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Math Problems
Algebra 2
Composition of linear functions: find an equation
Let
m
+
p
=
23
m + p = 23
m
+
p
=
23
\newline
m
−
7
=
p
m - 7 = p
m
−
7
=
p
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Given the function
f
(
x
)
=
−
1
+
5
x
f(x)=-1+5 x
f
(
x
)
=
−
1
+
5
x
, then what is
−
3
f
(
x
)
-3 f(x)
−
3
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
5
x
−
1
f(x)=-5 x-1
f
(
x
)
=
−
5
x
−
1
, then what is
−
2
f
(
x
)
-2 f(x)
−
2
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Find
y
y
y
using substitution.
\newline
y
=
x
+
3
y=x+3
y
=
x
+
3
\newline
x
=
2
x=2
x
=
2
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Reduce to simplest form.
\newline
−
7
8
−
(
−
5
6
)
=
-\frac{7}{8}-\left(-\frac{5}{6}\right)=
−
8
7
−
(
−
6
5
)
=
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(
21
+
2
i
)
+
(
13
+
8
i
)
=
(21+2 i)+(13+8 i)=
(
21
+
2
i
)
+
(
13
+
8
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
8
−
10
i
)
−
(
−
16
+
2
i
)
=
(8-10 i)-(-16+2 i)=
(
8
−
10
i
)
−
(
−
16
+
2
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
3
+
4
i
)
−
(
6
−
10
i
)
=
(3+4 i)-(6-10 i)=
(
3
+
4
i
)
−
(
6
−
10
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
9
+
52
i
)
−
(
1
)
=
(9+52 i)-(1)=
(
9
+
52
i
)
−
(
1
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
12
)
−
(
23
+
13
i
)
=
(12)-(23+13 i)=
(
12
)
−
(
23
+
13
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
−
30
i
)
+
(
52
−
30
i
)
=
(-30 i)+(52-30 i)=
(
−
30
i
)
+
(
52
−
30
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
−
13
+
16
i
)
−
(
3
+
4
i
)
=
(-13+16 i)-(3+4 i)=
(
−
13
+
16
i
)
−
(
3
+
4
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
−
90
−
27
i
)
−
(
66
+
34
i
)
=
(-90-27 i)-(66+34 i)=
(
−
90
−
27
i
)
−
(
66
+
34
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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(
4
)
+
(
14
−
4
i
)
=
(4)+(14-4 i)=
(
4
)
+
(
14
−
4
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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What is
y
=
−
2
9
x
+
2
y=-\frac{2}{9} x+2
y
=
−
9
2
x
+
2
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
+
9
y
=
2
2 x+9 y=2
2
x
+
9
y
=
2
\newline
(B)
2
x
+
9
y
=
18
2 x+9 y=18
2
x
+
9
y
=
18
\newline
(C)
2
x
+
y
=
18
2 x+y=18
2
x
+
y
=
18
\newline
(D)
2
x
+
y
=
2
2 x+y=2
2
x
+
y
=
2
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What is
y
−
8
=
3
(
x
+
1
)
y-8=3(x+1)
y
−
8
=
3
(
x
+
1
)
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
x
+
y
=
11
-3 x+y=11
−
3
x
+
y
=
11
\newline
(B)
y
−
8
=
3
x
+
3
y-8=3 x+3
y
−
8
=
3
x
+
3
\newline
(C)
y
=
3
x
+
11
y=3 x+11
y
=
3
x
+
11
\newline
(D)
−
3
x
+
y
−
11
=
0
-3 x+y-11=0
−
3
x
+
y
−
11
=
0
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Find
(
r
∘
s
)
(
x
)
(r \circ s)(x)
(
r
∘
s
)
(
x
)
.
\newline
r(x) =
3
3
3
x
\newline
s(x) =
2
2
2
x +
5
5
5
\newline
Write your answer as a polynomial in simplest form.
\newline
(
r
∘
s
)
(
x
)
=
(r \circ s)(x) =
(
r
∘
s
)
(
x
)
=
____
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