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Math Problems
Algebra 2
Complex conjugate theorem
Find all solutions of the equation below.
\newline
5
3
x
−
2
=
2
5^{3 x-2}=2
5
3
x
−
2
=
2
\newline
The solution(s) is/are
x
=
□
x=\square
x
=
□
□
\square
□
\newline
(Simplify your answer. Use a comma to separate answers as needed. Round to four decimal places as needed.)
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Select all the expressions that are equivalent to
(
2
1
)
2
(2^1)^2
(
2
1
)
2
.
\newline
Multi-select Choices:
\newline
(A)
2
3
2^3
2
3
\newline
(B)
1
2
2
\frac{1}{2^2}
2
2
1
\newline
(C)
2
2
2^2
2
2
\newline
(D)
1
2
3
\frac{1}{2^3}
2
3
1
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(iii) Write the whole number that succeeds
9999
9999
9999
.
\newline
(iv) Write the whole number that precedes
1000
1000
1000
.
\newline
7
7
7
. Write the place value and also the face value of
4
4
4
in each of
\newline
(i)
5324
5324
5324
\newline
(ii)
6345
6345
6345
\newline
(iii)
6438
6438
6438
\newline
(iv)
\newline
4
4
4
. Consider the number
87650324
87650324
87650324
. Name the values of the digit
\newline
(i) thousand's place
\newline
(v) Zten million's place
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find the area of the figure bonded by
y
=
x
y=\sqrt{x}
y
=
x
,
y
=
x
−
2
y=x-2
y
=
x
−
2
,
y
=
0
y=0
y
=
0
. use integral
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find the area of the figure bonded by
y
=
x
2
−
2
x
+
5
y=x^2-2x+5
y
=
x
2
−
2
x
+
5
,
y
=
5
x
−
5
y=5x-5
y
=
5
x
−
5
. use integral
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101
101
101
is a root of
f
(
x
)
=
x
2
+
10
,
201
f(x) = x^2 + 10,201
f
(
x
)
=
x
2
+
10
,
201
. Find the other roots of
f
(
x
)
f(x)
f
(
x
)
.
\newline
Write your answer as a list of simplified values separated by commas, if there is more than one value.
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−
176
-176
−
176
is a root of
f
(
x
)
=
x
2
+
30
,
976
f(x) = x^2 + 30,976
f
(
x
)
=
x
2
+
30
,
976
. Find the other roots of
f
(
x
)
f(x)
f
(
x
)
.
\newline
Write your answer as a list of simplified values separated by commas, if there is more than one value.
\newline
______
\newline
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8
8
8
. Find all points of the graph of
y
=
x
3
−
2
x
2
+
1
y=x^{3}-2 x^{2}+1
y
=
x
3
−
2
x
2
+
1
where the gradient equals the
y
y
y
-coordinate.
\newline
[
5
5
5
marks]
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∴
\therefore
∴
www-awu.aleks.com/alekscgi/x/Isl.exe/
10
10
10
_u-IgNsIkr
7
7
7
j
8
8
8
P
3
3
3
jH-IBluonLF
7
7
7
GsfmBxLWEUDiYeCmloA
5
5
5
WJ
3
3
3
\newline
Unit
7
7
7
Homework
\newline
Question
10
10
10
of
20
20
20
(
1
1
1
point) | Question Attempt:
1
1
1
of Unlimited
\newline
6
6
6
\newline
7
7
7
\newline
8
8
8
\newline
✓
9
\checkmark 9
✓
9
\newline
10
10
10
\newline
11
11
11
\newline
12
12
12
\newline
13
13
13
\newline
Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.
\newline
Check
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Graph the parabola.
\newline
y
=
x
2
−
10
x
+
27
y=x^{2}-10 x+27
y
=
x
2
−
10
x
+
27
\newline
Plot five points on the parabola: the vertex, two points to the left of the vertex button.
