-6 x^{3}+x^{2} y
−
6
x
3
+
x
2
y
\newline
(B)
−
6
x
2
y
+
y
3
-6 x^{2} y+y^{3}
−
6
x
2
y
+
y
3
\newline
(C)
−
6
x
y
2
+
y
3
-6 x y^{2}+y^{3}
−
6
x
y
2
+
y
3
\newline
(D)
6
x
y
2
−
y
3
6 x y^{2}-y^{3}
6
x
y
2
−
y
3
Get tutor help
x
2
+
5
x
−
3
x
−
2
x
−
100
x^{2}+5 x-3 x-2 x-100
x
2
+
5
x
−
3
x
−
2
x
−
100
\newline
Which of the follow expressions is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
x
2
−
2
x
−
100
6 x^{2}-2 x-100
6
x
2
−
2
x
−
100
\newline
(B)
6
x
2
−
5
x
−
100
6 x^{2}-5 x-100
6
x
2
−
5
x
−
100
\newline
(C)
x
2
−
10
x
−
100
x^{2}-10 x-100
x
2
−
10
x
−
100
\newline
(D)
x
2
−
100
x^{2}-100
x
2
−
100
Get tutor help
Which of the following is equivalent to
x
(
x
−
1
)
x(x-1)
x
(
x
−
1
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
−
1
2 x-1
2
x
−
1
\newline
(B)
x
2
−
x
x^{2}-x
x
2
−
x
\newline
(C)
x
2
−
1
x^{2}-1
x
2
−
1
\newline
(D)
2
x
2
−
x
2 x^{2}-x
2
x
2
−
x
Get tutor help
(
a
3
)
3
⋅
a
−
9
\left(a^{3}\right)^{3} \cdot a^{-9}
(
a
3
)
3
⋅
a
−
9
\newline
Which of the following expressions is equivalent to the given expression for all
a
≠
0
a \neq 0
a
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
a
3
a^{3}
a
3
\newline
(D)
a
18
a^{18}
a
18
Get tutor help
a
5
l
2
3
⋅
b
a
2
\frac{a^{5} l^{2}}{3} \cdot \frac{b}{a^{2}}
3
a
5
l
2
⋅
a
2
b
\newline
Which expression is equivalent to the product for all
a
>
0
a>0
a
>
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
b
l
2
3
a
3
\frac{b l^{2}}{3 a^{3}}
3
a
3
b
l
2
\newline
(B)
a
7
l
2
3
b
\frac{a^{7} l^{2}}{3 b}
3
b
a
7
l
2
\newline
(C)
b
l
2
3
\frac{b l^{2}}{3}
3
b
l
2
\newline
(D)
a
3
b
l
2
3
\frac{a^{3} b l^{2}}{3}
3
a
3
b
l
2
Get tutor help
Which of the following is equivalent to
(
2
x
)
3
\left(2^{x}\right)^{3}
(
2
x
)
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
x
6^{x}
6
x
\newline
(B)
6
x
3
6^{x^{3}}
6
x
3
\newline
(C)
8
x
8^{x}
8
x
\newline
(D)
8
3
x
8^{3 x}
8
3
x
Get tutor help
Which of the following is equivalent to
(
3
a
)
2
\left(3^{a}\right)^{2}
(
3
a
)
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
2
a
9^{2 a}
9
2
a
\newline
(B)
9
a
9^{a}
9
a
\newline
(C)
6
a
6^{a}
6
a
\newline
(D)
6
2
a
6^{2 a}
6
2
a
Get tutor help
a
8
b
−
2
a
2
b
10
\frac{a^{8} b^{-2}}{a^{2} b^{10}}
a
2
b
10
a
8
b
−
2
\newline
Which of the following is equivalent to the given expression for
a
,
b
≠
0
a, b \neq 0
a
,
b
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
a
4
b
−
5
a^{4} b^{-5}
a
4
b
−
5
\newline
(B)
a
6
b
12
a^{6} b^{12}
a
6
b
12
\newline
(C)
a
4
b
−
5
\frac{a^{4}}{b^{-5}}
b
−
5
a
4
\newline
(D)
a
6
b
12
\frac{a^{6}}{b^{12}}
b
12
a
6
Get tutor help
(
a
m
)
n
⋅
a
m
n
\left(a^{m}\right)^{n} \cdot a^{m n}
(
a
m
)
n
⋅
a
mn
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
a
m
n
2 a^{m n}
2
a
mn
\newline
(B)
a
2
m
n
a^{2 m n}
a
2
mn
\newline
(C)
a
m
2
n
2
a^{m^{2} n^{2}}
a
m
2
n
2
\newline
(D)
a
m
n
+
m
n
a^{m^{n}+m n}
a
m
n
+
mn
Get tutor help
(
1
2
)
−
2
+
3
0
\left(\frac{1}{2}\right)^{-2}+3^{0}
(
2
1
)
−
2
+
3
0
\newline
What is the value of the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
