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Math Problems
Algebra 2
Evaluate expression when two complex numbers are given
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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#
6
6
6
* Triangle
A
B
C
ABC
A
BC
is shown. What is
tan
(
A
)
\tan(A)
tan
(
A
)
? Your answer #
7
7
7
.
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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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If
A
E
=
2
AE=2
A
E
=
2
,
C
E
=
9
CE=9
CE
=
9
, and
B
E
=
3
BE=3
BE
=
3
, find the length of
D
E
‾
\overline{DE}
D
E
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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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Solve the Poisson's equation \(\newlineabla^{2} f=x y \) and
f
=
2
f=2
f
=
2
on boundary by assuming square domain
0
≤
x
≤
3
0 \leq x \leq 3
0
≤
x
≤
3
and
0
≤
y
≤
3
0 \leq y \leq 3
0
≤
y
≤
3
and
h
=
1
h=1
h
=
1
.
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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
(iiven 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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Example
1
1
1
. If the first term of an AP is
67
67
67
and the common difference is
−
13
-13
−
13
, find the sum of the first
20
20
20
terms.
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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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Q
5
5
5
\newline
If
4
x
+
4
y
=
9
4 x+4 y=9
4
x
+
4
y
=
9
and
x
2
−
y
2
=
−
6
16
x^{2}-y^{2}=-\frac{6}{16}
x
2
−
y
2
=
−
16
6
, what is the value of
2
x
−
2
y
?
2 x-2 y ?
2
x
−
2
y
?
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(
x
−
10
)
(
x
+
1
)
\left(x - 10\right)\left(x + 1\right)
(
x
−
10
)
(
x
+
1
)
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Let
f
(
x
)
=
1
x
4
+
5
f(x)=\frac{1}{x^4+5}
f
(
x
)
=
x
4
+
5
1
and
g
(
x
)
=
1
x
2
+
1
g(x) = \frac{1}{x^2+1}
g
(
x
)
=
x
2
+
1
1
. What is the value of
f
(
1
−
g
(
0
)
)
f(1-g(0))
f
(
1
−
g
(
0
))
?
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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
(
x
)
=
3
x
−
9
f(x)=3x-9
f
(
x
)
=
3
x
−
9
, what is
f
−
1
(
12
)
f^{-1}(12)
f
−
1
(
12
)
?
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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
)
=
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
)
=
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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2
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