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Math Problems
Algebra 2
Simplify rational expressions
Which expression is equivalent to
2
a
+
6
a
2a + 6a
2
a
+
6
a
?
\newline
Choices:
\newline
(A)
7
a
7a
7
a
\newline
(B)
a
8
a^8
a
8
\newline
(C)
8
a
8a
8
a
\newline
(D)
a
+
8
a + 8
a
+
8
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Which expression is equivalent to the expression below?
\newline
s
+
s
+
s
s+s+s
s
+
s
+
s
\newline
3
+
s
3+s
3
+
s
\newline
s
3
\frac{s}{3}
3
s
\newline
3
s
3 s
3
s
\newline
s
3
s^{3}
s
3
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Which expression is equivalent to the expression below?
\newline
h
+
h
+
h
h+h+h
h
+
h
+
h
\newline
3
3
3
\newline
h
3
h^{3}
h
3
\newline
3
h
3 h
3
h
\newline
3
+
h
3+h
3
+
h
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Which expression is equivalent to the expression below?
\newline
n
+
n
+
n
n+n+n
n
+
n
+
n
\newline
3
3
3
\newline
n
3
n^{3}
n
3
\newline
3
+
n
3+n
3
+
n
\newline
3
n
3 n
3
n
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Which of the following is a whole number?
\newline
Choices:
\newline
(A)
0
0
0
\newline
(B)
π
\pi
π
\newline
(C)
7
\sqrt{7}
7
\newline
(D)
−
5
-5
−
5
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Simplify.
\newline
Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
y
−
7
y
−
13
=
\frac{y^{-7}}{y^{-13}}=
y
−
13
y
−
7
=
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37
,
28
,
80
,
66
37,28,80,66
37
,
28
,
80
,
66
\newline
What is the range of the values shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
29
29
29
\newline
(B)
38
38
38
\newline
(C)
43
43
43
\newline
(D)
52
52
52
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Simplify the expression below and write your answer in simplest form:
\newline
x
2
+
10
x
x
(
x
+
10
)
2
⋅
(
x
+
10
)
2
x
2
+
19
x
+
90
\frac{x^{2}+10x}{x(x+10)^{2}} \cdot \frac{(x+10)^{2}}{x^{2}+19x+90}
x
(
x
+
10
)
2
x
2
+
10
x
⋅
x
2
+
19
x
+
90
(
x
+
10
)
2
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Prove the identity:
\newline
sin
4
x
sin
x
=
4
cos
x
cos
2
x
\frac{\sin 4x}{\sin x} = 4\cos x \cos 2x
sin
x
sin
4
x
=
4
cos
x
cos
2
x
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Select the answer which is equivalent to the given expression using your calculator.
\newline
−
6
−
17
−
7
\frac{-6}{-17-\sqrt{7}}
−
17
−
7
−
6
\newline
34
+
2
7
47
\frac{34+2 \sqrt{7}}{47}
47
34
+
2
7
\newline
34
−
2
7
47
\frac{34-2 \sqrt{7}}{47}
47
34
−
2
7
\newline
17
+
7
47
\frac{17+\sqrt{7}}{47}
47
17
+
7
\newline
17
−
7
47
\frac{17-\sqrt{7}}{47}
47
17
−
7
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Which of the following expressions is equivalent to
a
b
\frac{a}{b}
b
a
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
b
a
\frac{1}{\frac{b}{a}}
a
b
1
\newline
(B)
b
⋅
a
b \cdot a
b
⋅
a
\newline
(C)
b
a
\frac{b}{a}
a
b
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Convert
4
h
p
4 \mathrm{hp}
4
hp
to
f
t
⋅
l
b
s
\frac{\mathrm{ft} \cdot \mathrm{lb}}{\mathrm{s}}
s
ft
⋅
lb
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Simplify the following expression completely.