4
\frac{3}{4}
4
3
\newline
(B)
5
4
\frac{5}{4}
4
5
\newline
(C)
4
4
4
\newline
(D)
5
5
5
Get tutor help
If
b
3
⋅
(
b
4
)
2
=
b
x
b^{3} \cdot\left(b^{4}\right)^{2}=b^{x}
b
3
⋅
(
b
4
)
2
=
b
x
, what is the value of
x
x
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
9
9
\newline
(B)
11
11
11
\newline
(C)
18
18
18
\newline
(D)
19
19
19
Get tutor help
(
2
b
−
5
)
3
\left(2 b^{-5}\right)^{3}
(
2
b
−
5
)
3
\newline
Which of the following is equivalent to the given expression for all
b
≠
0
b \neq 0
b
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
b
15
\frac{2}{b^{15}}
b
15
2
\newline
(B)
8
b
15
\frac{8}{b^{15}}
b
15
8
\newline
(C)
1
2
b
15
\frac{1}{2 b^{15}}
2
b
15
1
\newline
(D)
1
8
b
15
\frac{1}{8 b^{15}}
8
b
15
1
Get tutor help
h
(
t
)
=
88
−
37
(
0.85
)
t
h(t)=88-37(0.85)^{t}
h
(
t
)
=
88
−
37
(
0.85
)
t
\newline
A human child grows rapidly in the first
36
36
36
months after birth. The given function models
h
h
h
, the child's height in centimeters,
t
t
t
months after birth for
0
≤
t
≤
36
0 \leq t \leq 36
0
≤
t
≤
36
. Between
36
36
36
to
72
72
72
months after birth, the child grows at an average rate of
0
0
0
.
5
5
5
centimeter per month. Approximately how many more centimeters does the child grow in their first
36
36
36
months after birth compared to their second
36
36
36
months (
36
36
36
to
72
72
72
months) after birth?
\newline
Choose
1
1
1
answer:
\newline
(A)
19
19
19
\newline
(B)
37
37
37
\newline
(C)
51
51
51
\newline
(D)
88
88
88
Get tutor help
T
(
t
)
=
25
+
65
⋅
(
0.78
)
t
T(t)=25+65 \cdot(0.78)^{t}
T
(
t
)
=
25
+
65
⋅
(
0.78
)
t
\newline
A pot of soup is heated and then left to cool in a room with a constant temperature. The equation gives the temperature of the soup,
T
(
t
)
T(t)
T
(
t
)
, in degrees Celsius
(
∘
C
)
,
t
\left({ }^{\circ} \mathrm{C}\right), t
(
∘
C
)
,
t
minutes after it is heated. What is the initial temperature of the soup before it begins to cool?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
5
∘
C
25^{\circ} \mathrm{C}
2
5
∘
C
\newline
(B)
6
5
∘
C
65^{\circ} \mathrm{C}
6
5
∘
C
\newline
(C)
7
8
∘
C
78^{\circ} \mathrm{C}
7
8
∘
C
\newline
(D)
9
0
∘
C
90^{\circ} \mathrm{C}
9
0
∘
C
Get tutor help
f
(
m
)
=
500
(
1
2
)
m
20
f(m)=500\left(\frac{1}{2}\right)^{\frac{m}{20}}
f
(
m
)
=
500
(
2
1
)
20
m
\newline
The function models
f
f
f
, the amount of a particular medicine in milligrams in a patient's bloodstream,
m
m
m
minutes after the medicine is fully absorbed. Based on the function, how many minutes does it take for the amount of medicine in the patient's bloodstream to reduce by half?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
\frac{1}{2}
2
1
\newline
(B)
10
\mathbf{1 0}
10
\newline
(C)
20
20
20
\newline
(D)
250
\mathbf{2 5 0}
250
Get tutor help
After
24
24
24
hours,
30
%
30 \%
30%
of a
25
25
25
milligram dose of a new antibiotic remains in the body. Which of the following functions,
M
M
M
, models the amount of the antibiotic (in milligrams) that remains in the body after
h
h
h
hours?
