Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Evaluate expression when a complex numbers and a variable term is given
1
1
1
. Let
a
,
b
>
0
a, b>0
a
,
b
>
0
satisfy
a
3
+
b
3
=
a
−
b
a^{3}+b^{3}=a-b
a
3
+
b
3
=
a
−
b
, then
\newline
(a)
a
2
+
b
2
=
1
a^{2}+b^{2}=1
a
2
+
b
2
=
1
\newline
(b)
a
2
+
a
b
+
b
2
<
1
a^{2}+a b+b^{2}<1
a
2
+
ab
+
b
2
<
1
\newline
(c)
a
2
+
b
2
>
1
a^{2}+b^{2}>1
a
2
+
b
2
>
1
\newline
(d) none of these
Get tutor help
Let
\newline
u
=
(
5
,
−
12
)
u=(5,-12)
u
=
(
5
,
−
12
)
and
\newline
c
=
−
3
c=-3
c
=
−
3
. What is
\newline
∣
∣
c
u
∣
∣
||cu||
∣∣
c
u
∣∣
?
\newline
51
51
51
\newline
−
39
-39
−
39
\newline
21
21
21
\newline
39
39
39
Get tutor help
Which expression is equivalent to
3
m
+
9
m
3m + 9m
3
m
+
9
m
?
\newline
Choices:
\newline
(A)
11
m
11m
11
m
\newline
(B)
m
+
12
m + 12
m
+
12
\newline
(C)
m
12
m^{12}
m
12
\newline
(D)
12
m
12m
12
m
Get tutor help
32
32
32
: It is known that
f
(
x
)
=
{
e
x
+
1
−
1
≤
x
≤
0
a
[
(
x
−
1
)
2
−
3
]
0
≤
x
≤
0.5
f(x)=\left\{\begin{array}{cc}e^{x+1} & -1 \leq x \leq 0 \\ a\left[(x-1)^{2}-3\right] & 0 \leq x \leq 0.5\end{array}\right.
f
(
x
)
=
{
e
x
+
1
a
[
(
x
−
1
)
2
−
3
]
−
1
≤
x
≤
0
0
≤
x
≤
0.5
, where
a
a
a
is a constant. Find the value of
a
a
a
.
Get tutor help
8
8
8
\newline
5
5 \quad
5
The variables
x
x
x
and
y
y
y
are such that
y
=
0
y=0
y
=
0
when
x
=
0
x=0
x
=
0
and
\newline
(
x
+
1
)
y
+
(
x
+
y
+
1
)
3
=
1.
(x+1) y+(x+y+1)^{3}=1 .
(
x
+
1
)
y
+
(
x
+
y
+
1
)
3
=
1.
\newline
(a) Show that
d
y
d
x
=
−
3
4
\frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{3}{4}
d
x
d
y
=
−
4
3
when
x
=
0
x=0
x
=
0
.
Get tutor help
(a) Is
f
f
f
one-to-one? (Answer
Get tutor help
If
5
2
x
−
1
−
100
=
2
5
x
−
1
5^{2x-1}-100=25^{x-1}
5
2
x
−
1
−
100
=
2
5
x
−
1
, then the value of
6
x
6^{x}
6
x
.
Get tutor help
1
1
1
\newline
If the expression
(
x
−
3
)
(
2
x
+
5
)
(x-3)(2 x+5)
(
x
−
3
)
(
2
x
+
5
)
can be expressed as
a
x
2
+
b
x
+
c
a x^{2}+b x+c
a
x
2
+
b
x
+
c
, what is
a
b
−
c
a b-c
ab
−
c
?
Get tutor help
8
8
8
. [
15
15
15
] Let
f
(
x
)
=
ln
(
4
−
x
)
+
1
f(x)=\ln (4-x)+1
f
(
x
)
=
ln
(
4
−
x
)
+
1
. Please find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
Get tutor help
(
7
7
7
) Given that
y
y
y
is a positive integer and
y
−
1
y
=
6
y-\frac{1}{y}=6
y
−
y
1
=
6
, find the value of
y
2
+
1
y
2
y^{2}+\frac{1}{y^{2}}
y
2
+
y
2
1
.