\newline
x
2
+
15
x
+
56
x
2
+
3
x
−
28
\frac{x^{2}+15 x+56}{x^{2}+3 x-28}
x
2
+
3
x
−
28
x
2
+
15
x
+
56
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
8
x
+
15
x
2
+
7
x
+
12
\frac{x^{2}+8 x+15}{x^{2}+7 x+12}
x
2
+
7
x
+
12
x
2
+
8
x
+
15
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
15
x
+
56
x
2
+
2
x
−
63
\frac{x^{2}-15 x+56}{x^{2}+2 x-63}
x
2
+
2
x
−
63
x
2
−
15
x
+
56
\newline
Answer:
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x
2
+
6
x
−
30
30
−
6
x
−
x
2
\frac{x^{2}+6 x-30}{30-6 x-x^{2}}
30
−
6
x
−
x
2
x
2
+
6
x
−
30
\newline
Which expression is equivalent to the given expression for all
x
2
+
6
x
−
30
≠
0
x^{2}+6 x-30 \neq 0
x
2
+
6
x
−
30
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
1
1
1
\newline
(C)
0
0
0
\newline
(D)
(
x
+
6
)
(
x
−
5
)
(
6
−
x
)
(
5
+
x
)
\frac{(x+6)(x-5)}{(6-x)(5+x)}
(
6
−
x
)
(
5
+
x
)
(
x
+
6
)
(
x
−
5
)
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f
(
t
)
=
100
(
1.1
)
3
t
f(t)=100(1.1)^{3t}
f
(
t
)
=
100
(
1.1
)
3
t
\newline
Which of the following is an equivalent form of the function
f
f
f
in which the exponent is
t
t
t
?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
t
)
=
100
(
1.331
)
t
f(t)=100(1.331)^{t}
f
(
t
)
=
100
(
1.331
)
t
\newline
(B)
f
(
t
)
=
100
(
3.3
)
t
f(t)=100(3.3)^{t}
f
(
t
)
=
100
(
3.3
)
t
\newline
(C)
f
(
t
)
=
100
(
4.1
)
t
f(t)=100(4.1)^{t}
f
(
t
)
=
100
(
4.1
)
t
\newline
(D)
f
(
t
)
=
300
(
1.1
)
t
f(t)=300(1.1)^{t}
f
(
t
)
=
300
(
1.1
)
t
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x
3
+
9
x
2
x
3
\frac{x^{3}+9 x^{2}}{x^{3}}
x
3
x
3
+
9
x
2
\newline
Which expression is equivalent to the given expression for all
x
>
1
x>1
x
>
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
x
2
9 x^{2}
9
x
2
\newline
(B)
1
+
9
x
2
1+9 x^{2}
1
+
9
x
2
\newline
(C)
x
+
9
x
\frac{x+9}{x}
x
x
+
9
\newline
(D)
1
+
9
x
x
\frac{1+9 x}{x}
x
1
+
9
x
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b)
1
sec
x
−
1
\frac{1}{\sec x - 1}
s
e
c
x
−
1
1
=
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7
7
7
watermelons cost
$
8.96
\$8.96
$8.96
.
\newline
Which equation would help determine the cost of
5
5
5
watermelons?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
5
=
$
8.96
7
\frac{x}{5} = \frac{\$8.96}{7}
5
x
=
7
$8.96
\newline
(B)
x
5
=
7
$
8.96
\frac{x}{5} = \frac{7}{\$8.96}
5
x
=
$8.96
7
\newline
(C)
7
5
=
x
$
8.96
\frac{7}{5} = \frac{x}{\$8.96}
5
7
=
$8.96
x
\newline
(D)
5
x
=
$
8.96
7
\frac{5}{x} = \frac{\$8.96}{7}
x
5
=
7
$8.96
\newline
(E) None of the above
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7
7
7
watermelons cost
$
8.96
\$8.96
$8.96
. Which equation would help determine the cost of
5
5
5
watermelons? Choose
1
1
1
answer:
\newline
(A)
x
5
=
$
8.96
7
\frac{x}{5} = \frac{\$8.96}{7}
5
x
=
7
$8.96
\newline
(B)
x
5
=
7
$
8.96
\frac{x}{5} = \frac{7}{\$8.96}
5
x
=
$8.96
7
\newline
(C)
7
5
=
x
$
8.96
\frac{7}{5} = \frac{x}{\$8.96}
5
7
=
$8.96
x
\newline
(D)
5
x
=
$
8.96
7
\frac{5}{x} = \frac{\$8.96}{7}
x
5
=
7
$8.96
\newline
(E) None of the above
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What is the product of
\newline
6
,
x
2
−
3
x
6,x^{2}-3x
6
,
x
2
−
3
x
, and
x
−
10
x-10
x
−
10
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
42
x
+
180
-42x+180
−
42
x
+
180
\newline
(B)
6
x
2
−
