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Math Problems
Algebra 2
Solve a quadratic equation using the zero product property
100
−
121
k
2
=
0
100-121 k^{2}=0
100
−
121
k
2
=
0
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
=
100
121
k=\frac{100}{121}
k
=
121
100
\newline
(B)
k
=
−
100
121
k=-\frac{100}{121}
k
=
−
121
100
and
k
=
100
121
k=\frac{100}{121}
k
=
121
100
\newline
(c)
k
=
10
11
k=\frac{10}{11}
k
=
11
10
\newline
(D)
k
=
−
10
11
k=-\frac{10}{11}
k
=
−
11
10
and
k
=
10
11
k=\frac{10}{11}
k
=
11
10
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(
x
+
13
2
)
(
x
−
13
2
)
=
0
\left(x+\frac{13}{2}\right)\left(x-\frac{13}{2}\right)=0
(
x
+
2
13
)
(
x
−
2
13
)
=
0
\newline
How many distinct real solutions does the given equation have?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
2
2
2
\newline
(D)
3
3
3
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−
81
x
2
=
−
11
-81 x^{2}=-11
−
81
x
2
=
−
11
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
11
81
x=\frac{\sqrt{11}}{81}
x
=
81
11
\newline
(B)
x
=
−
11
81
x=-\frac{\sqrt{11}}{81}
x
=
−
81
11
and
x
=
11
81
x=\frac{\sqrt{11}}{81}
x
=
81
11
\newline
(C)
x
=
−
11
9
x=-\frac{\sqrt{11}}{9}
x
=
−
9
11
and
x
=
11
9
x=\frac{\sqrt{11}}{9}
x
=
9
11
\newline
(D)
x
=
11
9
x=\frac{\sqrt{11}}{9}
x
=
9
11
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Solve for
d
d
d
.
\newline
(
d
−
8
)
(
d
−
1
)
=
0
(d - 8)(d - 1) = 0
(
d
−
8
)
(
d
−
1
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
d
=
d =
d
=
_____ or
d
=
d =
d
=
_____
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Solve for
t
t
t
.
\newline
t
(
t
−
1
)
=
0
t(t - 1) = 0
t
(
t
−
1
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
t
=
t =
t
=
_____ or
t
=
t =
t
=
_____
Get tutor help
Solve for
z
z
z
.
\newline
z
(
z
+
9
)
=
0
z(z + 9) = 0
z
(
z
+
9
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
z
=
z =
z
=
_____ or
z
=
z =
z
=
_____
Get tutor help
Solve for
y
y
y
.
\newline
(
y
+
4
)
(
y
−
1
)
=
0
(y + 4)(y - 1) = 0
(
y
+
4
)
(
y
−
1
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
y
=
y =
y
=
_____ or
y
=
y =
y
=
_____
Get tutor help
Solve for
u
u
u
.
\newline
(
u
−
3
)
(
u
+
1
)
=
0
(u - 3)(u + 1) = 0
(
u
−
3
)
(
u
+
1
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
u
=
_
_
_
_
u = \_\_\_\_
u
=
____
or
u
=
_
_
_
_
u = \_\_\_\_
u
=
____
Get tutor help
Solve for
n
n
n
.
\newline
n
(
n
−
5
)
=
0
n(n - 5) = 0
n
(
n
−
5
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
n
=
n =
n
=
_____ or
n
=
n =
n
=
_____
Get tutor help
Solve for
k
k
k
.
\newline
(
k
+
2
)
(
k
+
8
)
=
0
(k + 2)(k + 8) = 0
(
k
+
2
)
(
k
+
8
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
k
=
k =
k
=
_____ or
k
=
k =
k
=
_____
Get tutor help
Solve for
u
u
u
.
\newline
u
(
u
+
5
)
=
0
u(u + 5) = 0
u
(
u
+
5
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
u
=
u =
u
=
_____ or
u
=
u =
u
=
_____
Get tutor help
Solve for
y
y
y
.
\newline
y
(
y
+
2
)
=
0
y(y + 2) = 0
y
(
y
+
2
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
y
=
y =
y
=
_____ or
y
=
y =
y
=
_____
Get tutor help
Solve for
n
n
n
.
