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Math Problems
Algebra 2
Transformations of functions
Evalutate
(
h
∘
g
)
(
−
6
)
(h \circ g)(-6)
(
h
∘
g
)
(
−
6
)
\newline
g
(
b
)
=
5
b
−
9
g(b) =5b-9
g
(
b
)
=
5
b
−
9
\newline
h
(
b
)
=
(
b
−
1
)
2
h(b) = (b-1)^{2}
h
(
b
)
=
(
b
−
1
)
2
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Which of these are equal to
8
8
8
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
−
40
5
-\frac{40}{5}
−
5
40
\newline
(B)
−
40
−
5
-\frac{40}{-5}
−
−
5
40
\newline
(C)
40
5
\frac{40}{5}
5
40
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Which polynomial represents the sum below?
\newline
\space
\space
\space
\space
\space
3
x
2
+
4
x
+
3
3x^{2}+4x+3
3
x
2
+
4
x
+
3
\newline
+
+
+
\space
3
x
2
+
6
x
3x^{2}+6x
3
x
2
+
6
x
\newline
_____________________
\newline
\newline
A.
9
x
2
+
10
x
+
3
9x^{2}+10x+3
9
x
2
+
10
x
+
3
\newline
B.
6
x
2
+
24
x
+
3
6x^{2}+24x+3
6
x
2
+
24
x
+
3
\newline
C.
6
x
2
+
10
x
+
3
6x^{2}+10x+3
6
x
2
+
10
x
+
3
\newline
D.
9
x
2
+
24
x
+
3
9x^{2}+24x+3
9
x
2
+
24
x
+
3
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∠
1
\angle 1
∠1
and
∠
2
\angle 2
∠2
are supplementary angles. If
m
∠
1
=
(
4
x
−
16
)
∘
\mathrm{m} \angle 1=(4 x-16)^{\circ}
m
∠1
=
(
4
x
−
16
)
∘
and
m
∠
2
=
(
x
+
1
)
∘
\mathrm{m} \angle 2=(x+1)^{\circ}
m
∠2
=
(
x
+
1
)
∘
, then find the measure of
∠
2
\angle 2
∠2
.
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Find the common ratio of the geometric sequence
{
a
n
}
n
=
1
∞
\left\{a_{n}\right\}_{n=1}^{\infty}
{
a
n
}
n
=
1
∞
given that:
\newline
a
2
=
−
1
4
a
6
=
−
12
2
/
3
\begin{array}{ll} a_{2}=-\frac{1}{4} \\ a_{6}=-\frac{12}{2 / 3}\end{array}
a
2
=
−
4
1
a
6
=
−
2/3
12
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Given
f
(
x
)
=
−
x
+
3
f(x)=-x+3
f
(
x
)
=
−
x
+
3
and
g
(
x
)
=
1
2
x
2
−
1
g(x)=\frac{1}{2} x^{2}-1
g
(
x
)
=
2
1
x
2
−
1
, which is a solution to
f
(
x
)
=
g
(
x
)
f(x)=g(x)
f
(
x
)
=
g
(
x
)
\newline
A)
−
2
-2
−
2
\newline
B)
−
1
-1
−
1
\newline
C)
1
1
1
\newline
D)
2
2
2
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Show that
H
=
(
x
,
y
,
z
)
∈
R
3
∣
x
+
2
y
=
0
\mathrm{H}=(x, y, z) \in \mathbb{R}^{3} \mid x+2 y=0
H
=
(
x
,
y
,
z
)
∈
R
3
∣
x
+
2
y
=
0
is a subspace of
R
3
\mathbb{R}^{3}
R
3
.
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20
−
2
20-2
20
−
2
=
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Consider the function
f
(
x
)
=
−
1
3
(
x
−
2
)
2
+
1
f(x)=-\frac{1}{3}(x-2)^{2}+1
f
(
x
)
=
−
3
1
(
x
−
2
)
2
+
1
. Algebraically determine which of the following are the zeros for
f
(
x
)
f(x)
f
(
x
)
. Select all correct answers below.