Get tutor help
10
10
10
The equation of a curve is
y
=
4
x
3
+
4
p
x
2
+
16
x
−
9
y=4 x^{3}+4 p x^{2}+16 x-9
y
=
4
x
3
+
4
p
x
2
+
16
x
−
9
. Find the range of values of
p
p
p
such that
y
y
y
is an increasing function.
Get tutor help
(a) Given that
y
=
6
−
3
x
y=6-3 x
y
=
6
−
3
x
, find the value of
y
y
y
when
x
=
−
4
x=-4
x
=
−
4
.
\newline
(b) Make
d
d
d
the subject of the formula
c
=
3
d
+
2
e
c=3 d+2 e
c
=
3
d
+
2
e
.
Get tutor help
Score:
\qquad
130
130
130
\newline
Question
1
1
1
:
\newline
(
6
6
6
marks)
\newline
\begin{tabular}{|l|l|l|l|l|}
\newline
\hline Polynomlal & Coefficients & Degree & Varlable & Constant \\
\newline
\hline
5
x
2
−
8
x
+
2
5 x^{2}-8 x+2
5
x
2
−
8
x
+
2
& & & & \\
\newline
\hline
−
6
x
−
7
-6 x-7
−
6
x
−
7
& & & & \\
\newline
\hline
−
10
x
2
+
3
x
-10 x^{2}+3 x
−
10
x
2
+
3
x
& & & & \\
\newline
\hline
\newline
\end{tabular}
Get tutor help
(e) It is given that
x
2
−
10
x
=
4
y
2
−
25
x^{2}-10 x=4 y^{2}-25
x
2
−
10
x
=
4
y
2
−
25
. Find the value of
x
+
2
y
x+2 y
x
+
2
y
.
Get tutor help
(a) Construct triangle
A
B
C
A B C
A
BC
where angle
B
A
C
=
6
5
∘
B A C=65^{\circ}
B
A
C
=
6
5
∘
and angle
A
B
C
=
5
4
∘
A B C=54^{\circ}
A
BC
=
5
4
∘
.
A
B
A B
A
B
has already been drawn.
\newline
∣
\mid
∣
Get tutor help
(a) Calculate the value of
u
3
−
2
u
2
v
+
u
v
2
−
3
u
v
+
3
v
2
u^{3}-2 u^{2} v+u v^{2}-3 u v+3 v^{2}
u
3
−
2
u
2
v
+
u
v
2
−
3
uv
+
3
v
2
if
u
−
v
=
3
u-v=3
u
−
v
=
3
.
\newline
(b) Find the smallest possible value of
3
a
2
+
27
b
2
+
5
c
2
−
18
a
b
−
30
c
+
125
3 a^{2}+27 b^{2}+5 c^{2}-18 a b-30 c+125
3
a
2
+
27
b
2
+
5
c
2
−
18
ab
−
30
c
+
125
.
Get tutor help
Suppose that a sequence is defined as follows.
\newline
a
1
=
10
,
a
n
=
−
3
a
n
−
1
for
n
≥
2
a_{1}=10, \quad a_{n}=-3 a_{n-1} \text { for } n \geq 2
a
1
=
10
,
a
n
=
−
3
a
n
−
1
for
n
≥
2
Get tutor help
MAITHEMININS
\newline
If
\newline
x=\left(\begin{array}{c}6\3\end{array}\right),y=\left(\begin{array}{c}-1\5\end{array}\right),z=\left(\begin{array}{c}-4\2\end{array}\right),w=\left(\begin{array}{c}0\-3\end{array}\right),y=0
\newline
(
a
)
(a)
(
a
)
\newline
x
−
y
x-y
x
−
y
Get tutor help
If
x
=
2
y
x=2y
x
=
2
y
, then which of the following is equivalent to
2
y
+
2
2y+2
2
y
+
2
?
?
?
