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Math Problems
Algebra 2
Simplify rational expressions
Khan Academy
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Calculator
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Solve for
x
x
x
.
\newline
12
x
+
7
<
−
11
OR
5
x
−
8
>
40
12 x+7<-11 \text { OR } 5 x-8>40
12
x
+
7
<
−
11
OR
5
x
−
8
>
40
\newline
Choose
1
1
1
answer:
\newline
(A)
x
<
−
3
2
x<-\frac{3}{2}
x
<
−
2
3
or
x
>
48
5
x>\frac{48}{5}
x
>
5
48
\newline
(B)
−
3
2
<
x
<
48
5
-\frac{3}{2}<x<\frac{48}{5}
−
2
3
<
x
<
5
48
\newline
(C)
x
>
3
2
x>\frac{3}{2}
x
>
2
3
or
x
<
48
5
x<\frac{48}{5}
x
<
5
48
\newline
(D) There are no solutions
\newline
E All values of
x
x
x
are solutions
\newline
Show Calculator
\newline
9
9
9
of
10
10
10
\newline
Ash___ull_Bo....webp
\newline
download.jpeg
\newline
035
e
2
a
57
−
8
b
b
a
…
.
.
p
n
g
035 e 2 a 57-8 b b a \ldots . . p n g
035
e
2
a
57
−
8
bba
…
..
p
n
g
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a)
lim
x
→
0
1
−
cos
2
(
x
)
x
tan
(
x
)
\lim _{x \rightarrow 0} \frac{1-\cos ^{2}(x)}{x \tan (x)}
lim
x
→
0
x
t
a
n
(
x
)
1
−
c
o
s
2
(
x
)
Get tutor help
Simplify.
7
v
−
21
v
−
3
⋅
v
+
10
7
v
−
42
\frac{7 v-21}{v-3} \cdot \frac{v+10}{7 v-42}
v
−
3
7
v
−
21
⋅
7
v
−
42
v
+
10
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5
+
4
m
2
+
7
m
−
m
2
+
3
m
−
13
5+4 m^{2}+7 m-m^{2}+3 m-13
5
+
4
m
2
+
7
m
−
m
2
+
3
m
−
13
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
3
m
−
4
)
(
m
+
2
)
(3 m-4)(m+2)
(
3
m
−
4
)
(
m
+
2
)
\newline
(B)
(
3
m
+
4
)
(
m
−
2
)
(3 m+4)(m-2)
(
3
m
+
4
)
(
m
−
2
)
\newline
(C)
(
3
m
−
2
)
(
m
+
4
)
(3 m-2)(m+4)
(
3
m
−
2
)
(
m
+
4
)
\newline
(D)
(
3
m
+
2
)
(
m
−
4
)
(3 m+2)(m-4)
(
3
m
+
2
)
(
m
−
4
)
Get tutor help
Simplify the expression to a + bi form:
\newline
(
2
−
9
i
)
2
(2-9 i)^{2}
(
2
−
9
i
)
2
\newline
Answer:
Get tutor help
tudent/work/RDLKRTI
3
3
3
Q
12
12
12
Hd
48
48
48
Zn
8
8
8
SFTg
\newline
Overlapping Triangles
\newline
Skip
\newline
Which of the following relationships proves why
△
A
E
C
\triangle \mathrm{AEC}
△
AEC
and
△
B
D
C
\triangle \mathrm{BDC}
△
BDC
are congruent?
\newline
Overlapping Triangles
\newline
SSS
\newline
SAA
\newline
SAS
\newline
Segments DC and EC are congruent.
\newline
∠
A
\angle A
∠
A
and
∠
B
\angle B
∠
B
are congruent.
\newline
∠
F
D
C
\angle \mathrm{FDC}
∠
FDC
and
∠
F
E
C
\angle \mathrm{FEC}
∠
FEC
are congruent.
Get tutor help
Which of the following relationships proves why
△
A
E
C
\triangle \mathrm{AEC}
△
AEC
and
△
B
D
C
\triangle \mathrm{BDC}
△
BDC
are congruent?
\newline
H
L
\mathrm{HL}
HL
\newline
Overlapping Triangles
\newline
SSS
\newline
SAA
SAS
\begin{array}{l} \text { SAA } \\ \text { SAS } \end{array}
SAA
SAS
\newline
Segments DC and EC are congruent.
\newline
∠
A
\angle \mathrm{A}
∠
A
and
∠
B
\angle \mathrm{B}
∠
B
are congruent.
\newline
∠
F
D
C
\angle F D C
∠
F
D
C
and
∠
F
E
C
\angle F E C
∠
FEC
are congruent.
