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Math Problems
Algebra 2
Solve complex trigonomentric equations
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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x
2
+
6
x
+
9
=
0
x^{2}+6 x+9=0
x
2
+
6
x
+
9
=
0
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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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A)
12
12
12
\newline
B)
8
8
8
\newline
C)
15
15
15
\newline
D)
9
9
9
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5
5
5
. Se ha observado que en una carretera de salida de una gran ciudad la velocidad de los coches entre las
2
2
2
horas y las
6
6
6
horas de la tarde viene dada por:
V
=
t
3
−
15
t
2
+
72
t
+
8
V=t^{3}-15 t^{2}+72 t+8
V
=
t
3
−
15
t
2
+
72
t
+
8
para
t
∈
[
2
,
6
]
t \in[2,6]
t
∈
[
2
,
6
]
\newline
a. ¿A qué hora circulan los coches con mayor velocidad?
\newline
b. ¿A qué hora circulan los coches con menor velocidad?
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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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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
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
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
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
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
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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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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Solve for
x
x
x
:
\newline
4
⋅
3
5
x
−
5
=
72
4 \cdot 3^{5 x-5}=72
4
⋅
3
5
x
−
5
=
72
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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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13
13
13
.
m
∠
B
=
10
5
∘
,
b
=
23
,
a
=
14
\mathrm{m} \angle \mathrm{B}=105^{\circ}, \mathrm{b}=23, \mathrm{a}=14
m
∠
B
=
10
5
∘
,
b
=
23
,
a
=
14
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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
x
=
−
6
x=-6
x
=
−
6
\newline
x
=
−
1.8
x=-1.8
x
=
−
1.8
\newline
x
=
4
x=4
x
=
4
\newline
x
=
1.2
x=1.2
x
=
1.2
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f
(
x
)
=
9
x
2
−
60
x
+
80
f(x)=9x^{2}-60x+80
f
(
x
)
=
9
x
2
−
60
x
+
80
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What are the solutions to the equation
2
x
2
−
5
x
−
1
=
0
2 x^{2}-5 x-1=0
2
x
2
−
5
x
−
1
=
0
?
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j
2
−
17
j
+
72
=
0
j^{2}-17 j+72=0
j
2
−
17
j
+
72
=
0
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\begin{tabular}{c|c|c|c|c|c|c|c|}
\newline
\hline
E
E
E
&
H
H
H
&
G
G
G
&
K
K
K
&
I
I
I
&
M
M
M
&
L
L
L
&
L
L
L
\\
\newline
\hline
E
E
E
&
J
J
J
&
G
G
G
&
K
K
K
&
I
I
I
&
M
M
M
&
L
L
L
&
L
L
L
\\
\newline
\hline
J
J
J
&
J
J
J
&
G
G
G
&
K
K
K
&
I
I
I
&
M
M
M
&
L
L
L
&
L
L
L
\\
\newline
\hline
\newline
\end{tabular}
\newline
#
2
x
4
+
12
=
20
\begin{array}{c} \# 2 \\ \frac{x}{4}+12=20 \end{array}
#2
4
x
+
12
=
20
\newline
C)
G
G
G
4
4
4
\newline
D)
G
G
G
5
5
5
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ग)
\newline
x
2
+
3
x
+
21
=
22
x^{2}+3 x+21=22
x
2
+
3
x
+
21
=
22
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(
4
x
+
3
)
2
=
24
x
(4 x+3)^{2}=24 x
(
4
x
+
3
)
2
=
24
x
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x
2
+
12
x
+
32
=
(
x^{2}+12 x+32=(
x
2
+
12
x
+
32
=
(
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f
(
x
)
=
3
x
2
−
10
+
18
x
f(x)=3 x^{2}-10+18 x
f
(
x
)
=
3
x
2
−
10
+
18
x
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6
6
6
.
