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Math Problems
Algebra 2
Evaluate functions
If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
4
f
(
n
−
1
)
−
n
f(n)=4 f(n-1)-n
f
(
n
)
=
4
f
(
n
−
1
)
−
n
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
3
f(1)=3
f
(
1
)
=
3
and
f
(
n
)
=
n
f
(
n
−
1
)
+
2
f(n)=n f(n-1)+2
f
(
n
)
=
n
f
(
n
−
1
)
+
2
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
)
=
n
f
(
n
−
1
)
−
2
f(n)=n f(n-1)-2
f
(
n
)
=
n
f
(
n
−
1
)
−
2
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
10
f(1)=10
f
(
1
)
=
10
and
f
(
n
)
=
4
f
(
n
−
1
)
+
n
f(n)=4 f(n-1)+n
f
(
n
)
=
4
f
(
n
−
1
)
+
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
+
1
)
=
4
f
(
n
)
−
2
f(n+1)=4 f(n)-2
f
(
n
+
1
)
=
4
f
(
n
)
−
2
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
+
1
)
=
−
5
f
(
n
)
−
1
f(n+1)=-5 f(n)-1
f
(
n
+
1
)
=
−
5
f
(
n
)
−
1
then find the value of
f
(
3
)
f(3)
f
(
3
)
\newline
Answer:
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If
f
(
1
)
=
9
f(1)=9
f
(
1
)
=
9
and
f
(
n
+
1
)
=
−
5
f
(
n
)
−
1
f(n+1)=-5 f(n)-1
f
(
n
+
1
)
=
−
5
f
(
n
)
−
1
then find the value of
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
+
1
)
=
−
5
f
(
n
)
−
4
f(n+1)=-5 f(n)-4
f
(
n
+
1
)
=
−
5
f
(
n
)
−
4
then find the value of
f
(
5
)
f(5)
f
(
5
)
\newline
Answer:
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If
f
(
1
)
=
3
f(1)=3
f
(
1
)
=
3
and
f
(
n
+
1
)
=
−
5
f
(
n
)
+
1
f(n+1)=-5 f(n)+1
f
(
n
+
1
)
=
−
5
f
(
n
)
+
1
then find the value of
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
+
1
)
=
5
f
(
n
)
−
1
f(n+1)=5 f(n)-1
f
(
n
+
1
)
=
5
f
(
n
)
−
1
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
+
1
)
=
−
5
f
(
n
)
−
3
f(n+1)=-5 f(n)-3
f
(
n
+
1
)
=
−
5
f
(
n
)
−
3
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
7
f(1)=7
f
(
1
)
=
7
and
f
(
n
+
1
)
=
−
4
f
(
n
)
−
3
f(n+1)=-4 f(n)-3
f
(
n
+
1
)
=
−
4
f
(
n
)
−
3
then find the value of
f
(
5
)
f(5)
f
(
5
)
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
+
1
)
=
−
5
f
(
n
)
−
4
f(n+1)=-5 f(n)-4
f
(
n
+
1
)
=
−
5
f
(
n
)
−
4
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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Given that
f
(
x
)
=
x
+
4
,
g
(
x
)
=
−
3
x
f(x)=x+4, \quad g(x)=-3 x
f
(
x
)
=
x
+
4
,
g
(
x
)
=
−
3
x
and
h
(
x
)
=
f
(
x
+
2
)
−
2
g
(
x
)
h(x)=f(x+2)-2 g(x)
h
(
x
)
=
f
(
x
+
2
)
−
2
g
(
x
)
, then what is the value of
h
(
7
)
h(7)
h
(
7
)
?
\newline
Answer:
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Given that
f
(
x
)
=
x
−
4
,
g
(
x
)
=
4
x
f(x)=x-4, \quad g(x)=4 x
f
(
x
)
=
x
−
4
,
g
(
x
)
=
4
x
and
h
(
x
)
=
−
3
f
(
x
)
−
g
(
x
−
1
)
h(x)=-3 f(x)-g(x-1)
h
(
x
)
=
−
3
f
(
x
)
−
g
(
x
−
1
)
, then what is the value of
h
(
6
)
h(6)
h
(
6
)
?
