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Math Problems
Algebra 2
Evaluate expression when two complex numbers are given
1
1
1
-) Evaluate lom
+
n
2
4
+\frac{n^{2}}{4}
+
4
n
2
When
m
=
5
m=5
m
=
5
and
n
=
4
n=4
n
=
4
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2
2
2
) If
sin
A
=
3
5
\sin A=\frac{3}{5}
sin
A
=
5
3
, calculate
cos
A
\cos A
cos
A
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The graph of
y
=
1
2
(
y=\frac{1}{2}(
y
=
2
1
(
is shown. Based on the equation and the graph, which of the following statements is true?
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If
x
+
y
=
−
4
x+y = -4
x
+
y
=
−
4
and
x
−
y
=
2
x-y=2
x
−
y
=
2
, what is the value of
(
x
+
y
)
(
x
2
−
y
2
)
(x+y)(x^2-y^2)
(
x
+
y
)
(
x
2
−
y
2
)
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What is the value of
x
(
3
)
×
y
(
4
)
x(3) \times y(4)
x
(
3
)
×
y
(
4
)
when
x
=
3
x=3
x
=
3
and
y
=
0
y=0
y
=
0
?
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4
4
4
,
23
23
23
May
\newline
Infinite limits: alsebraic
\newline
Let
g
(
x
)
=
x
ln
(
x
−
2
)
g(x)=\frac{x}{\ln (x-2)}
g
(
x
)
=
l
n
(
x
−
2
)
x
\newline
Select the correct description of the one-sided limits of
g
g
g
at
x
=
3
x=3
x
=
3
.
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j
=
m
c
⋅
78
j=\frac{m}{c} \cdot 78
j
=
c
m
⋅
78
\newline
Which of the following equations correctly expresses
c
c
c
in terms of
j
j
j
and
m
m
m
?
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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
)
=
3
x
2
+
2
f(x)=\frac{3}{x^{2}+2}
f
(
x
)
=
x
2
+
2
3
, what is
f
(
3
)
f(3)
f
(
3
)
? What is
f
(
p
2
)
f\left(p^{2}\right)
f
(
p
2
)
?
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Let
g
g
g
be a differentiable function such that
g
(
2
)
=
e
2
g(2)=e^{2}
g
(
2
)
=
e
2
and
g
′
(
x
)
=
e
sin
(
x
2
)
g^{\prime}(x)=e^{\sin \left(x^{2}\right)}
g
′
(
x
)
=
e
s
i
n
(
x
2
)
. What is the value of
g
(
7
)
g(7)
g
(
7
)
pts.
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x
−
4
=
−
1.11
\dfrac{x}{-4}=-1.11
−
4
x
=
−
1.11
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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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6
6
6
. If
x
−
log
5
(
1000
)
x-\log _{5}(1000)
x
−
lo
g
5
(
1000
)
and
y
−
log
7
(
2058
)
y-\log _{7}(2058)
y
−
lo
g
7
(
2058
)
then
\newline
(a)
x
>
y
x>y
x
>
y
\newline
(b)
x
<
y
x<y
x
<
y
\newline
(c)
x
−
y
x-y
x
−
y
\newline
(d) None of these
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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
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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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Given
sin
(
x
y
3
)
=
y
3
\sin \left(x y^{3}\right)=y^{3}
sin
(
x
y
3
)
=
y
3
, 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 Attempt
1
1
1
out of
2
2
2
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5
5
5
.
0.6
+
0.
7
‾
+
0.3
7
‾
0.6+0 . \overline{7}+0.3 \overline{7}
0.6
+
0.
7
+
0.3
7
in form of
p
q
\frac{p}{q}
q
p
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If
h
(
x
5
)
=
x
2
h\left(\frac{x}{5}\right)=x^{2}
h
(
5
x
)
=
x
2
, what is the value of
h
(
2
)
?
h(2) ?
h
(
2
)?
