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Math Problems
Algebra 2
Solve complex trigonomentric equations
Solve the equation.
\newline
6
w
7
=
98
,
304
6 w^{7}=98,304
6
w
7
=
98
,
304
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Simplify:
g
(
x
)
=
3
x
3
cos
x
−
2
x
sin
x
+
5
csc
x
g(x)=3x^{3}\cos x-2x \sin x+5\csc x
g
(
x
)
=
3
x
3
cos
x
−
2
x
sin
x
+
5
csc
x
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What value of
a
a
a
is a solution to this equation?
\newline
a
−
7
=
4
a - 7 = 4
a
−
7
=
4
\newline
Choices:
\newline
(A)
a
=
10
a = 10
a
=
10
\newline
(B)
a
=
11
a = 11
a
=
11
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What value of
c
c
c
is a solution to this equation?
\newline
15
+
c
=
21
15 + c = 21
15
+
c
=
21
\newline
Choices:
\newline
(A)
c
=
6
c = 6
c
=
6
\newline
(B)
c
=
7
c = 7
c
=
7
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What value of
z
z
z
is a solution to this equation?
\newline
15
+
z
=
22
15 + z = 22
15
+
z
=
22
\newline
Choices:
\newline
(A)
z
=
7
z = 7
z
=
7
\newline
(B)
z
=
8
z = 8
z
=
8
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What value of
d
d
d
is a solution to this equation?
\newline
13
+
d
=
13
13 + d = 13
13
+
d
=
13
\newline
Choices:
\newline
(A)
d
=
0
d = 0
d
=
0
\newline
(B)
d
=
2
d = 2
d
=
2
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What value of
w
w
w
is a solution to this equation?
\newline
w
+
11
=
20
w + 11 = 20
w
+
11
=
20
\newline
Choices:
\newline
(A)
w
=
8
w = 8
w
=
8
\newline
(B)
w
=
9
w = 9
w
=
9
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What value of
y
y
y
is a solution to this equation?
\newline
4
y
=
12
4y = 12
4
y
=
12
\newline
Choices:
\newline
(A)
y
=
2
y = 2
y
=
2
\newline
(B)
y
=
3
y = 3
y
=
3
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What value of
a
a
a
is a solution to this equation?
\newline
a
+
20
=
32
a + 20 = 32
a
+
20
=
32
\newline
Choices:
\newline
(A)
a
=
10
a = 10
a
=
10
\newline
(B)
a
=
12
a = 12
a
=
12
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What value of
q
q
q
is a solution to this equation?
\newline
11
+
q
=
20
11 + q = 20
11
+
q
=
20
\newline
Choices:
\newline
(A)
q
=
8
q = 8
q
=
8
\newline
(B)
q
=
9
q = 9
q
=
9
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What value of
v
v
v
is a solution to this equation?
\newline
4
v
=
24
4v = 24
4
v
=
24
\newline
Choices:
\newline
(A)
v
=
4
v = 4
v
=
4
\newline
(B)
v
=
6
v = 6
v
=
6
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What value of
c
c
c
is a solution to this equation?
\newline
8
c
=
32
8c = 32
8
c
=
32
\newline
Choices:
\newline
(A)
c
=
4
c = 4
c
=
4
\newline
(B)
c
=
6
c = 6
c
=
6
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What value of
w
w
w
is a solution to this equation?
\newline
3
+
w
=
5
3 + w = 5
3
+
w
=
5
\newline
Choices:
\newline
(A)
w
=
2
w = 2
w
=
2
\newline
(B)
w
=
4
w = 4
w
=
4
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What value of
y
y
y
is a solution to this equation?
\newline
7
y
=
70
7y = 70
7
y
=
70
\newline
Choices:
\newline
(A)
y
=
8
y = 8
y
=
8
\newline
(B)
y
=
10
y = 10
y
=
10
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What value of
y
y
y
is a solution to this equation?
\newline
19
+
y
=
29
19 + y = 29
19
+
y
=
29
\newline
Choices:
\newline
(A)
y
=
8
y = 8
y
=
8
\newline
(B)
y
=
10
y = 10
y
=
10
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What value of
y
y
y
is a solution to this equation?