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
n
f
(
n
−
1
)
−
4
f(n)=n f(n-1)-4
f
(
n
)
=
n
f
(
n
−
1
)
−
4
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
−
3
f
(
n
−
1
)
+
n
f(n)=-3 f(n-1)+n
f
(
n
)
=
−
3
f
(
n
−
1
)
+
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
−
3
f
(
n
−
1
)
+
n
f(n)=-3 f(n-1)+n
f
(
n
)
=
−
3
f
(
n
−
1
)
+
n
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
)
=
−
5
f
(
n
−
1
)
−
n
f(n)=-5 f(n-1)-n
f
(
n
)
=
−
5
f
(
n
−
1
)
−
n
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
7
f(1)=7
f
(
1
)
=
7
and
f
(
n
)
=
n
f
(
n
−
1
)
+
4
f(n)=n f(n-1)+4
f
(
n
)
=
n
f
(
n
−
1
)
+
4
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
4
f
(
n
−
1
)
+
n
f(n)=4 f(n-1)+n
f
(
n
)
=
4
f
(
n
−
1
)
+
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
)
=
n
f
(
n
−
1
)
+
1
f(n)=n f(n-1)+1
f
(
n
)
=
n
f
(
n
−
1
)
+
1
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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Given that
f
(
x
)
=
x
−
4
,
g
(
x
)
=
4
x
f(x)=x-4, \quad g(x)=4 x
f
(
x
)
=
x
−
4
,
g
(
x
)
=
4
x
and
h
(
x
)
=
3
f
(
x
)
−
g
(
x
+
3
)
h(x)=3 f(x)-g(x+3)
h
(
x
)
=
3
f
(
x
)
−
g
(
x
+
3
)
, then what is the value of
h
(
5
)
h(5)
h
(
5
)
?
\newline
Answer:
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You want to be able to withdraw
$
30
,
000
\$ 30,000
$30
,
000
each year for
20
20
20
years.
\newline
Your account earns
7
%
7 \%
7%
interest.
\newline
How much do you need in your account at the beginning?
\newline
Fill out the information given:
\newline
d
=
r
=
k
=
N
=
\begin{array}{l} d= \\ r= \\ k= \\ N= \end{array}
d
=
r
=
k
=
N
=
\newline
Find
P
0
P_{0}
P
0
.
\newline
P
0
=
P_{0}=
P
0
=
Get tutor help
If
f
(
1
)
=
3
f(1)=3
f
(
1
)
=
3
and
f
(
n
)
=
4
f
(
n
−
1
)
−
1
f(n)=4 f(n-1)-1
f
(
n
)
=
4
f
(
n
−
1
)
−
1
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
5
f
(
n
−
1
)
+
3
f(n)=5 f(n-1)+3
f
(
n
)
=
5
f
(
n
−
1
)
+
3
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
Get tutor help
If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
)
=
−
3
f
(
n
−
1
)
+
1
f(n)=-3 f(n-1)+1
f
(
n
)
=
−
3
f
(
n
−
1
)
+
1
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
)
=
−
2
f
(
n
−
1
)
+
1
f(n)=-2 f(n-1)+1
f
(
n
)
=
−
2
f
(
n
−
1
)
+
1
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
4
f
(
n
−
1
)
+
1
f(n)=4 f(n-1)+1
f
(
n
)
=
4
f
(
n
−
1
)
+
1
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
−
3
f
(
n
−
1
)
+
3
f(n)=-3 f(n-1)+3
f
(
n
)
=
−
3
f
(
n
−
1
)
+
3
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
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If
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
and
f
(
n
)
=
−
5
f
(
n
−
1
)
+
2
f(n)=-5 f(n-1)+2
f
(
n
)
=
−
5
f
(
n
−
1
)
+
2
then find the value of
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
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Let
g
(
t
)
=
(
t
+
2
)
(
t
−
3
)
g(t)=(t+2)(t-3)
g
(
t
)
=
(
t
+
2
)
(
t
−
3
)
and
h
(
t
)
=
(
t
−
3
)
h(t)=(t-3)
h
(
t
)
=
(
t
−
3
)
. Find
(
h
g
)
(
t
)
\left(\frac{h}{g}\right)(t)
(
g
h
)
(
t
)
Get tutor help
If
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
+
1
=
4
a
n
−
4
a_{n+1}=4 a_{n}-4
a
n
+
1
=
4
a
n
−
4
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
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Given the function
y
=
−
5
4
x
5
y=-\frac{5}{4 \sqrt[5]{x}}
y
=
−
4
5
x
5
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
. Express your answer in radical form without using negative exponents, simplifying all fractions.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Solve for
x
\mathrm{x}
x
.