\newline
(
n
−
6
)
(
n
−
3
)
=
0
(n - 6)(n - 3) = 0
(
n
−
6
)
(
n
−
3
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
n
=
n =
n
=
_____ or
n
=
n =
n
=
_____
Get tutor help
Solve for
c
c
c
.
\newline
c
(
c
−
5
)
=
0
c(c - 5) = 0
c
(
c
−
5
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
c
=
c =
c
=
_____ or
c
=
c =
c
=
_____
Get tutor help
Solve for
z
z
z
.
\newline
(
z
−
4
)
(
z
−
3
)
=
0
(z - 4)(z - 3) = 0
(
z
−
4
)
(
z
−
3
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
z
=
z =
z
=
_____ or
z
=
z =
z
=
_____
Get tutor help
Solve for
d
d
d
.
\newline
(
d
+
9
)
(
d
+
4
)
=
0
(d + 9)(d + 4) = 0
(
d
+
9
)
(
d
+
4
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
d
=
d =
d
=
_____ or
d
=
d =
d
=
_____
Get tutor help
Solve for
m
m
m
.
\newline
m
(
m
−
1
)
=
0
m(m - 1) = 0
m
(
m
−
1
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
m
=
m =
m
=
_____ or
m
=
m =
m
=
_____
Get tutor help
Solve for
k
k
k
.
\newline
(
k
−
1
)
(
k
−
3
)
=
0
(k - 1)(k - 3) = 0
(
k
−
1
)
(
k
−
3
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
k
=
k =
k
=
_____ or
k
=
k =
k
=
_____
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
+
1
)
=
0
x(x + 1) = 0
x
(
x
+
1
)
=
0
\newline
Write your answers as integers or as proper or improper fractions in simplest form.
\newline
x
=
x =
x
=
_____ or
x
=
x =
x
=
_____
Get tutor help
g
(
x
)
=
cos
(
x
)
−
sin
(
x
)
cos
(
2
x
)
g(x)=\frac{\cos (x)-\sin (x)}{\cos (2 x)}
g
(
x
)
=
cos
(
2
x
)
cos
(
x
)
−
sin
(
x
)
\newline
We want to find
lim
x
→
π
4
g
(
x
)
\lim _{x \rightarrow \frac{\pi}{4}} g(x)
lim
x
→
4
π
g
(
x
)
.
\newline
What happens when we use direct substitution?
\newline
Choose
1
1
1
answer:
\newline
(A) The limit exists, and we found it!
\newline
(B) The limit doesn't exist (probably an asymptote).
\newline
(C) The result is indeterminate.
Get tutor help
(
2
x
−
3
)
(
x
+
4
)
=
0
(2 x-3)(x+4)=0
(
2
x
−
3
)
(
x
+
4
)
=
0
\newline
Let
x
=
a
x=a
x
=
a
and
x
=
b
x=b
x
=
b
be unique solutions to the given equation. What is the value of
−
a
−
b
-a-b
−
a
−
b
?
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The function
m
m
m
is given in three equivalent forms.
\newline
Which form most quickly reveals the
y
y
y
-intercept?
\newline
Choose
1
1
1
answer:
\newline
(A)
m
(
x
)
=
2
x
2
+
16
x
+
24
m(x)=2 x^{2}+16 x+24
m
(
x
)
=
2
x
2
+
16
x
+
24
\newline
(B)
m
(
x
)
=
2
(
x
+
4
)
2
−
8
m(x)=2(x+4)^{2}-8
m
(
x
)
=
2
(
x
+
4
)
2
−
8
\newline
(C)
m
(
x
)
=
2
(
x
+
6
)
(
x
+
2
m(x)=2(x+6)(x+2
m
(
x
)
=
2
(
x
+
6
)
(
x
+
2
)
\newline
What is the
y
y
y
-intercept?
\newline
y
y
y
-intercept
=
(
0
,
□
)
=(0, \square)
=
(
0
,
□
)
Get tutor help