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Given:
sin
θ
=
−
1
4
\sin \theta=-\frac{1}{4}
sin
θ
=
−
4
1
and
cos
θ
>
0
\cos \theta>0
cos
θ
>
0
. Find
tan
θ
\tan \theta
tan
θ
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1
1
1
\newline
If
32
x
5
y
6
\sqrt{32 x^{5} y^{6}}
32
x
5
y
6
is equal to
a
x
b
y
c
d
x
a x^{b} y^{c} \sqrt{d x}
a
x
b
y
c
d
x
, what is the value of
a
c
a c
a
c
?
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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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Find
d
z
d
t
\frac{\mathrm{dz}}{\mathrm{dt}}
dt
dz
given
z
=
x
y
2
\mathrm{z}=x \mathrm{y}^{2}
z
=
x
y
2
and
x
=
(
t
−
1
)
\mathrm{x}=(\mathrm{t}-1)
x
=
(
t
−
1
)
and
y
=
1
(
t
−
1
)
2
y=\frac{1}{(t-1)^{2}}
y
=
(
t
−
1
)
2
1
.
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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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le of
a
a
a
in these diagrams.
\newline
b
\newline
C
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Two-variable equations: Quiz
3
3
3
\newline
Graph
y
=
−
3
2
x
−
3
y=-\frac{3}{2} x-3
y
=
−
2
3
x
−
3
.
\newline
Check
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9
9
9
Given that
x
−
y
=
5
x-y=5
x
−
y
=
5
and
x
y
=
−
6
1
2
x y=-6 \frac{1}{2}
x
y
=
−
6
2
1
, find the value of
x
2
+
y
2
x^{2}+y^{2}
x
2
+
y
2
.
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2
2
2
. If
A
E
=
2
,
C
E
=
9
A E=2, C E=9
A
E
=
2
,
CE
=
9
, and
B
E
=
3
B E=3
BE
=
3
, find the length of
D
E
‾
\overline{D E}
D
E
.
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PROBLEM
2
2
2
\newline
Reduce
x
3
−
3
x
2
4
x
2
−
5
x
\frac{x^{3}-3 x^{2}}{4 x^{2}-5 x}
4
x
2
−
5
x
x
3
−
3
x
2
to lowest terms.
\newline
for
x
≠
x \neq
x
=
\newline
Check
\newline
Explain
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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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If
1
5
h
+
25
=
d
\frac{1}{5} h+25=d
5
1
h
+
25
=
d
, which of the following expressions is equivalent to
h
h
h
?
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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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For Problems
3
3
3
−
10
-10
−
10
, simplify the expressic
\newline
3
3
3
.
15
,
000
(
1
+
0.1
)
3
15,000(1+0.1)^{3}
15
,
000
(
1
+
0.1
)
3
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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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Google Classroom
\newline
If
2
+
2
(
8347
−
4783
)
=
−
2
j
2+2(8347-4783)=-2 j
2
+
2
(
8347
−
4783
)
=
−
2
j
, then what is the value of
−
j
-j
−
j
?
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Example
16
16
16
.
5
5
5
\newline
Given that
R
=
2
,
d
=
4
R=2, d=4
R
=
2
,
d
=
4
and
L
=
16
L=16
L
=
16
, find the value of
K
K
K
, if
K
=
R
d
2
L
K=\frac{R d^{2}}{L}
K
=
L
R
d
2
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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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If
Q
−
1
3
P
=
30
Q-\dfrac{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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In the right triangle shown, the length of
A
C
‾
=
6
\overline{A C}=6
A
C
=
6
and the length of
B
C
‾
=
4
\overline{B C}=4
BC
=
4
. What is the length of
A
B
‾
\overline{A B}
A
B
?
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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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If
y
=
(
x
−
2
)
(
x
−
1
)
(
2
x
2
+
3
)
+
4
y=(x-2)(x-1)\left(2 x^{2}+3\right)+4
y
=
(
x
−
2
)
(
x
−
1
)
(
2
x
2
+
3
)
+
4
, what is the value of
y
y
y
when
x
=
1
x=1
x
=
1
?
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Evaluate:
\newline
48
x
y
48 x^{y}
48
x
y
for
x
=
2
x=2
x
=
2
and
y
=
−
3
y=-3
y
=
−
3
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1
2
3
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