\newline
(A)
0
0
0
\newline
(B)
3
+
2
3+\sqrt{2}
3
+
2
\newline
(C)
4
4
4
\newline
(D)
2
+
3
2+\sqrt{3}
2
+
3
\newline
(E)
3
−
2
3-\sqrt{2}
3
−
2
\newline
(F)
2
−
3
2-\sqrt{3}
2
−
3
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Twice one number added to three times another number equals
−
3
-3
−
3
. If the first number is tripled and subtracted from
8
8
8
and the result is divided by
2
2
2
, then the second number is obtained. Find the two numbers.
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Twice one number added to thee limes another number equals
3
3
3
. If the firat number is tripled and subtracted from
8
8
8
and the result is divided by
2
2
2
, then the second number is obtained. Find the two numbers.
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Find the derivative of
−
7
x
2
y
4
−
4
x
y
3
=
x
+
3
-7 x^{2} y^{4}-4 x y^{3}=x+3
−
7
x
2
y
4
−
4
x
y
3
=
x
+
3
using implicit differentiation.
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If the product of
t
2
+
k
t
−
5
t^{2}+kt-5
t
2
+
k
t
−
5
and
2
t
−
3
2t-3
2
t
−
3
is
2
t
3
−
11
t
2
+
2
t
+
15
2t^{3}-11t^{2}+2t+15
2
t
3
−
11
t
2
+
2
t
+
15
, then what is the value of
k
k
k
?
\newline
A.
−
5
-5
−
5
\newline
B.
−
4
-4
−
4
\newline
C.
2
2
2
\newline
D.
3
3
3
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What is the
x
x
x
-intercept of the graph of
y
=
(
x
−
5
)
2
y=(x-5)^{2}
y
=
(
x
−
5
)
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
25
-25
−
25
\newline
(B)
−
5
-5
−
5
\newline
(C)
5
5
5
\newline
(D)
25
25
25
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If
f
(
x
)
=
−
x
2
−
2
7
x
f(x)=\frac{-x^{2}-2}{7 x}
f
(
x
)
=
7
x
−
x
2
−
2
, what is the value of
f
(
8
)
f(8)
f
(
8
)
, to the nearest tenth (if necessary)?
\newline
Answer:
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What is the discriminant of the quadratic equation
3
x
2
−
3
x
−
7
=
0
3 x^{2}-3 x-7=0
3
x
2
−
3
x
−
7
=
0
?
\newline
93
93
93
\newline
−
75
-75
−
75
\newline
−
93
-93
−
93
\newline
75
75
75
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What is the discriminant of the quadratic equation
5
x
2
−
8
x
+
9
=
0
5 x^{2}-8 x+9=0
5
x
2
−
8
x
+
9
=
0
?
\newline
−
244
-244
−
244
\newline
244
244
244
\newline
116
116
116
\newline
−
116
-116
−
116
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What is the discriminant of the quadratic equation
4
x
2
−
3
x
−
5
=
0
4 x^{2}-3 x-5=0
4
x
2
−
3
x
−
5
=
0
?
\newline
−
71
-71
−
71
\newline
−
89
-89
−
89
\newline
89
89
89
\newline
71
71
71
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What is the discriminant of the quadratic equation
2
x
2
−
9
x
−
8
=
0
2 x^{2}-9 x-8=0
2
x
2
−
9
x
−
8
=
0
?
\newline
−
17
-17
−
17
\newline
145
145
145
\newline
17
17
17
\newline
−
145
-145
−
145
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What is the discriminant of the quadratic equation
−
x
2
+
8
x
−
8
=
0
-x^{2}+8 x-8=0
−
x
2
+
8
x
−
8
=
0
?
\newline
32
32
32
\newline
96
96
96
\newline
−
96
-96
−
96
\newline
−
32
-32
−
32
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What is the discriminant of the quadratic equation
−
5
x
2
−
6
x
−
9
=
0
-5 x^{2}-6 x-9=0
−
5
x
2
−
6
x
−
9
=
0
?