\newline
Choose
1
1
1
answer:
\newline
(A)
M
(
h
)
=
30
⋅
(
0.3
)
h
24
M(h)=30 \cdot(0.3)^{\frac{h}{24}}
M
(
h
)
=
30
⋅
(
0.3
)
24
h
\newline
(B)
M
(
h
)
=
25
⋅
(
0.3
)
h
24
M(h)=25 \cdot(0.3)^{\frac{h}{24}}
M
(
h
)
=
25
⋅
(
0.3
)
24
h
\newline
(C)
M
(
h
)
=
25
⋅
(
0.3
)
h
M(h)=25 \cdot(0.3)^{h}
M
(
h
)
=
25
⋅
(
0.3
)
h
\newline
(D)
M
(
h
)
=
25
⋅
(
0.7
)
h
24
M(h)=25 \cdot(0.7)^{\frac{h}{24}}
M
(
h
)
=
25
⋅
(
0.7
)
24
h
Get tutor help
P
(
t
)
=
20
(
0.95
)
t
P(t)=20(0.95)^{t}
P
(
t
)
=
20
(
0.95
)
t
\newline
The function models
P
P
P
, the population of Leetown in thousands,
t
t
t
years after
2007
2007
2007
. What was the population of Leetown in
2007
2007
2007
?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
thousand
\newline
(B)
19
19
19
thousand
\newline
(C)
20
20
20
thousand
\newline
(D)
95
95
95
thousand
Get tutor help
f
(
x
)
=
10
(
1.25
)
x
f(x)=10(1.25)^{x}
f
(
x
)
=
10
(
1.25
)
x
\newline
The function models
f
f
f
, the price of a rare trading card in dollars
x
x
x
years after its initial release in
1993
1993
1993
. Based on the model, what is the price of the trading card
20
20
20
years after its initial release?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
15.63
\$ 15.63
$15.63
\newline
(B)
$
16.39
\$ 16.39
$16.39
\newline
(C)
$
93.13
\$ 93.13
$93.13
\newline
(D)
$
867.36
\$ 867.36
$867.36
Get tutor help
h
(
t
)
=
56
−
4.9
t
2
h(t)=56-4.9 t^{2}
h
(
t
)
=
56
−
4.9
t
2
\newline
The function models
h
h
h
, the height of a flower pot in meters,
t
t
t
seconds after it falls from a fourth floor balcony. What is the height of the flower pot, in meters,
3
3
3
seconds after it falls?
\newline
Choose
1
1
1
answer:
\newline
(A)
51
51
51
.
1
1
1
\newline
(B)
44
44
44
.
1
1
1
\newline
(C)
36
36
36
.
4
4
4
\newline
(D)
11
11
11
.