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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
\newline
g
(
y
)
=
y
−
1
y
2
−
3
y
+
3
y
=
□
\begin{array}{l} g(y)=\frac{y-1}{y^{2}-3 y+3} \\ y=\square \end{array}
g
(
y
)
=
y
2
−
3
y
+
3
y
−
1
y
=
□
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In
△
V
W
X
,
x
=
2.1
c
m
,
w
=
9.5
c
m
\triangle \mathrm{VWX}, x=2.1 \mathrm{~cm}, w=9.5 \mathrm{~cm}
△
VWX
,
x
=
2.1
cm
,
w
=
9.5
cm
and
∠
W
=
11
0
∘
\angle \mathrm{W}=110^{\circ}
∠
W
=
11
0
∘
. Find all possible values of
∠
X
\angle \mathrm{X}
∠
X
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
Q
R
S
,
r
=
86
c
m
,
q
=
66
c
m
\triangle \mathrm{QRS}, r=86 \mathrm{~cm}, q=66 \mathrm{~cm}
△
QRS
,
r
=
86
cm
,
q
=
66
cm
and
∠
Q
=
5
∘
\angle \mathrm{Q}=5^{\circ}
∠
Q
=
5
∘
. Find all possible values of
∠
R
\angle \mathrm{R}
∠
R
, to the nearest degree.
\newline
Answer:
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For which values of
b
b
b
will
b
x
+
x
2
+
35
b x+x^{2}+35
b
x
+
x
2
+
35
have a minimum value of
19
19
19
? If there is more than one answer, separate them using a comma.
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Solve the equation
x
3
+
2
x
2
−
5
x
−
6
=
0
x^{3}+2 x^{2}-5 x-6=0
x
3
+
2
x
2
−
5
x
−
6
=
0
given that
2
2
2
is a zero of
f
(
x
)
=
x
3
+
2
x
2
−
5
x
−
6
f(x)=x^{3}+2 x^{2}-5 x-6
f
(
x
)
=
x
3
+
2
x
2
−
5
x
−
6
\newline
The solution set is
{
∵
\{\because
{
∵
. (Use a comma to separate answers as needed.)
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Given
P
=
23
,
467
,
894
,
057
,
475
×
753
+
1984
P = 23,467,894,057,475 \times 753 + 1984
P
=
23
,
467
,
894
,
057
,
475
×
753
+
1984
Find the exact values of the quotient and the remainder when
P
P
P
is divided by
753
753
753
. IMPORTANT: you have to solve this problem without performing multiplication, addition, and division.
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Find all points
c
c
c
satisfying the conclusion of the MVT for the function
f
(
x
)
=
9
x
ln
(
x
)
+
9
f(x)=9 x \ln (x)+9
f
(
x
)
=
9
x
ln
(
x
)
+
9
and interval
[
1
,
9
]
[1,9]
[
1
,
9
]
. (Use decimal notation. Give your answer to three decimal places. Give your answer as comma-separated list.)
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Given that
1
−
i
1-i
1
−
i
is a zero of
p
(
x
)
=
x
3
−
6
x
2
+
10
x
−
8
p(x)=x^{3}-6x^{2}+10x-8
p
(
x
)
=
x
3
−
6
x
2
+
10
x
−
8
, find the remaining zeroes.
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Find all critical points of the function
\newline
f
(
x
)
=
9
x
+
∣
8
x
+
1
∣
f(x)=9x+|8x+1|
f
(
x
)
=
9
x
+
∣8
x
+
1∣
\newline
(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. If the function does not have any critical points, enter DNE.)
\newline
critical points:
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Find all critical points of the function
\newline
f
(
x
)
=
5
x
2
5
x
2
−
2
x
+
10
.
f(x)=\frac{5x^{2}}{5x^{2}-2x+10}.
f
(
x
)
=
5
x
2
−
2
x
+
10
5
x
2
.
\newline
(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. If the function does not have any critical points, enter DNE.)
\newline
critical points:
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If
f
(
x
)
=
−
2
x
2
+
7
f(x)=-2x^{2}+7
f
(
x
)
=
−
2
x
2
+
7
and
g
(
x
)
=
∣
x
−
1
∣
g(x)=|x-1|
g
(
x
)
=
∣
x
−
1∣
, find all values of
x
x
x
, to the nearest tenth, for which
f
(
x
)
=
g
(
x
)
f(x)=g(x)
f
(
x
)
=
g
(
x
)
,
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[
0
0
0
/
16
16
16
.
