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Math Problems
Algebra 2
Evaluate expression when two complex numbers are given
If
Q
−
1
3
P
=
30
Q-\frac{1}{3} P=30
Q
−
3
1
P
=
30
, which of the following correctly gives
P
P
P
in terms of
Q
Q
Q
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Let
y
=
1
x
sin
(
x
)
y=\frac{1}{x} \sin (x)
y
=
x
1
sin
(
x
)
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
\newline
□
\square
□
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Simplify:
x
5
=
8
9
\dfrac{x}{5} = \dfrac{8}{9}
5
x
=
9
8
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if
f
(
x
)
=
2
tan
(
x
)
f(x) = 2^{\tan(x)}
f
(
x
)
=
2
t
a
n
(
x
)
then
f
′
(
π
4
)
f'(\frac{\pi}{4})
f
′
(
4
π
)
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Select the expressions that are equivalent to
6
(
6
y
)
6(6y)
6
(
6
y
)
.
\newline
Multi-select Choices:
\newline
(A)
6
(
5
y
+
y
)
6(5y + y)
6
(
5
y
+
y
)
\newline
(B)
36
y
36y
36
y
\newline
(C)
y
+
12
y + 12
y
+
12
\newline
(D)
(
6
y
)
6
(6y)6
(
6
y
)
6
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What is the value of
(
x
2
y
4
)
(\frac{x^{2}}{y^{4}})
(
y
4
x
2
)
when
\newline
x
=
8
x=8
x
=
8
and
y
=
2
y=2
y
=
2
?
\newline
◻
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What is the value of
x
6
+
y
2
x^{6}+y^{2}
x
6
+
y
2
when
x
=
1
x=1
x
=
1
and
y
=
9
y=9
y
=
9
?
\newline
□
\square
□
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Let
y
=
x
2
ln
(
x
)
y=x^{2} \ln (x)
y
=
x
2
ln
(
x
)
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
4
(
−
2
x
−
1
)
=
−
2
(
4
x
+
2
)
4(-2 x-1)=-2(4 x+2)
4
(
−
2
x
−
1
)
=
−
2
(
4
x
+
2
)
\newline
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2
θ
2 \theta
2
θ
, given
cos
θ
=
−
12
13
\cos \theta=\frac{-12}{13}
cos
θ
=
13
−
12
and
sin
θ
>
0
\sin \theta>0
sin
θ
>
0
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Question
3
3
3
\newline
Given that
−
6
≤
x
≤
3
-6 \leq x \leq 3
−
6
≤
x
≤
3
and
1
≤
y
≤
5
1 \leq y \leq 5
1
≤
y
≤
5
, find the greatest possible value of
x
2
+
y
2
x^{2}+y^{2}
x
2
+
y
2
.
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Determine whether or not the ordered pair is a solution to the equation
\newline
y
=
3
x
+
8
y=3 x+8
y
=
3
x
+
8
\newline
(a)
(
−
5
,
−
7
)
(-5,-7)
(
−
5
,
−
7
)
\newline
(b)
(
−
1
,
3
)
(-1,3)
(
−
1
,
3
)
\newline
(c)
(
1
3
,
g
)
\left(\frac{1}{3}, g\right)
(
3
1
,
g
)
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If
x
(
x
−
3
)
=
−
1
x(x-3)=-1
x
(
x
−
3
)
=
−
1
then the value of
x
3
(
x
3
−
18
)
x^{3}\left(x^{3}-18\right)
x
3
(
x
3
−
18
)
will be,
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Exercise: G.M.V.T. use generalized mean value theorem
\newline
1
<
e
x
−
1
ln
(
x
+
1
)
<
(
x
+
1
)
e
x
1<\frac{e^{x}-1}{\ln (x+1)}<(x+1) e^{x}
1
<
ln
(
x
+
1
)
e
x
−
1
<
(
x
+
1
)
e
x
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given that
x
y
=
5
xy = 5
x
y
=
5
and
x
+
y
=
7
x + y = 7
x
+
y
=
7
, find the value of
(
x
−
y
)
2
(x-y)^2
(
x
−
y
)
2
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x
2
+
3
x
−
a
x
−
2
=
x
+
5
\frac{x^{2}+3 x-a}{x-2}=x+5
x
−
2
x
2
+
3
x
−
a
=
x
+
5
\newline
Given the equation for all
x
≠
2
x \neq 2
x
=
2
, what is the value of
a
a
a
?