\newline
144
144
144
\newline
216
216
216
\newline
−
144
-144
−
144
\newline
−
216
-216
−
216
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For the following quadratic equation, find the discriminant.
\newline
5
x
2
−
78
x
+
471
=
−
8
x
−
4
5 x^{2}-78 x+471=-8 x-4
5
x
2
−
78
x
+
471
=
−
8
x
−
4
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
11
x
2
+
90
x
−
160
=
−
6
x
2
-11 x^{2}+90 x-160=-6 x^{2}
−
11
x
2
+
90
x
−
160
=
−
6
x
2
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
6
x
2
−
18
x
+
102
=
−
7
x
2
+
2
x
+
2
-6 x^{2}-18 x+102=-7 x^{2}+2 x+2
−
6
x
2
−
18
x
+
102
=
−
7
x
2
+
2
x
+
2
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
7
x
2
+
54
x
−
231
=
−
4
x
2
-7 x^{2}+54 x-231=-4 x^{2}
−
7
x
2
+
54
x
−
231
=
−
4
x
2
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
6
x
2
−
8
x
+
29
=
−
7
x
2
−
4
-6 x^{2}-8 x+29=-7 x^{2}-4
−
6
x
2
−
8
x
+
29
=
−
7
x
2
−
4
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
7
x
2
+
32
x
−
108
=
−
4
x
2
−
4
x
-7 x^{2}+32 x-108=-4 x^{2}-4 x
−
7
x
2
+
32
x
−
108
=
−
4
x
2
−
4
x
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
12
x
2
−
16
x
−
16
=
8
x
2
12 x^{2}-16 x-16=8 x^{2}
12
x
2
−
16
x
−
16
=
8
x
2
\newline
Answer:
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What is the discriminant of the quadratic equation
−
7
x
2
−
2
x
−
1
=
0
-7 x^{2}-2 x-1=0
−
7
x
2
−
2
x
−
1
=
0
?
\newline
−
24
-24
−
24
\newline
−
32
-32
−
32
\newline
24
24
24
\newline
32
32
32
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What is the discriminant of the quadratic equation
x
2
−
6
x
−
8
=
0
x^{2}-6 x-8=0
x
2
−
6
x
−
8
=
0
?
\newline
4
4
4
\newline
−
4
-4
−
4
\newline
−
68
-68
−
68
\newline
68
68
68
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What is the discriminant of the quadratic equation
7
x
2
−
7
x
−
8
=
0
7 x^{2}-7 x-8=0
7
x
2
−
7
x
−
8
=
0
?
\newline
273
273
273
\newline
−
175
-175
−
175
\newline
175
175
175
\newline
−
273
-273
−
273
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What is the discriminant of the quadratic equation
7
x
2
−
9
x
−
2
=
0
7 x^{2}-9 x-2=0
7
x
2
−
9
x
−
2
=
0
?
\newline
25
25
25
\newline
137
137
137
\newline
−
137
-137
−
137
\newline
−
25
-25
−
25
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For the following quadratic equation, find the discriminant.