\newline
6
y
=
72
6y = 72
6
y
=
72
\newline
Choices:
\newline
(A)
y
=
11
y = 11
y
=
11
\newline
(B)
y
=
12
y = 12
y
=
12
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Solve the following equations:
\newline
45
−
6
a
=
3
45-6 a=3
45
−
6
a
=
3
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Solve
2
x
3
−
24
x
2
+
54
x
=
0
2 x^{3}-24 x^{2}+54 x=0
2
x
3
−
24
x
2
+
54
x
=
0
\newline
The roots are
x
=
x=
x
=
□
\square
□
x
=
x=
x
=
□
\square
□
, and
x
=
x=
x
=
□
\square
□
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2
x
2
+
4
x
=
0
2 x^{2}+4 x=0
2
x
2
+
4
x
=
0
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What value of
c
c
c
is a solution to this equation?
\newline
c
+
17
=
20
c + 17 = 20
c
+
17
=
20
\newline
Choices:
\newline
(A)
c
=
3
c = 3
c
=
3
\newline
(B)
c
=
5
c = 5
c
=
5
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What value of
c
c
c
is a solution to this equation?
\newline
c
−
1
=
4
c - 1 = 4
c
−
1
=
4
\newline
Choices:
\newline
(A)
c
=
3
c = 3
c
=
3
\newline
(B)
c
=
5
c = 5
c
=
5
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What value of
s
s
s
is a solution to this equation?
\newline
s
+
20
=
25
s + 20 = 25
s
+
20
=
25
\newline
Choices:
\newline
(A)
s
=
3
s = 3
s
=
3
\newline
(B)
s
=
5
s = 5
s
=
5
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What value of
s
s
s
is a solution to this equation?
\newline
s
−
7
=
4
s - 7 = 4
s
−
7
=
4
\newline
Choices:
\newline
(A)
s
=
10
s = 10
s
=
10
\newline
(B)
s
=
11
s = 11
s
=
11
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What value of
u
u
u
is a solution to this equation?
\newline
9
u
=
99
9u = 99
9
u
=
99
\newline
Choices:
\newline
(A)
u
=
10
u = 10
u
=
10
\newline
(B)
u
=
11
u = 11
u
=
11
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What value of
w
w
w
is a solution to this equation?
\newline
10
w
=
20
10w = 20
10
w
=
20
\newline
Choices:
\newline
(A)
w
=
2
w = 2
w
=
2
\newline
(B)
w
=
3
w = 3
w
=
3
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What value of
u
u
u
is a solution to this equation?
\newline
4
u
=
20
4u = 20
4
u
=
20
\newline
Choices:
\newline
(A)
u
=
4
u = 4
u
=
4
\newline
(B)
u
=
5
u = 5
u
=
5
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Which equation has both
6
6
6
and
−
6
-6
−
6
as possible values of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
x
2
=
3
x^2 = 3
x
2
=
3
\newline
(B)
x
3
=
3
x^3 = 3
x
3
=
3
\newline
(C)
x
2
=
12
x^2 = 12
x
2
=
12
\newline
(D)
x
3
=
12
x^3 = 12
x
3
=
12
\newline
(E)
x
2
=
36
x^2 = 36
x
2
=
36
\newline
(F)
x
3
=
36
x^3 = 36
x
3
=
36
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Find the line's slope and a point on the line.
\newline
y
−
2
=
3
(
x
+
1
)
y-2=3(x+1)
y
−
2
=
3
(
x
+
1
)
\newline
slope:
□
\square
□
\newline
point on the line: (ㅁ,ㅁ)
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Which value of
x
x
x
is a solution to this equation?
\newline
5
x
2
−
36
x
+
36
=
0
5x^{2}-36x+36=0
5
x
2
−
36
x
+
36
=
0
\newline
a)
x
=
−
6
x=-6
x
=
−
6
\newline
b)
x
=
−
1.8
x=-1.8
x
=
−
1.8
\newline
c)
x
=
4
x=4
x
=
4
\newline
d)
x
=
1.2
x=1.2
x
=
1.2
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Given the quadratic function:
f
(
x
)
=
9
x
2
−
60
x
+
80
f(x)=9x^{2}-60x+80
f
(
x
)
=
9
x
2
−
60
x
+
80
\newline
Find the
𝑥
𝑥
x
-intercepts.