\newline
A)
x
2
+
2
\frac{x}{2}+2
2
x
+
2
\newline
B)
x
+
2
x+2
x
+
2
\newline
C)
2
x
+
2
2x+2
2
x
+
2
\newline
D)
4
x
+
2
4x+2
4
x
+
2
Get tutor help
2
m
2
,
−
5
m
−
3
2m^{2}, -5m-3
2
m
2
,
−
5
m
−
3
Get tutor help
6
6
6
Consider the points
P
(
4
,
7
)
,
Q
(
8
,
4
)
,
R
(
7
,
0
)
\mathrm{P}(4,7), \mathrm{Q}(8,4), \mathrm{R}(7,0)
P
(
4
,
7
)
,
Q
(
8
,
4
)
,
R
(
7
,
0
)
, and
S
(
−
1
,
t
)
\mathrm{S}(-1, t)
S
(
−
1
,
t
)
. Find
t
t
t
given that
P
Q
∥
S
R
\mathrm{PQ} \| \mathrm{SR}
PQ
∥
SR
.
Get tutor help
If
A
=
[
2
−
3
−
4
1
]
A=\left[\begin{array}{cc}2 & -3 \ -4 & 1\end{array}\right]
A
=
[
2
−
3
−
4
1
]
, then
adj
(
3
A
2
+
12
A
)
\text{adj}(3A^{2}+12 A)
adj
(
3
A
2
+
12
A
)
is equal to
Get tutor help
Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
g
(
f
(
2
)
)
g(f(2))
g
(
f
(
2
))
.
\newline
f
(
x
)
=
3
x
2
−
6
x
−
9
g
(
x
)
=
5
x
−
8
\begin{array}{l} f(x)=3 x^{2}-6 x-9 \\ g(x)=5 x-8 \end{array}
f
(
x
)
=
3
x
2
−
6
x
−
9
g
(
x
)
=
5
x
−
8
\newline
Answer:
Get tutor help
44
44
44
. If triangles
A
B
C
A B C
A
BC
and
D
E
C
D E C
D
EC
are both equilateral, show that
D
E
∥
A
B
D E \| A B
D
E
∥
A
B
.
Get tutor help
If
P
(
B
)
=
0.55
,
P
(
A
∣
B
)
=
0.80
,
P
(
B
′
)
=
0.45
P(B)=0.55, P(A \mid B)=0.80, P\left(B^{\prime}\right)=0.45
P
(
B
)
=
0.55
,
P
(
A
∣
B
)
=
0.80
,
P
(
B
′
)
=
0.45
, and
P
(
A
∣
B
′
)
=
0.40
P\left(A \mid B^{\prime}\right)=0.40
P
(
A
∣
B
′
)
=
0.40
, find
P
(
B
∣
A
)
P(B \mid A)
P
(
B
∣
A
)
Get tutor help
Given the functions
f
(
x
)
=
5
x
+
3
f(x)=5 x+3
f
(
x
)
=
5
x
+
3
and
g
(
x
)
=
x
2
−
7
g(x)=x^{2}-7
g
(
x
)
=
x
2
−
7
, what is
f
(
g
(
−
3
)
)
?
f(g(-3)) ?
f
(
g
(
−
3
))?
\newline
A.
−
77
-77
−
77
\newline
B.
−
12
-12
−
12
\newline
C.
3
3
3
\newline
D.
13
13
13
\newline
E.
137
137
137
Get tutor help
Given that
1
+
2
i
1+2i
1
+
2
i
is a zero of
k
(
x
)
=
x
4
−
6
x
3
+
26
x
2
−
46
x
+
65
k(x)=x^{4}-6x^{3}+26x^{2}-46x+65
k
(
x
)
=
x
4
−
6
x
3
+
26
x
2
−
46
x
+
65
, find the remaining zeroes
Get tutor help
If
3
x
2
−
18
x
−
15
=
0
3x^{2}-18x-15=0
3
x
2
−
18
x
−
15
=
0
, what is the value of
x
2
−
6
x
x^{2}-6x
x
2
−
6
x
?
Get tutor help
Note: Figures not drawn to scale.
\newline
The angles shown above are acute and
\newline
sin
(
a
∘
)
=
cos
(
b
∘
)
\sin(a^{\circ})=\cos(b^{\circ})
sin
(
a
∘
)
=
cos
(
b
∘
)
. If
\newline
a
=
4
k
−
22
a=4k-22
a
=
4
k
−
22
and
\newline
b
=
6
k
−
13
b=6k-13
b
=
6
k
−
13
, what is the value of
\newline
k
k
k
?