m
2
=
0
m^{2}=0
m
2
=
0
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5
5
5
)
x
4
−
13
x
2
+
40
x^{4}-13 x^{2}+40
x
4
−
13
x
2
+
40
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Solve by completing the square
\newline
5
x
2
+
3
x
−
4
=
0
5 x^{2}+3 x-4=0
5
x
2
+
3
x
−
4
=
0
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Solve by Finding the
\newline
9
9
9
)
x
2
=
49
x^{2}=49
x
2
=
49
\newline
x
=
7
x=7
x
=
7
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find the area of the figure bonded by
y
=
x
y=\sqrt{x}
y
=
x
,
y
=
x
−
2
y=x-2
y
=
x
−
2
,
y
=
0
y=0
y
=
0
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x
+
2
y
=
5
x + 2y = 5
x
+
2
y
=
5
3
x
−
y
=
1
3x - y = 1
3
x
−
y
=
1
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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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2
x
2
−
11
x
−
6
=
0
2 x^{2}-11 x-6=0
2
x
2
−
11
x
−
6
=
0
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x
2
+
α
⋅
x
+
β
=
0
x^{2}+\alpha \cdot x+\beta=0
x
2
+
α
⋅
x
+
β
=
0
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x
2
−
9
x
+
10
=
32
x^{2}-9 x+10=32
x
2
−
9
x
+
10
=
32
\newline
D.
6
x
(
x
−
8
)
=
29
6 x(x-8)=29
6
x
(
x
−
8
)
=
29
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Se
x
=
10
x=10
x
=
10
, então
1
(
x
−
4
)
=
1(x-4)=
1
(
x
−
4
)
=
□
\square
□
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Resolva para
p
p
p
:
\newline
−
4
p
−
6
=
34
p
=
?
\begin{array}{l} -4 p-6=34 \\ p=? \end{array}
−
4
p
−
6
=
34
p
=
?
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Resolva para
c
c
c
:
\newline
3
c
+
8
=
32
c
=
?
\begin{array}{l} 3 c+8=32 \\ c=? \end{array}
3
c
+
8
=
32
c
=
?
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1
1
1
. 已知集合
A
=
{
x
∣
x
−
1
⩽
2
}
⋅
B
=
{
y
∣
−
y
2
+
3
y
>
0
}
A=\{x \mid \sqrt{x-1} \leqslant 2\} \cdot B=\left\{y \mid-y^{2}+3 y>0\right\}
A
=
{
x
∣
x
−
1
⩽
2
}
⋅
B
=
{
y
∣
−
y
2
+
3
y
>
0
}
, 则
A
∩
B
=
A \cap B=
A
∩
B
=
\newline
C
3
\mathrm{C}_{3}
C
3
\newline
A.
8
8
8
\newline
B.
(
0.3
)
(0.3)
(
0.3
)
\newline
C.
(
0
,
5
]
(0,5]
(
0
,
5
]
\newline
D.
[
1
,
3
)
[1,3)
[
1
,
3
)
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24
24
24
.
75
g
3
=
147
g
75 g^{3}=147 g
75
g
3
=
147
g
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Which values of
x
x
x
are solutions of the equation
5
x
=
x
+
13
6
\frac{5}{x}=\frac{x+13}{6}
x
5
=
6
x
+
13
? Select all that apply.
\newline
A.
□
\square
□
−
15
-15
−
15
\newline
B.
□
\square
□
15
15
15
\newline
C.
□
\square
□
2
2
2
\newline
D.
□
\square
□
−
3
-3
−
3
\newline
E.
□
\square
□
−
10
-10
−
10
\newline
F.
□
\square
□
5
x
=
x
+
13
6
\frac{5}{x}=\frac{x+13}{6}
x
5
=
6
x
+
13
1
1
1
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1
1
1
)
x
2
+
x
−
2
=
0
x^{2}+x-2=0
x
2
+
x
−
2
=
0
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x
2
+
16
x
+
5
=
0
x^{2}+16 x+5=0
x
2
+
16
x
+
5
=
0
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10
w
2
+
45
w
=
7
10 w^{2}+45 w=7
10
w
2
+
45
w
=
7
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Solve
9
2
x
−
1
=
27
9^{2 x-1}=27
9
2
x
−
1
=
27
for
x
x
x
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\#
5
5
5
Solve
−
2
x
2
+
12
x
−
16
=
0
-2 x^{2}+12 x-16=0
−
2
x
2
+
12
x
−
16
=
0
by graphing.
\newline
Solutions:
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Which graph can be used to solve the equation
2
x
−
1
=
x
+
2
2^{x}-1=x+2
2
x
−
1
=
x
+
2
?
\newline
My Progress
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Solve each equation by takin
\newline
5
5
5
)
m
2
−
8
=
88
m^{2}-8=88
m
2
−
8
=
88
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8
8
8
Solve the equation
5
2
x
−
6
(
5
x
)
+
5
=
0
5^{2 x}-6\left(5^{x}\right)+5=0
5
2
x
−
6
(
5
x
)
+
5
=
0
.
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1
2
3
...
4
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