\newline
−
6
x
2
−
12
x
−
3
=
−
5
x
2
−
4
x
-6 x^{2}-12 x-3=-5 x^{2}-4 x
−
6
x
2
−
12
x
−
3
=
−
5
x
2
−
4
x
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
6
x
2
+
20
x
+
36
=
−
7
x
2
-6 x^{2}+20 x+36=-7 x^{2}
−
6
x
2
+
20
x
+
36
=
−
7
x
2
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
4
x
2
+
10
x
−
18
=
−
3
x
2
+
7
-4 x^{2}+10 x-18=-3 x^{2}+7
−
4
x
2
+
10
x
−
18
=
−
3
x
2
+
7
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
9
x
2
−
70
x
−
245
=
−
4
x
2
-9 x^{2}-70 x-245=-4 x^{2}
−
9
x
2
−
70
x
−
245
=
−
4
x
2
\newline
Answer:
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Factor completely:
\newline
(
5
x
−
4
)
(
2
x
+
3
)
−
(
2
x
+
3
)
2
(
4
x
−
5
)
(5 x-4)(2 x+3)-(2 x+3)^{2}(4 x-5)
(
5
x
−
4
)
(
2
x
+
3
)
−
(
2
x
+
3
)
2
(
4
x
−
5
)
\newline
Answer:
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Factor completely:
\newline
x
2
(
5
x
−
6
)
−
12
x
(
5
x
−
6
)
+
20
(
5
x
−
6
)
x^{2}(5 x-6)-12 x(5 x-6)+20(5 x-6)
x
2
(
5
x
−
6
)
−
12
x
(
5
x
−
6
)
+
20
(
5
x
−
6
)
\newline
Answer:
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Factor completely:
\newline
(
2
x
+
3
)
4
+
(
2
x
+
3
)
3
(2 x+3)^{4}+(2 x+3)^{3}
(
2
x
+
3
)
4
+
(
2
x
+
3
)
3
\newline
Answer:
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Factor completely:
\newline
(
2
x
−
1
)
5
−
6
(
2
x
−
1
)
4
(2 x-1)^{5}-6(2 x-1)^{4}
(
2
x
−
1
)
5
−
6
(
2
x
−
1
)
4
\newline
Answer:
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The graph of
g
(
x
)
=
−
1
2
(
x
+
3
)
2
−
4
g(x)=-\frac{1}{2}(x+3)^{2}-4
g
(
x
)
=
−
2
1
(
x
+
3
)
2
−
4
is translated
4
4
4
units right. What is the value of
h
h
h
when the equation of the transformed graph is written in vertex form?
\newline
(A)
−
7
-7
−
7
\newline
(B)
1
1
1
\newline
(C)
−
3
-3
−
3
\newline
(D)
4
4
4
\newline
(E)
−
1
-1
−
1
\newline
(F)
7
7
7
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If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
(
a
n
−
1
)
2
+
1
a_{n}=\left(a_{n-1}\right)^{2}+1
a
n
=
(
a
n
−
1
)
2
+
1
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
+
1
=
(
a
n
)
2
−
5
a_{n+1}=\left(a_{n}\right)^{2}-5
a
n
+
1
=
(
a
n
)
2
−
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
+
1
=
(
a
n
)
2
−
1
a_{n+1}=\left(a_{n}\right)^{2}-1
a
n
+
1
=
(
a
n
)
2
−
1
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
+
1
=
(
a
n
)
2
−
2
a_{n+1}=\left(a_{n}\right)^{2}-2
a
n
+
1
=
(
a
n
)
2
−
2
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
+
1
=
(
a
n
)
2
−
1
a_{n+1}=\left(a_{n}\right)^{2}-1
a
n
+
1
=
(
a
n
)
2
−
1
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
+
1
=
(
a
n
)
2
−
2
a_{n+1}=\left(a_{n}\right)^{2}-2
a
n
+
1
=
(
a
n
)
2
−
2
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
1
a_{1}=1
a
1
=
1
and
a
n
+
1
=
(
a
n
)
2
−
1
a_{n+1}=\left(a_{n}\right)^{2}-1
a
n
+
1
=
(
a
n
)
2
−
1
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
+
1
=
(
a
n
)
2
−
4
a_{n+1}=\left(a_{n}\right)^{2}-4
a
n
+
1
=
(
a
n
)
2
−
4
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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Find the
y
y
y
-coordinate of the
y
y
y
-intercept of the polynomial function defined below.
\newline
f
(
x
)
=
−
x
(
5
x
+
3
)
(
x
−
4
)
2
f(x)=-x(5 x+3)(x-4)^{2}
f
(
x
)
=
−
x
(
5
x
+
3
)
(
x
−
4
)
2
\newline
Answer:
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1
2
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