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Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
g
(
f
(
−
1
)
)
g(f(-1))
g
(
f
(
−
1
))
.
\newline
f
(
x
)
=
x
2
−
3
x
−
10
g
(
x
)
=
3
x
−
10
\begin{array}{l} f(x)=x^{2}-3 x-10 \\ g(x)=3 x-10 \end{array}
f
(
x
)
=
x
2
−
3
x
−
10
g
(
x
)
=
3
x
−
10
\newline
Answer:
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If
p
=
−
3
p=-3
p
=
−
3
and
q
=
5
q=5
q
=
5
, find the value of
p
2
−
q
2
p
−
p
3
p^{2}-q^{2} p-p^{3}
p
2
−
q
2
p
−
p
3
.
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Let
y
4
−
2
x
=
5
\text { Let } \mathrm{y}^{4}-2 \mathrm{x}=5
Let
y
4
−
2
x
=
5
\newline
What is the value of
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
at the point
(
−
2
,
1
)
(-2,1)
(
−
2
,
1
)
? Give an exact number.
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If
j
k
=
4
5
\dfrac{j}{k}=\dfrac{4}{5}
k
j
=
5
4
, Express
k
k
k
in terms of
j
j
j
?
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What is the value of the expression below when
y
=
4
y=4
y
=
4
?
\newline
6
y
2
+
10
y
−
5
6 y^{2}+10 y-5
6
y
2
+
10
y
−
5
\newline
Answer:
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Given
f
(
x
)
=
3
x
+
2
f(x)=\frac{3}{x+2}
f
(
x
)
=
x
+
2
3
, find
f
′
(
1
)
f^{\prime}(1)
f
′
(
1
)
using the definition of a derivative.
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Given that
tan
θ
=
1
3
\tan \theta = \frac{1}{3}
tan
θ
=
3
1
and
sin
θ
>
0
\sin \theta > 0
sin
θ
>
0
, what is
cos
θ
\cos \theta
cos
θ
?
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If
f
−
1
(
−
25
)
=
7
f^{-1}(-25) = 7
f
−
1
(
−
25
)
=
7
, then what is
f
(
7
)
f(7)
f
(
7
)
?
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
+
1
)
=
f
(
n
)
2
+
4
f(n+1)=f(n)^{2}+4
f
(
n
+
1
)
=
f
(
n
)
2
+
4
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
)
=
f
(
n
−
1
)
2
−
n
f(n)=f(n-1)^{2}-n
f
(
n
)
=
f
(
n
−
1
)
2
−
n
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
+
1
)
=
f
(
n
)
2
+
4
f(n+1)=f(n)^{2}+4
f
(
n
+
1
)
=
f
(
n
)
2
+
4
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
+
1
)
=
f
(
n
)
2
+
5
f(n+1)=f(n)^{2}+5
f
(
n
+
1
)
=
f
(
n
)
2
+
5
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
+
1
)
=
f
(
n
)
2
+
5
f(n+1)=f(n)^{2}+5
f
(
n
+
1
)
=
f
(
n
)
2
+
5
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
+
1
)
=
f
(
n
)
2
+
3
f(n+1)=f(n)^{2}+3
f
(
n
+
1
)
=
f
(
n
)
2
+
3
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
+
1
)
=
f
(
n
)
2
−
4
f(n+1)=f(n)^{2}-4
f
(
n
+
1
)
=
f
(
n
)
2
−
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
+
1
)
=
f
(
n
)
2
+
4
f(n+1)=f(n)^{2}+4
f
(
n
+
1
)
=
f
(
n
)
2
+
4
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
+
1
)
=
f
(
n
)
2
−
1
f(n+1)=f(n)^{2}-1
f
(
n
+
1
)
=
f
(
n
)
2
−
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
)
=
f
(
n
−
1
)
2
−
n
f(n)=f(n-1)^{2}-n
f
(
n
)
=
f
(
n
−
1
)
2
−
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
)
=
f
(
n
−
1
)
2
−
n
f(n)=f(n-1)^{2}-n
f
(
n
)
=
f
(
n
−
1
)
2
−
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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Example
4
4
4
Evaluate
lim
x
→
4
x
2
−
16
x
−
4
\lim _{x \rightarrow 4} \frac{x^{2}-16}{x-4}
lim
x
→
4
x
−
4
x
2
−
16
.