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Prove that
cot
2
θ
+
tan
2
θ
=
2
sin
4
θ
\cot 2\theta + \tan 2\theta = \frac{2}{\sin 4\theta}
cot
2
θ
+
tan
2
θ
=
sin
4
θ
2
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Calculate
(
22
+
m
)
÷
4
(22 + m) \div 4
(
22
+
m
)
÷
4
for
m
=
56
m = 56
m
=
56
.
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Write the expression in simplest form.
\newline
20
x
2
−
30
x
20 x^{2}-30 x
20
x
2
−
30
x
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Solve for
x
x
x
.
\newline
4
x
2
+
52
=
−
8
x
4 x^{2}+52=-8 x
4
x
2
+
52
=
−
8
x
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Solve for
x
x
x
.
\newline
x
2
−
x
=
1
x^{2}-x=1
x
2
−
x
=
1
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If
4
x
2
−
12
x
=
40
4 x^{2}-12 x=40
4
x
2
−
12
x
=
40
, what are the possible values for
x
x
x
?
\newline
A)
−
2
-2
−
2
and
5
5
5
\newline
B)
−
5
-5
−
5
and
2
2
2
\newline
C)
−
5
-5
−
5
and
−
8
-8
−
8
\newline
D)
−
5
-5
−
5
and
−
16
-16
−
16
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Solve
2
x
2
=
162
2 x^{2}=162
2
x
2
=
162
.
\newline
The solutions are
x
=
x=
x
=
□
\square
□
and
x
=
x=
x
=
□
\square
□
.
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10
=
17
b
−
6
b
2
10=17 b-6 b^{2}
10
=
17
b
−
6
b
2
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5
x
2
=
30
x
−
45
5 x^{2}=30 x-45
5
x
2
=
30
x
−
45
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m
2
−
5
m
=
0
m^{2}-5 m=0
m
2
−
5
m
=
0
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cos
2
x
+
2
sin
x
=
−
2
\cos ^{2} x+2 \sin x=-2
cos
2
x
+
2
sin
x
=
−
2
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(ii) the values of
x
x
x
when
5
+
4
x
−
x
2
=
0
5+4 x-x^{2}=0
5
+
4
x
−
x
2
=
0
,
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x
2
+
x
+
2
=
0
x^{2}+x+2=0
x
2
+
x
+
2
=
0
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Solve by Factoring
\newline
x
2
+
14
x
+
48
=
0
x^{2}+14 x+48=0
x
2
+
14
x
+
48
=
0
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Solve for n.
\newline
6
n
2
=
45
+
3
n
6n^{2} = 45 + 3n
6
n
2
=
45
+
3
n
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Without dividing, determine if
96
96
96
,
090
090
090
is divisible by
6
6
6
and explain how you know.
\newline
96
,
090
□
divisible by
6
96,090 \square \text { divisible by } 6
96
,
090
□
divisible by
6
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What value of
w
w
w
is a solution to this equation?
\newline
w
+
8
=
14
w + 8 = 14
w
+
8
=
14
\newline
Choices:
\newline
(A)
w
=
6
w = 6
w
=
6
\newline
(B)
w
=
7
w = 7
w
=
7
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What value of
w
w
w
is a solution to this equation?
\newline
w
+
17
=
20
w + 17 = 20
w
+
17
=
20
\newline
Choices:
\newline
(A)
w
=
2
w = 2
w
=
2
\newline
(B)
w
=
3
w = 3
w
=
3
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What value of
y
y
y
is a solution to this equation?
\newline
y
+
2
=
9
y + 2 = 9
y
+
2
=
9
\newline
Choices:
\newline
(A)
y
=
5
y = 5
y
=
5
\newline
(B)
y
=
7
y = 7
y
=
7
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What value of
w
w
w
is a solution to this equation?
\newline
10
w
=
100
10w = 100
10
w
=
100
\newline
Choices:
\newline
(A)
w
=
8
w = 8
w
=
8
\newline
(B)
w
=
10
w = 10
w
=
10
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