Get tutor help
Which expression is equivalent to
3
w
+
3
w
3w + 3w
3
w
+
3
w
?
\newline
Choices:
\newline
(A)
w
6
w^6
w
6
\newline
(B)
6
w
6w
6
w
\newline
(C)
w
+
6
w + 6
w
+
6
\newline
(D)
5
w
5w
5
w
Get tutor help
Which expression is equivalent to
2
n
+
3
n
2n + 3n
2
n
+
3
n
?
\newline
Choices:
\newline
(A)
n
+
5
n + 5
n
+
5
\newline
(B)
n
5
n^5
n
5
\newline
(C)
4
n
4n
4
n
\newline
(D)
5
n
5n
5
n
Get tutor help
Which expression is equivalent to
2
z
+
z
2z + z
2
z
+
z
?
\newline
Choices:
\newline
(A)
4
z
4z
4
z
\newline
(B)
z
3
z^3
z
3
\newline
(C)
3
z
3z
3
z
\newline
(D) $z + \(3\)
Get tutor help
Which expression is equivalent to
2
w
+
w
2w + w
2
w
+
w
?
\newline
Choices:
\newline
(A)
w
3
w^3
w
3
\newline
(B)
w
+
3
w + 3
w
+
3
\newline
(C)
2
w
2w
2
w
\newline
(D)
3
w
3w
3
w
Get tutor help
Which expression is equivalent to
9
w
+
7
w
9w + 7w
9
w
+
7
w
?
\newline
Choices:
\newline
(A)
16
w
16w
16
w
\newline
(B)
w
16
w^{16}
w
16
\newline
(C)
w
+
16
w + 16
w
+
16
\newline
(D)
15
w
15w
15
w
Get tutor help
Which expression is equivalent to
4
t
+
t
4t + t
4
t
+
t
?
\newline
Choices:
\newline
(A)
5
t
5t
5
t
\newline
(B)
t
5
t^5
t
5
\newline
(C)
t
+
5
t + 5
t
+
5
\newline
(D)
6
t
6t
6
t
Get tutor help
Which expression is equivalent to
8
k
+
8
k
8k + 8k
8
k
+
8
k
?
\newline
Choices:
\newline
(A)
k
16
k^{16}
k
16
\newline
(B)
17
k
17k
17
k
\newline
(C)
16
k
16k
16
k
\newline
(D)
k
+
16
k + 16
k
+
16
Get tutor help
Which expression is equivalent to
8
u
+
6
u
8u + 6u
8
u
+
6
u
?
\newline
Choices:
\newline
(A)
14
u
14u
14
u
\newline
(B)
15
u
15u
15
u
\newline
(C)
u
14
u^{14}
u
14
\newline
(D)
u
+
14
u + 14
u
+
14
Get tutor help
Which expression is equivalent to
4
g
+
g
4g + g
4
g
+
g
?
\newline
Choices:
\newline
(A)
4
g
4g
4
g
\newline
(B)
g
5
g^5
g
5
\newline
(C)
5
g
5g
5
g
\newline
(D)
g
+
5
g + 5
g
+
5
Get tutor help
Which expression is equivalent to
5
d
+
9
d
5d + 9d
5
d
+
9
d
?
\newline
Choices:
\newline
(A)
d
+
14
d + 14
d
+
14
\newline
(B)
d
14
d^{14}
d
14
\newline
(C)
15
d
15d
15
d
\newline
(D)
14
d
14d
14
d
Get tutor help
Which expression is equivalent to
3
d
+
6
d
3d + 6d
3
d
+
6
d
?
\newline
Choices:
\newline
(A)
d
9
d^9
d
9
\newline
(B)
10
d
10d
10
d
\newline
(C)
9
d
9d
9
d
\newline
(D)
d
+
9
d + 9
d
+
9
Get tutor help
Which expression is equivalent to
5
x
+
2
x
5x + 2x
5
x
+
2
x
?
\newline
Choices:
\newline
(A)
7
x
7x
7
x
\newline
(B)
x
7
x^7
x
7
\newline
(C)
8
x
8x
8
x
\newline
(D)
x
+
7
x + 7
x
+
7
Get tutor help
Which expression is equivalent to
5
u
+
4
u
5u + 4u
5
u
+
4
u
?
\newline
Choices:
\newline
(A)
u
+
9
u + 9
u
+
9
\newline
(B)
u
9
u^9
u
9
\newline
(C)
9
u
9u
9
u
\newline
(D)
8
u
8u
8
u
Get tutor help
Which expression is equivalent to
6
u
+
9
u
6u + 9u
6
u
+
9
u
?