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The functions
f
(
x
)
=
8
(
2
5
)
x
f(x)=8\left(\frac{2}{5}\right)^{x}
f
(
x
)
=
8
(
5
2
)
x
and
g
(
x
)
=
8
(
b
)
x
g(x)=8(b)^{x}
g
(
x
)
=
8
(
b
)
x
are graphed in the
y
y
y
-plane. For what value of
b
b
b
would the graphs of functions
f
f
f
and
g
g
g
be symmetric with respect to the
y
y
y
-axis?
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Given
f
(
x
)
=
−
x
2
+
10
f(x)=-x^{2}+10
f
(
x
)
=
−
x
2
+
10
, find
f
(
−
8
)
f(-8)
f
(
−
8
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
+
17
f(x)=-x^{2}+17
f
(
x
)
=
−
x
2
+
17
, find
f
(
−
3
)
f(-3)
f
(
−
3
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
−
9
x
+
19
f(x)=-x^{2}-9 x+19
f
(
x
)
=
−
x
2
−
9
x
+
19
, find
f
(
−
4
)
f(-4)
f
(
−
4
)
\newline
Answer:
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Given
f
(
x
)
=
−
3
x
2
−
8
f(x)=-3 x^{2}-8
f
(
x
)
=
−
3
x
2
−
8
, find
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
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Given
f
(
x
)
=
−
4
x
2
−
5
f(x)=-4 x^{2}-5
f
(
x
)
=
−
4
x
2
−
5
, find
f
(
−
7
)
f(-7)
f
(
−
7
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
f(x)=-x^{2}
f
(
x
)
=
−
x
2
, find
f
(
−
4
)
f(-4)
f
(
−
4
)
\newline
Answer:
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Given
f
(
x
)
=
−
2
x
2
−
6
x
−
6
f(x)=-2 x^{2}-6 x-6
f
(
x
)
=
−
2
x
2
−
6
x
−
6
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
\newline
Answer:
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Given
f
(
x
)
=
−
4
x
2
+
x
f(x)=-4 x^{2}+x
f
(
x
)
=
−
4
x
2
+
x
, find
f
(
−
2
)
f(-2)
f
(
−
2
)
\newline
Answer:
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If
f
(
1
)
=
3
f(1)=3
f
(
1
)
=
3
and
f
(
n
)
=
f
(
n
−
1
)
2
−
1
f(n)=f(n-1)^{2}-1
f
(
n
)
=
f
(
n
−
1
)
2
−
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
)
=
f
(
n
−
1
)
2
−
3
f(n)=f(n-1)^{2}-3
f
(
n
)
=
f
(
n
−
1
)
2
−
3
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
3
f(1)=3
f
(
1
)
=
3
and
f
(
n
)
=
f
(
n
−
1
)
2
+
5
f(n)=f(n-1)^{2}+5
f
(
n
)
=
f
(
n
−
1
)
2
+
5
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
)
=
f
(
n
−
1
)
2
−
5
f(n)=f(n-1)^{2}-5
f
(
n
)
=
f
(
n
−
1
)
2
−
5
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
)
=
f
(
n
−
1
)
2
−
1
f(n)=f(n-1)^{2}-1
f
(
n
)
=
f
(
n
−
1
)
2
−
1
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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