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Math Problems
Algebra 2
Evaluate recursive formulas for sequences
Solve for
b
b
b
.
\newline
b
−
(
−
633
)
=
839
b - (-633) = 839
b
−
(
−
633
)
=
839
\newline
b
=
b =
b
=
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P
(
x
)
=
x
4
−
2
x
3
+
k
x
−
4
P(x)=x^{4}-2 x^{3}+k x-4
P
(
x
)
=
x
4
−
2
x
3
+
k
x
−
4
\newline
where
k
k
k
is an unknown integer.
\newline
P
(
x
)
P(x)
P
(
x
)
divided by
(
x
−
1
)
(x-1)
(
x
−
1
)
has a remainder of
0
0
0
.
\newline
What is the value of
k
k
k
?
\newline
k
=
k=
k
=
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P
(
x
)
=
x
4
−
3
x
2
+
k
x
−
2
P(x)=x^{4}-3 x^{2}+k x-2
P
(
x
)
=
x
4
−
3
x
2
+
k
x
−
2
\newline
where
k
k
k
is an unknown integer.
\newline
P
(
x
)
P(x)
P
(
x
)
divided by
(
x
−
2
)
(x-2)
(
x
−
2
)
has a remainder of
10
10
10
.
\newline
What is the value of
k
k
k
?
\newline
k
=
k=
k
=
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P
(
x
)
=
2
x
4
−
x
3
+
2
x
2
−
k
P(x)=2 x^{4}-x^{3}+2 x^{2}-k
P
(
x
)
=
2
x
4
−
x
3
+
2
x
2
−
k
\newline
where
k
k
k
is an unknown integer.
\newline
P
(
x
)
P(x)
P
(
x
)
divided by
(
x
+
1
)
(x+1)
(
x
+
1
)
has a remainder of
2
2
2
.
\newline
What is the value of
k
k
k
?
\newline
k
=
k=
k
=
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Kaylee solves the equation below by first squaring both sides of the equation.
\newline
1
−
y
=
2
y
2
−
7
1-y=\sqrt{2 y^{2}-7}
1
−
y
=
2
y
2
−
7
\newline
What extraneous solution does Kaylee obtain?
\newline
y
=
y=
y
=
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Tessa solves the equation below by first squaring both sides of the equation.
\newline
x
2
−
3
x
−
6
=
x
−
1
\sqrt{x^{2}-3 x-6}=x-1
x
2
−
3
x
−
6
=
x
−
1
\newline
What extraneous solution does Tessa obtain?
\newline
x
=
x=
x
=
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Li Juan solves the equation below by first squaring both sides of the equation.
\newline
3
−
2
w
=
w
+
6
\sqrt{3-2 w}=w+6
3
−
2
w
=
w
+
6
\newline
What extraneous solution does
L
i
\mathrm{Li}
Li
Juan obtain?
\newline
w
=
w=
w
=
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Zhang Li solves the equation below by first squaring both sides of the equation.
\newline
−
4
=
5
z
+
7
-4=\sqrt{5 z+7}
−
4
=
5
z
+
7
\newline
What extraneous solution does Zhang Li obtain?
\newline
z
=
z=
z
=
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Avery solves the equation below by first squaring both sides of the equation.
\newline
z
2
+
8
=
1
−
2
z
\sqrt{z^{2}+8}=1-2 z
z
2
+
8
=
1
−
2
z
\newline
What extraneous solution does Avery obtain?
\newline
z
=
z=
z
=
Get tutor help
Lea solves the equation below by first squaring both sides of the equation.
\newline
3
+
2
y
=
−
y
3+2 y=\sqrt{-y}
3
+
2
y
=
−
y
\newline
What extraneous solution does Lea obtain?
\newline
y
=
y=
y
=
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Addison solves the equation below by first squaring both sides of the equation.
\newline
2
x
−
1
=
8
−
x
2 x-1=\sqrt{8-x}
2
x
−
1
=
8
−
x
\newline
What extraneous solution does Addison obtain?
\newline
x
=
x=
x
=
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Rania solves the equation below by first squaring both sides of the equation.
\newline
−
5
=
3
x
−
7
-5=\sqrt{3 x-7}
−
5
=
3
x
−
7
\newline
What extraneous solution does Rania obtain?
\newline
x
=
x=
x
=
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Miku solves the equation below by first squaring both sides of the equation.
\newline
z
2
+
2
z
−
3
=
z
−
3
\sqrt{z^{2}+2 z-3}=z-3
z
2
+
2
z
−
3
=
z
−
3
\newline
What extraneous solution does Miku obtain?
\newline
z
=
z=
z
=
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z
=
−
302
+
19.3
i
z=-302+19.3 i
z
=
−
302
+
19.3
i
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
−
19
i
+
14
z=-19 i+14
z
=
−
19
i
+
14
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
91
−
27
i
z=91-27 i
z
=
91
−
27
i
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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If
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the system of equations shown, what is the product of the
y
y
y
-coordinates of the solutions?
\newline
x
2
+
4
y
2
=
40
x^{2}+4 y^{2}=40
x
2
+
4
y
2
=
40
\newline
x
+
2
y
=
8
x+2 y=8
x
+
2
y
=
8
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If
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the system of equations shown, what is the product of the
y
y
y
-coordinates of the solutions?
\newline
x
2
+
y
2
=
9
x^{2}+y^{2}=9
x
2
+
y
2
=
9
\newline
x
+
y
=
3
x+y=3
x
+
y
=
3
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8
y
=
4
x
2
−
12
x
+
46
8 y=4 x^{2}-12 x+46
8
y
=
4
x
2
−
12
x
+
46
\newline
y
=
3
2
x
+
5
4
y=\frac{3}{2} x+\frac{5}{4}
y
=
2
3
x
+
4
5
\newline
If
(
a
,
b
)
(a, b)
(
a
,
b
)
is the solution to the system of equations shown, what is the value of
a
a
a
?
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5
y
=
3478
−
3
c
5 y=3478-3 c
5
y
=
3478
−
3
c
\newline
In the given equation,
c
c
c
is a constant. If
y
=
8
y=8
y
=
8
is a solution to the equation, what is the value of
c
c
c
?
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Find
a
2
a_2
a
2
and
a
3
a_3
a
3
.
a
1
=
1
a_1 = 1
a
1
=
1
a
n
=
8
a
n
−
1
a_n = 8a_{n - 1}
a
n
=
8
a
n
−
1
Write your answers as integers or fractions in simplest form.
a
2
=
a_2 =
a
2
=
______
a
3
=
a_3 =
a
3
=
______
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