\newline
Choices:
\newline
(A)
u
+
15
u + 15
u
+
15
\newline
(B)
u
15
u^{15}
u
15
\newline
(C)
15
u
15u
15
u
\newline
(D)
16
u
16u
16
u
Get tutor help
Which expression is equivalent to
9
(
4
q
)
9(4q)
9
(
4
q
)
?
\newline
Choices:
\newline
(A)
q
+
13
q + 13
q
+
13
\newline
(B)
q
+
36
q + 36
q
+
36
\newline
(C)
4
q
+
9
4q + 9
4
q
+
9
\newline
(D)
36
q
36q
36
q
Get tutor help
Which expression is equivalent to
6
c
+
4
c
6c + 4c
6
c
+
4
c
?
\newline
Choices:
\newline
(A)
c
+
10
c + 10
c
+
10
\newline
(B)
10
c
10c
10
c
\newline
(C)
9
c
9c
9
c
\newline
(D)
c
10
c^{10}
c
10
Get tutor help
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
Get tutor help
11
11
11
. PROOF Write a paragraph proof of the following.
\newline
Given:
□
P
R
S
T
\square P R S T
□
PRST
and
□
P
Q
V
U
\square P Q V U
□
PQ
V
U
\newline
Prove:
∠
V
≅
∠
S
\angle V \cong \angle S
∠
V
≅
∠
S
Get tutor help
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
Get tutor help
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
Get tutor help
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
Get tutor help
a
+
b
c
−
d
−
a
+
b
d
−
c
\frac{a+b}{c-d}-\frac{a+b}{d-c}
c
−
d
a
+
b
−
d
−
c
a
+
b
\newline
Which of the following is equivalent to the given expression for
c
≠
d
c \neq d
c
=
d
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
2
b
c
−
d
\frac{2 b}{c-d}
c
−
d
2
b
\newline
(C)
2
(
a
+
b
)
c
−
d
\frac{2(a+b)}{c-d}
c
−
d
2
(
a
+
b
)
\newline
(D)
2
a
+
2
b
2
c
−
2
d
\frac{2 a+2 b}{2 c-2 d}
2
c
−
2
d
2
a
+
2
b
Get tutor help
4
4
4
. Which of the following is a solution to the equation
(
x
−
2
)
2
=
25
(x-2)^{2}=25
(
x
−
2
)
2
=
25
?
\newline
(
1
1
1
)
−
7
-7
−
7
\newline
(
2
2
2
)
7
7
7
\newline
(
3
3
3
)
27
27
27
\newline
(
4
4
4
)
29
29
29
Get tutor help
8
z
3
−
12
z
−
15
8 z^{3}-12 z-15
8
z
3
−
12
z
−
15
at
z
=
3
2
z=\frac{3}{2}
z
=
2
3
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
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 ?
\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
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
Get tutor help
Consider the identity:
cos
θ
sin
θ
−
cos
2
θ
sin
θ
cos
θ
=
tan
θ
\frac{\cos \theta}{\sin \theta}-\frac{\cos 2 \theta}{\sin \theta \cos \theta}=\tan \theta
s
i
n
θ
c
o
s
θ
−
s
i
n
θ
c
o
s
θ
c
o
s
2
θ
=
tan
θ
\newline
5
5
5
.
4
4
4
.
1
1
1
Prove the identity.
Get tutor help
दिश्नाहोस । If
5
cos
A
+
12
sin
A
=
13
5 \cos A+12 \sin A=13
5
cos
A
+
12
sin
A
=
13
, find the alue of
tan
A
\tan A
tan
A
. Ans:
12
5
\frac{12}{5}
5
12
Get tutor help
Which expression is equivalent to
3
x
+
3
15
3
x
+
15
\frac{3 x+\sqrt{3}}{15 \sqrt{3} x+15}
15
3
x
+
15
3
x
+
3
?