66
66
66
Points]
\newline
DETAILS
\newline
PREVIOUS ANSWERS
\newline
SCALCET
8
8
8
4
4
4
.
1
1
1
.
036
036
036
.
\newline
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
\newline
\newline
h
(
p
)
=
p
−
4
p
2
+
8
h(p)=\frac{p-4}{p^{2}+8}
h
(
p
)
=
p
2
+
8
p
−
4
\newline
p
=
DNE
p=\text{DNE}
p
=
DNE
\newline
Submit Answer
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For the equation
\newline
y
=
3
x
+
2
y=3^{x}+2
y
=
3
x
+
2
, complete a table of coordinates and then select the graph of the equation.
\newline
Next
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The profit for a product is given by
\newline
P
(
x
)
=
−
11
x
2
+
770
x
−
6600
P(x)=-11x^{2}+770x-6600
P
(
x
)
=
−
11
x
2
+
770
x
−
6600
, where
\newline
x
x
x
is the number of units produced and sold. How many units give break even (that is, give zero profit) for this product?
\newline
The number of units that give the break even for this product are
\newline
000
\boxed{\phantom{000}}
000
.
\newline
(Use a comma to separate answers as needed.)
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Rewrite the expression as a product of four linear factors:
\newline
(
x
2
+
5
x
)
2
−
20
(
x
2
+
5
x
)
+
84
\left(x^{2}+5 x\right)^{2}-20\left(x^{2}+5 x\right)+84
(
x
2
+
5
x
)
2
−
20
(
x
2
+
5
x
)
+
84
\newline
Answer:
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Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
6
x
)
2
−
11
(
x
2
−
6
x
)
−
80
\left(x^{2}-6 x\right)^{2}-11\left(x^{2}-6 x\right)-80
(
x
2
−
6
x
)
2
−
11
(
x
2
−
6
x
)
−
80
\newline
Answer:
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Rewrite the expression as a product of four linear factors:
\newline
(
x
2
+
6
x
)
2
−
11
(
x
2
+
6
x
)
−
80
\left(x^{2}+6 x\right)^{2}-11\left(x^{2}+6 x\right)-80
(
x
2
+
6
x
)
2
−
11
(
x
2
+
6
x
)
−
80
\newline
Answer:
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Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
9
x
)
2
−
2
(
x
2
−
9
x
)
−
80
\left(x^{2}-9 x\right)^{2}-2\left(x^{2}-9 x\right)-80
(
x
2
−
9
x
)
2
−
2
(
x
2
−
9
x
)
−
80
\newline
Answer:
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Rewrite the expression as a product of four linear factors:
\newline
(
12
x
2
−
19
x
)
2
−
5
(
12
x
2
−
19
x
)
−
50
\left(12 x^{2}-19 x\right)^{2}-5\left(12 x^{2}-19 x\right)-50
(
12
x
2
−
19
x
)
2
−
5
(
12
x
2
−
19
x
)
−
50
\newline
Answer:
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Find the
z
z
z
-scores for which
15
%
15 \%
15%
of the distribution's area lies between
−
z
-z
−
z
and
z
z
z
.
\newline
Click to view bace I I the click to view page
2
2
2
of the table.
\newline
The
z
z
z
-scores are
□
\square
□
.
\newline
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
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Find the
1
3
th
13^{\text {th }}
1
3
th
term of the geometric sequence
7
,
−
21
,
63
,
…
7,-21,63, \ldots
7
,
−
21
,
63
,
…
\newline
Answer:
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Find all critical points of the function
\newline
f
(
x
)
=
3
x
2
7
x
2
−
2
x
+
2
.
f(x)=\frac{3x^{2}}{7x^{2}-2x+2}.
f
(
x
)
=
7
x
2
−
2
x
+
2
3
x
2
.
\newline
(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. If the function does not have any critical points, enter DNE.)