78
x
+
180
6x^{2}-78x+180
6
x
2
−
78
x
+
180
\newline
(C)
6
x
3
−
42
x
2
+
180
x
6x^{3}-42x^{2}+180x
6
x
3
−
42
x
2
+
180
x
\newline
(D)
6
x
3
−
78
x
2
+
180
x
6x^{3}-78x^{2}+180x
6
x
3
−
78
x
2
+
180
x
\newline
Get tutor help
y
=
−
x
−
11
y=-x-11
y
=
−
x
−
11
\newline
y
=
x
2
−
5
x
−
7
y=x^2-5x-7
y
=
x
2
−
5
x
−
7
\newline
Which of the following is a solution to the system of equations?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
−
2
,
−
9
)
(-2,-9)
(
−
2
,
−
9
)
\newline
(B)
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
\newline
(C)
(
2
,
−
13
)
(2,-13)
(
2
,
−
13
)
\newline
(D)
(
3
,
−
13
)
(3,-13)
(
3
,
−
13
)
Get tutor help
5
∫
1
1
−
sin
x
d
x
⇒
5\int \frac{1}{1-\sin x}\,dx\Rightarrow
5
∫
1
−
s
i
n
x
1
d
x
⇒
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d
y
d
x
=
5
x
y
\frac{dy}{dx} = \frac{5x}{y}
d
x
d
y
=
y
5
x
Get tutor help
For
t
≠
0
t\neq 0
t
=
0
, which of the following expressions is equivalent to
−
12
t
2
−
18
t
8
t
2
+
18
t
\frac{-12t^{2}-18t}{8t^{2}+18t}
8
t
2
+
18
t
−
12
t
2
−
18
t
?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
t
+
9
4
t
+
9
\frac{6t+9}{4t+9}
4
t
+
9
6
t
+
9
\newline
(B)
−
6
t
+
9
4
t
+
9
\frac{-6t+9}{4t+9}
4
t
+
9
−
6
t
+
9
\newline
(C)
−
6
t
−
1
4
t
+
1
\frac{-6t-1}{4t+1}
4
t
+
1
−
6
t
−
1
\newline
(D)
−
6
t
−
9
4
t
+
9
\frac{-6t-9}{4t+9}
4
t
+
9
−
6
t
−
9
Get tutor help
Find
d
d
x
(
−
cos
(
−
3
x
−
10
)
)
\frac{d}{d x}(-\cos (-3 x-10))
d
x
d
(
−
cos
(
−
3
x
−
10
))
\newline
Answer:
Get tutor help
Find
d
d
x
(
sin
7
x
)
\frac{d}{d x}(\sin 7 x)
d
x
d
(
sin
7
x
)
\newline
Answer:
Get tutor help
d
y
d
t
=
2
y
\frac{d y}{d t}=2 y
d
t
d
y
=
2
y
, and
y
=
8
y=8
y
=
8
when
t
=
0
t=0
t
=
0
.
\newline
Solve the equation.
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
e
8
t
y=e^{8 t}
y
=
e
8
t
\newline
(B)
y
=
e
2
t
y=e^{2 t}
y
=
e
2
t
\newline
(C)
y
=
8
e
2
t
y=8 e^{2 t}
y
=
8
e
2
t
\newline
(D)
y
=
2
e
8
t
y=2 e^{8 t}
y
=
2
e
8
t
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d
y
d
t
=
2
y
\frac{d y}{d t}=2 y
d
t
d
y
=
2
y
, and
y
=
8
y=8
y
=
8
when
t
=
0
t=0
t
=
0
.
\newline
Solve the equation.
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
e
2
t
y=e^{2 t}
y
=
e
2
t
\newline
(B)
y
=
2
e
8
t
y=2 e^{8 t}
y
=
2
e
8
t
\newline
(C)
y
=
e
8
t
y=e^{8 t}
y
=
e
8
t
\newline
(D)
y
=
8
e
2
t
y=8 e^{2 t}
y
=
8
e
2
t
Get tutor help
Let
y
=
2
e
4
x
y=2 e^{4 x}
y
=
2
e
4
x
.
\newline
Find
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
.
\newline
Choose
1
1
1
answer:
\newline
(A)
40
e
6
x
40 e^{6 x}
40
e
6
x
\newline
(B)
8
e
x
8 e^{x}
8
e
x
\newline
(C)
32
e
4
x
32 e^{4 x}
32
e
4
x
\newline
(D)
e
4
x
8
\frac{e^{4 x}}{8}
8
e
4
x
Get tutor help
d
d
x
[
8
x
2
+
2
x
−
3
]
=
?
\frac{d}{d x}\left[\sqrt{8 x^{2}+2 x-3}\right]=?
d
x
d
[
8
x
2
+
2
x
−
3
]
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
x
+
1
8
x
2
+
2
x
−
3
\frac{8 x+1}{\sqrt{8 x^{2}+2 x-3}}
8
x
2
+
2
x
−
3
8
x
+
1
\newline
(B)
8
x
+
1
x
\frac{8 x+1}{\sqrt{x}}
x
8
x
+
1
\newline
(c)
16
x
+
2
\sqrt{16 x+2}
16
x
+
2
\newline
(D)
1
2
16
x
+
2
\frac{1}{2 \sqrt{16 x+2}}
2
16
x
+
2
1
Get tutor help
Simplify. Write your answer using whole numbers and variables.
\newline
9
k
+
4
9
k
2
+
4
k
\frac{9k + 4}{9k^2 + 4k}
9
k
2
+
4
k
9
k
+
4
\newline
______
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