9
9
9
Get tutor help
h
(
t
)
=
−
4.9
t
2
+
12
t
+
0.5
h(t)=-4.9 t^{2}+12 t+0.5
h
(
t
)
=
−
4.9
t
2
+
12
t
+
0.5
\newline
The function models
h
h
h
, the height of a soccer ball in meters
t
t
t
seconds after it is kicked. About what is the height, in meters, of the soccer ball
2
2
2
.
3
3
3
seconds after it is kicked?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
.
7
7
7
\newline
(B)
2
2
2
.
2
2
2
\newline
(C)
4
4
4
.
9
9
9
\newline
(D)
16
16
16
.
8
8
8
Get tutor help
y
=
3
x
−
15
y=3 x-15
y
=
3
x
−
15
\newline
y
=
x
2
−
2
x
−
15
y=x^{2}-2 x-15
y
=
x
2
−
2
x
−
15
\newline
If
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the system of equations and
x
>
0
x>0
x
>
0
, what is the value of
x
x
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
5
5
5
\newline
(C)
6
6
6
\newline
(D)
15
15
15
Get tutor help
j
3
+
3
j
2
k
+
3
j
k
2
+
k
3
j^{3}+3 j^{2} k+3 j k^{2}+k^{3}
j
3
+
3
j
2
k
+
3
j
k
2
+
k
3
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
j
3
+
3
(
j
k
)
2
+
k
3
j^{3}+3(j k)^{2}+k^{3}
j
3
+
3
(
jk
)
2
+
k
3
\newline
(B)
j
3
+
6
(
j
k
)
2
+
k
3
j^{3}+6(j k)^{2}+k^{3}
j
3
+
6
(
jk
)
2
+
k
3
\newline
(C)
j
3
+
3
j
k
(
j
+
k
)
+
k
3
j^{3}+3 j k(j+k)+k^{3}
j
3
+
3
jk
(
j
+
k
)
+
k
3
\newline
(D)
j
3
+
6
j
k
(
j
+
k
)
+
k
3
j^{3}+6 j k(j+k)+k^{3}
j
3
+
6
jk
(
j
+
k
)
+
k
3
Get tutor help
x
2
x
−
2
+
4
2
−
x
\frac{x^{2}}{x-2}+\frac{4}{2-x}
x
−
2
x
2
+
2
−
x
4
\newline
Which of the following is equivalent to the given expression shown for
x
≠
2
x \neq 2
x
=
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
+
2
x+2
x
+
2
\newline
(B)
x
−
2
x-2
x
−
2
\newline
(C)
x
2
−
4
2
−
x
\frac{x^{2}-4}{2-x}
2
−
x
x
2
−
4
\newline
(D)
x
2
+
4
x
−
2
\frac{x^{2}+4}{x-2}
x
−
2
x
2
+
4
Get tutor help
3
14
y
+
y
14
\frac{3}{14 y}+\frac{y}{14}
14
y
3
+
14
y
\newline
Which expression is equivalent to the sum for
y
≠
0
y \neq 0
y
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
+
y
14
y
+
14
\frac{3+y}{14 y+14}
14
y
+
14
3
+
y
\newline
(B)
4
14
\frac{4}{14}
14
4
\newline
(C)
3
+
y
14
\frac{3+y}{14}
14
3
+
y
\newline
(D)
3
+
y
2
14
y
\frac{3+y^{2}}{14 y}
14
y
3
+
y
2
Get tutor help
5
x
6
y
⋅
3
10
y
\frac{5 x}{6 y} \cdot \frac{3}{10 y}
6
y
5
x
⋅
10
y
3
\newline
Which expression is equivalent to the product for all
y
>
0
y>0
y
>
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
2
\frac{x}{2}
2
x
\newline
(B)
25
x
9
\frac{25 x}{9}
9
25
x
\newline