\newline
critical points:
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For the function
f
(
x
)
=
x
2
+
2
x
+
4
f(x)=x^{2}+2 x+4
f
(
x
)
=
x
2
+
2
x
+
4
, find the slope of the secant line between
x
=
1
x=1
x
=
1
and
x
=
4
x=4
x
=
4
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
2
x
−
5
f(x)=x^{2}+2 x-5
f
(
x
)
=
x
2
+
2
x
−
5
, find the slope of the secant line between
x
=
−
3
x=-3
x
=
−
3
and
x
=
5
x=5
x
=
5
.
\newline
Answer:
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62
+
58
i
62+58i
62
+
58
i
is a root of
f
(
x
)
=
x
2
–
124
x
+
7208
f(x) = x^2–124x+7208
f
(
x
)
=
x
2
–124
x
+
7208
. Find the other roots of
f
(
x
)
f(x)
f
(
x
)
.
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Let
f
(
x
)
=
−
18
x
f(x)=-\frac{18}{x}
f
(
x
)
=
−
x
18
and
g
(
x
)
=
x
2
+
10
x
+
27
.
g(x)=x^{2}+10 x+27 \text {. }
g
(
x
)
=
x
2
+
10
x
+
27
.
\newline
Find the sum of the areas enclosed by the graphs of
f
f
f
and
g
g
g
between
x
=
−
6
x=-6
x
=
−
6
and
x
=
−
1
x=-1
x
=
−
1
.
\newline
Use a graphing calculator and round your answer to three decimal places.
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Let
f
(
x
)
=
8
−
2
x
f(x)=8-2 x
f
(
x
)
=
8
−
2
x
and
g
(
x
)
=
x
3
−
7
x
2
+
12
x
.
g(x)=x^{3}-7 x^{2}+12 x \text {. }
g
(
x
)
=
x
3
−
7
x
2
+
12
x
.
\newline
Find the sum of the areas enclosed by the graphs of
f
f
f
and
g
g
g
between
x
=
1
x=1
x
=
1
and
x
=
4
x=4
x
=
4
.
\newline
Use a graphing calculator and round your answer to three decimal places.
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Let
f
(
x
)
=
1
2
x
3
+
1
2
x
2
−
x
f(x)=\frac{1}{2} x^{3}+\frac{1}{2} x^{2}-x
f
(
x
)
=
2
1
x
3
+
2
1
x
2
−
x
and
g
(
x
)
=
x
2
+
2
x
g(x)=x^{2}+2 x
g
(
x
)
=
x
2
+
2
x
.
\newline
Find the sum of the areas enclosed by the graphs of
f
f
f
and
g
g
g
between
x
=
−
2
x=-2
x
=
−
2
and
x
=
3
x=3
x
=
3
.
\newline
Use a graphing calculator and round your answer to three decimal places.
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Let
f
(
x
)
=
1
2
x
3
−
2
x
+
3
f(x)=\frac{1}{2} x^{3}-2 x+3
f
(
x
)
=
2
1
x
3
−
2
x
+
3
and
g
(
x
)
=
x
2
+
7
2
x
−
3
g(x)=x^{2}+\frac{7}{2} x-3
g
(
x
)
=
x
2
+
2
7
x
−
3
\newline
Find the sum of the areas enclosed by the graphs of
f
f
f
and
g
g
g
between
x
=
−
3
x=-3
x
=
−
3
and
x
=
4
x=4
x
=
4
.
\newline
Use a graphing calculator and round your answer to three decimal places.
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A polynomial function
f
f
f
is defined as
f
(
x
)
=
3
(
x
−
4
)
(
2
x
−
1
)
f(x)=3(x-4)(2 x-1)
f
(
x
)
=
3
(
x
−
4
)
(
2
x
−
1
)
. What is the product of all of the zeros of function
f
f
f
?
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−
70
i
-70i
−
70
i
is a root of
f
(
x
)
=
x
2
+
4
,
900
f(x) = x^2 + 4,900
f
(
x
)
=
x
2
+
4
,
900
. Find the other roots of
f
(
x
)
f(x)
f
(
x
)
.
\newline
Write your answer as a list of simplified values separated by commas, if there is more than one value.
\newline
______
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