\newline
12
x
=
−
2
5
\frac{12}{x}=-\frac{2}{5}
x
12
=
−
5
2
\newline
Answer:
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Solve for
x
\mathrm{x}
x
in simplest form.
\newline
1
=
1
3
(
10
x
+
12
)
1=\frac{1}{3}(10 x+12)
1
=
3
1
(
10
x
+
12
)
\newline
Answer:
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If
−
2
x
−
5
y
2
+
4
+
5
x
3
=
0
-2 x-5 y^{2}+4+5 x^{3}=0
−
2
x
−
5
y
2
+
4
+
5
x
3
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
3
y
2
+
x
2
y
+
3
=
3
x
3 y^{2}+x^{2} y+3=3 x
3
y
2
+
x
2
y
+
3
=
3
x
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
3
−
5
y
+
x
y
=
0
3-5 y+x y=0
3
−
5
y
+
x
y
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
3
x
+
x
y
+
5
y
=
0
3 x+x y+5 y=0
3
x
+
x
y
+
5
y
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
0
=
5
x
2
+
5
y
+
x
3
y
0=5 x^{2}+5 y+x^{3} y
0
=
5
x
2
+
5
y
+
x
3
y
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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If
−
2
y
−
1
−
x
=
−
x
y
-2 y-1-x=-x y
−
2
y
−
1
−
x
=
−
x
y
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
x
y
+
2
x
=
−
2
+
2
y
x y+2 x=-2+2 y
x
y
+
2
x
=
−
2
+
2
y
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
2
y
3
−
x
3
=
5
x
y
-2 y^{3}-x^{3}=5 x y
−
2
y
3
−
x
3
=
5
x
y
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
3
+
4
x
2
=
4
y
3
+
3
y
+
5
y
2
-3+4 x^{2}=4 y^{3}+3 y+5 y^{2}
−
3
+
4
x
2
=
4
y
3
+
3
y
+
5
y
2
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
If
−
4
y
2
+
y
3
+
2
+
5
x
3
=
0
-4 y^{2}+y^{3}+2+5 x^{3}=0
−
4
y
2
+
y
3
+
2
+
5
x
3
=
0
then find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in terms of
x
x
x
and
y
y
y
.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Find an explicit formula for the arithmetic sequence
\newline
10
,
−
10
,
−
30
,
−
50
,
…
.
10,-10,-30,-50,\dots.
10
,
−
10
,
−
30
,
−
50
,
…
.
\newline
Note: the first term should be
c
(
1
)
.
c(1).
c
(
1
)
.
\newline
c
(
n
)
=
□
c(n)=\square
c
(
n
)
=
□
Get tutor help
Find
d
d
x
(
−
sin
x
+
1
)
\frac{d}{d x}(-\sin x+1)
d
x
d
(
−
sin
x
+
1
)
\newline
Answer:
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Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
5
3
16
)
\ln \left(\frac{\sqrt[3]{5}}{16}\right)
ln
(
16
3
5
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
Get tutor help
Given the substitutions
ln
2
=
a
,
ln
3
=
b
\ln 2=a, \ln 3=b
ln
2
=
a
,
ln
3
=
b
, and
ln
5
=
c
\ln 5=c
ln
5
=
c
, find the value of
ln
(
2
4
3
)
\ln \left(\frac{\sqrt[4]{2}}{3}\right)
ln
(
3
4
2
)
in terms of
a
,
b
a, b
a
,
b
, and
c
c
c
.
\newline
Answer:
Get tutor help
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