(C)
x
2
y
2
\frac{x}{2 y^{2}}
2
y
2
x
\newline
(D)
x
4
y
2
\frac{x}{4 y^{2}}
4
y
2
x
Get tutor help
3
g
2
+
12
g
g
+
7
⋅
4
8
g
2
\frac{3 g^{2}+12 g}{g+7} \cdot \frac{4}{8 g^{2}}
g
+
7
3
g
2
+
12
g
⋅
8
g
2
4
\newline
Which expression is equivalent to the product for all
g
>
0
g>0
g
>
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
g
+
48
g
2
+
56
g
\frac{3 g+48}{g^{2}+56 g}
g
2
+
56
g
3
g
+
48
\newline
(B)
12
g
+
12
8
g
2
+
7
g
\frac{12 g+12}{8 g^{2}+7 g}
8
g
2
+
7
g
12
g
+
12
\newline
(C)
3
g
+
12
2
g
2
+
14
g
\frac{3 g+12}{2 g^{2}+14 g}
2
g
2
+
14
g
3
g
+
12
\newline
(D)
3
+
12
g
2
g
+
14
\frac{3+12 g}{2 g+14}
2
g
+
14
3
+
12
g
Get tutor help
Wyatt put the
$
450
\$ 450
$450
she earned from her summer job into an account and will use it to pay for school expenses. She withdraws
10
%
10 \%
10%
of the remaining balance each month to pay for part of her living expenses. Which of the following functions models the balance,
B
B
B
, of Wyatt's money (in dollars)
t
t
t
months after she started school?
\newline
Choose
1
1
1
answer:
\newline
(A)
B
(
t
)
=
450
⋅
(
1.1
)
t
B(t)=450 \cdot(1.1)^{t}
B
(
t
)
=
450
⋅
(
1.1
)
t
\newline
(B)
B
(
t
)
=
450
⋅
(
0.9
)
t
B(t)=450 \cdot(0.9)^{t}
B
(
t
)
=
450
⋅
(
0.9
)
t
\newline
(C)
B
(
t
)
=
450
+
1.1
t
B(t)=450+1.1 t
B
(
t
)
=
450
+
1.1
t
\newline
(D)
B
(
t
)
=
450
−
0.9
t
B(t)=450-0.9 t
B
(
t
)
=
450
−
0.9
t
Get tutor help
Under ideal conditions, Lemna minor (common duckweed) is a fastgrowing fern that can double its area every
2
2
2
days. Assume the growth is unrestricted, and that the duckweed initially covers
10
10
10
square centimeters
(
c
m
2
)
\left(\mathrm{cm}^{2}\right)
(
cm
2
)
in area. Which of the following functions,
F
F
F
, models the area (in
c
m
2
\mathrm{cm}^{2}
cm
2
) the duckweed covers after
d
d
d
days?
\newline
Choose
1
1
1
answer:
\newline
(A)
F
(
d
)
=
10
(
0.5
)
d
2
F(d)=10(0.5)^{\frac{d}{2}}
F
(
d
)
=
10
(
0.5
)
2
d
\newline
(B)
F
(
d
)
=
2
(
10
)
d
F(d)=2(10)^{d}
F
(
d
)
=
2
(
10
)
d
\newline
(C)
F
(
d
)
=
10
(
2
)
d
F(d)=10(2)^{d}
F
(
d
)
=
10
(
2
)
d
\newline
(D)
F
(
d
)
=
10
(
2
)
d
2
F(d)=10(2)^{\frac{d}{2}}
F
(
d
)
=
10
(
2
)
2
d
Get tutor help
Rocio drops a ball from a height of
4
4
4
meters. Rocio observes that each time the ball bounces, it reaches a peak height which is
79
%
79 \%
79%
of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,
h
h
h
, in meters, after
b
b
b
bounces?