\newline
A:
3
3
x
+
1
\frac{3}{3 \sqrt{x}+1}
3
x
+
1
3
\newline
B:
3
15
\frac{\sqrt{3}}{15}
15
3
\newline
C:
1
15
s
3
\frac{1}{15 s \sqrt{3}}
15
s
3
1
\newline
D:
3
x
3
+
x
\frac{\sqrt{3} x}{\sqrt{3}+x}
3
+
x
3
x
Get tutor help
Which of the following expressions is equivalent to
9
x
−
12
−
12
x
−
3
\frac{9 x-12}{-12 x-3}
−
12
x
−
3
9
x
−
12
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
x
−
4
4
x
+
1
\frac{3 x-4}{4 x+1}
4
x
+
1
3
x
−
4
\newline
(B)
3
x
+
4
−
4
x
+
1
\frac{3 x+4}{-4 x+1}
−
4
x
+
1
3
x
+
4
\newline
(C)
3
x
−
4
−
4
x
−
1
\frac{3 x-4}{-4 x-1}
−
4
x
−
1
3
x
−
4
\newline
(D)
−
3
x
−
4
4
x
+
1
\frac{-3 x-4}{4 x+1}
4
x
+
1
−
3
x
−
4
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For
x
x
x
such that
0
<
x
<
π
2
0<x<\frac{\pi}{2}
0
<
x
<
2
π
, the expression
1
−
cos
2
x
sin
x
+
1
−
sin
2
x
cos
x
\frac{\sqrt{1-\cos ^{2} x}}{\sin x}+\frac{\sqrt{1-\sin ^{2} x}}{\cos x}
s
i
n
x
1
−
c
o
s
2
x
+
c
o
s
x
1
−
s
i
n
2
x
is equivalent to:
\newline
F.
0
0
0
\newline
G.
1
1
1
\newline
H.
2
2
2
\newline
−
tan
x
-\tan x
−
tan
x
\newline
sin
2
x
\sin 2 x
sin
2
x
Get tutor help
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
=
Get tutor help
properties into the table to explain the steps for solving the equation
\newline
2
x
+
14
=
34
2x+14 = 34
2
x
+
14
=
34
.
\newline
\newline
Step
\newline
Justification
\newline
\newline
2
x
+
14
=
34
2x+14=34
2
x
+
14
=
34
\newline
Given
\newline
\newline
14
+
(
−
14
)
=
34
+
(
−
14
)
14+(-14)=34+(-14)
14
+
(
−
14
)
=
34
+
(
−
14
)
\newline
\newline
2
x
+
0
=
20
2x+0=20
2
x
+
0
=
20
\newline
Addition
\newline
\newline
2
x
=
20
2x=20
2
x
=
20
\newline
\newline
1
2
(
2
x
)
=
1
2
(
20
)
\frac{1}{2}(2x)=\frac{1}{2}(20)
2
1
(
2
x
)
=
2
1
(
20
)
\newline
\newline
1
x
=
10
1x=10
1
x
=
10
\newline
Multiplication
\newline
\newline
x
=
10
x=10
x
=
10
\newline
\newline
Iditive identity Property
\newline
Additive inverse Property
\newline
Addition propeny cr \'e\'ru:
\newline
alicative identity Property
\newline
Multiplicative inverses property
\newline
Mulkplication propery of
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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
Get tutor help
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
Get tutor help
(x-y/
6
6
6
)/(x-y/
12
12
12
) Which of the following is equivalent to the given expression for
x
≠
y
x \neq y
x
=
y
Get tutor help
x
−
y
/
6
x
−
y
/
12
\frac{x-y/6}{x-y/12}
x
−
y
/12
x
−
y
/6
Which of the following is equivalent to the given expression for
x
≠
y
x \neq y
x
=
y
Get tutor help
If
3
(
T
−
R
)
=
10
3(T-R)=10
3
(
T
−
R
)
=
10
, which of the following correctly expresses
T
T
T
in terms of
R
R
R
? Choose
1
1
1
answer:
\newline
(A)
T
=
R
+
3
10
T=\frac{R+3}{10}
T
=
10
R
+
3
\newline
(B)
T
=
R
+
10
3
T=\frac{R+10}{3}
T
=
3
R
+
10
\newline
(C)
T
=
R
+
3
10
T=R+\frac{3}{10}
T
=
R
+
10
3
\newline
(D)
T
=
R
+
10
3
T=R+\frac{10}{3}
T
=
R
+
3
10
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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
Get tutor help
erify each identity:
\newline
1
1
−
sin
x
+
cot
2
x
cos
2
x
=
sin
x
+
csc
2
x
cos
2
x
\frac{1}{1-\sin x}+\frac{\cot ^{2} x}{\cos ^{2} x}=\frac{\sin x+\csc ^{2} x}{\cos ^{2} x}
1
−
sin
x
1
+
cos
2
x
cot
2
x
=
cos
2
x
sin
x
+
csc
2
x
Get tutor help
Linear equation word problems: foundations
\newline
Anton watched
x
x
x
movies in
2019
2019
2019
. If Michael watched
1
4
\frac{1}{4}
4
1
as many movies as Anton did in
2019
2019
2019
, which of the following best approximates the number of movies Michael watched in
2019
2019
2019
?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
4
\frac{x}{4}
4
x
\newline
(B)
3
x
4
\frac{3 x}{4}
4
3
x
\newline
(C)
x
−
4
x-4
x
−
4
\newline
(D)
4
x
4 x
4
x
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