Get tutor help
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:
Get tutor help
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:
Get tutor help
Given that
f
(
x
)
=
x
−
5
,
g
(
x
)
=
−
5
x
f(x)=x-5, \quad g(x)=-5 x
f
(
x
)
=
x
−
5
,
g
(
x
)
=
−
5
x
and
h
(
x
)
=
−
3
f
(
x
)
+
3
g
(
x
+
2
)
h(x)=-3 f(x)+3 g(x+2)
h
(
x
)
=
−
3
f
(
x
)
+
3
g
(
x
+
2
)
, then what is the value of
h
(
6
)
h(6)
h
(
6
)
?
\newline
Answer:
Get tutor help
If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
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:
Get tutor help
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:
Get tutor help
Simplify the following expression completely.
\newline
x
2
+
5
x
−
50
x
2
+
6
x
−
40
\frac{x^{2}+5 x-50}{x^{2}+6 x-40}
x
2
+
6
x
−
40
x
2
+
5
x
−
50
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
−
2
x
2
+
9
x
f(x)=-2 x^{2}+9 x
f
(
x
)
=
−
2
x
2
+
9
x
, find
f
(
−
4
)
f(-4)
f
(
−
4
)
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
−
3
x
2
+
16
f(x)=-3 x^{2}+16
f
(
x
)
=
−
3
x
2
+
16
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
4
x
2
+
10
x
f(x)=4 x^{2}+10 x
f
(
x
)
=
4
x
2
+
10
x
, find
f
(
−
4
)
f(-4)
f
(
−
4
)
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
−
x
2
+
5
x
−
6
f(x)=-x^{2}+5 x-6
f
(
x
)
=
−
x
2
+
5
x
−
6
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
2
x
2
+
7
x
+
1
f(x)=2 x^{2}+7 x+1
f
(
x
)
=
2
x
2
+
7
x
+
1
, find
f
(
−
5
)
f(-5)
f
(
−
5
)
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
2
x
2
−
7
x
−
18
f(x)=2 x^{2}-7 x-18
f
(
x
)
=
2
x
2
−
7
x
−
18
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
\newline
Answer:
Get tutor help
Given
f
(
x
)
=
−
x
2
−
10
x
−
15
f(x)=-x^{2}-10 x-15
f
(
x
)
=
−
x
2
−
10
x
−
15
, find
f
(
2
)
f(2)
f
(
2
)
\newline
Answer:
Get tutor help
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
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
Get tutor help
If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
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:
Get tutor help
If
f
(
x
)
=
3
x
−
1
f(x)=3x-1
f
(
x
)
=
3
x
−
1
and
g
(
x
)
=
x
2
+
1
g(x)=x^{2}+1
g
(
x
)
=
x
2
+
1
, what is the value of
g
(
f
(
3
)
)
g(f(3))
g
(
f
(
3
))
?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
8
8
\newline
(B)
10
10
10
\newline
(C)
29
29
29
\newline
(D)
65
65
65
Get tutor help
If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
(
a
n
−
1
)
2
+
n
a_{n}=\left(a_{n-1}\right)^{2}+n
a
n
=
(
a
n
−
1
)
2
+
n
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
+
n
a_{n}=\left(a_{n-1}\right)^{2}+n
a
n
=
(
a
n
−
1
)
2
+
n
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
+
1
=
(
a
n
)
2
+
2
a_{n+1}=\left(a_{n}\right)^{2}+2
a
n
+
1
=
(
a
n
)
2
+
2
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
+
1
=
(
a
n
)
2
+
2
a_{n+1}=\left(a_{n}\right)^{2}+2
a
n
+
1
=
(
a
n
)
2
+
2
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
(
x
−
5
a
)
(
x
+
5
a
)
(x-5 \sqrt{a})(x+5 \sqrt{a})
(
x
−
5
a
)
(
x
+
5
a
)
is equivalent to
x
2
−
375
x^{2}-375
x
2
−
375
, what must be the value of
a
a
a
?
Get tutor help
1
2
Next