\newline
Choose
1
1
1
answer:
\newline
(A)
h
=
4
⋅
0.7
9
(
b
−
1
)
h=4 \cdot 0.79^{(b-1)}
h
=
4
⋅
0.7
9
(
b
−
1
)
\newline
(B)
h
=
4
⋅
0.7
9
b
h=4 \cdot 0.79^{b}
h
=
4
⋅
0.7
9
b
\newline
(C)
h
=
4
−
0.79
⋅
b
2
h=4-0.79 \cdot b^{2}
h
=
4
−
0.79
⋅
b
2
\newline
(D)
h
=
4
⋅
(
1
−
0.79
⋅
b
2
)
h=4 \cdot\left(1-0.79 \cdot b^{2}\right)
h
=
4
⋅
(
1
−
0.79
⋅
b
2
)
Get tutor help
A
(
q
)
=
86
(
0.9
)
q
4
A(q)=86(0.9)^{\frac{q}{4}}
A
(
q
)
=
86
(
0.9
)
4
q
\newline
The function models
A
A
A
, the number of active players, in thousands, of a mobile game
q
q
q
quarter years after
2018
2018
2018
. Based on the function, how many quarter years does it take for the number of active players to decreases by
10
%
10 \%
10%
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
1
1
1
\newline
(B)
0
0
0
.
225
225
225
\newline
(C)
0
0
0
.
9
9
9
\newline
(D)
4
4
4
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a
2
a
−
5
a
−
3
a
0
⋅
(
a
2
a
3
)
−
4
=
a
x
\frac{a^{2} a^{-5}}{a^{-3} a^{0}} \cdot\left(\frac{a^{2}}{a^{3}}\right)^{-4}=a^{x}
a
−
3
a
0
a
2
a
−
5
⋅
(
a
3
a
2
)
−
4
=
a
x
\newline
What is the value of
x
x
x
?
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(
2
m
c
2
6
b
)
(
10
c
4
3
b
3
)
\frac{\left(\frac{2 m c^{2}}{6 b}\right)}{\left(\frac{10 c^{4}}{3 b^{3}}\right)}
(
3
b
3
10
c
4
)
(
6
b
2
m
c
2
)
\newline
Which expression is equivalent to the given quotient for all
b
>
0
b>0
b
>
0
and
c
>
0
c>0
c
>
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
m
10
\frac{m}{10}
10
m
\newline
(B)
m
b
2
10
c
2
\frac{m b^{2}}{10 c^{2}}
10
c
2
m
b
2
\newline
(C)
5
m
c
2
16
b
2
\frac{5 m c^{2}}{16 b^{2}}
16
b
2
5
m
c
2
\newline
(D)
10
m
c
6
9
b
4
\frac{10 m c^{6}}{9 b^{4}}
9
b
4
10
m
c
6
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(
10
p
9
r
5
)
(
5
p
7
3
r
2
)
\frac{\left(\frac{10 p}{9 r^{5}}\right)}{\left(\frac{5 p^{7}}{3 r^{2}}\right)}
(
3
r
2
5
p
7
)
(
9
r
5
10
p
)
\newline
Which expression is equivalent to the given quotient for all
p
>
2
p>2
p
>
2
and
r
<
−
2
r<-2
r
<
−
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
3
r
3
p
6
\frac{2}{3 r^{3} p^{6}}
3
r
3
p
6
2
\newline
(B)
2
p
6
3
r
3
\frac{2 p^{6}}{3 r^{3}}
3
r
3
2
p
6
\newline
(C)
3
r
3
p
6
2
\frac{3 r^{3} p^{6}}{2}
2
3
r
3
p
6
\newline
(D)
3
r
3
2
p
6
\frac{3 r^{3}}{2 p^{6}}
2
p
6
3
r
3
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Which of the following is equivalent to
(
2
x
3
y
4
z
5
)
3
\left(2 x^{3} y^{4} z^{5}\right)^{3}
(
2
x
3
y
4
z
5
)
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
x
9
y
12
z
15
6 x^{9} y^{12} z^{15}
6
x
9
y
12
z
15
\newline
(B)
8
x
9
y
12
z
15
8 x^{9} y^{12} z^{15}
8
x
9
y
12
z
15
\newline
(C)
6
x
6
y
7
z
8
6 x^{6} y^{7} z^{8}
6
x
6
y
7
z
8
\newline
(D)
8
x
6
y
7
z
8
8 x^{6} y^{7} z^{8}
8
x
6
y
7
z
8
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