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Math Problems
Algebra 2
Solve quadratic inequalities
(
x
+
4
)
(
2
x
−
a
)
=
0
(x+4)(2x-a)=0
(
x
+
4
)
(
2
x
−
a
)
=
0
if the equation has the solutions of
x
=
4
x=4
x
=
4
and
x
=
(
−
4
)
x=(-4)
x
=
(
−
4
)
what is the value of
a
a
a
?
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Solve:
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
h(x)=-5(x+1)(x-9)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
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Find solutions:
1
2
(
x
−
4
)
≤
1
3
(
x
+
1
)
+
2
\frac{1}{2}(x-4) \leq \frac{1}{3}(x+1)+2
2
1
(
x
−
4
)
≤
3
1
(
x
+
1
)
+
2
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-\frac{
3
3
3
}{
2
2
2
}x+
5
5
5
<
7
7
7
\newline
What values of
\newline
x satisfy the inequality?
\newline
Choose
1
1
1
answer:
\newline
(A) x <
−
8
-8
−
8
\newline
(B) x >
−
3
-3
−
3
\newline
(C) x > -\frac{
4
4
4
}{
3
3
3
}
\newline
(D) x >
8
8
8
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Question
\newline
Select the values that make the inequality
\newline
c
≥
−
7
c \geq -7
c
≥
−
7
true.
\newline
(Numbers written in order from least to greatest going across.)
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
−
15
-15
−
15
\newline
−
12
-12
−
12
\newline
−
10
-10
−
10
\newline
−
8
-8
−
8
\newline
−
7.1
-7.1
−
7.1
\newline
−
7.01
-7.01
−
7.01
\newline
−
7.001
-7.001
−
7.001
\newline
−
7
-7
−
7
\newline
−
6.999
-6.999
−
6.999
\newline
−
15
-15
−
15
0
0
0
\newline
−
15
-15
−
15
1
1
1
\newline
−
15
-15
−
15
2
2
2
\newline
−
15
-15
−
15
3
3
3
\newline
−
15
-15
−
15
4
4
4
\newline
−
15
-15
−
15
5
5
5
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What is the sum of the sonutions to the equation
\newline
(
t
+
3
)
(
t
−
357
)
=
0
(t+3)(t-357)=0
(
t
+
3
)
(
t
−
357
)
=
0
?
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What is the sum of the sonutions to the equation
\newline
(
t
+
3
)
(
t
−
357
)
=
0
(t+3)(t-357)=0
(
t
+
3
)
(
t
−
357
)
=
0
?
Get tutor help
Select the values that make the inequality
\newline
r
>
−
4
r > -4
r
>
−
4
true.
\newline
(Numbers written in order from least to greatest going across.)
\newline
Answer Mrpileter
\newline
−
12
-12
−
12
\newline
−
9
-9
−
9
\newline
−
7
-7
−
7
\newline
−
5
-5
−
5
\newline
−
4.1
-4.1
−
4.1
\newline
−
4.01
-4.01
−
4.01
\newline
−
4.001
-4.001
−
4.001
\newline
−
4
-4
−
4
\newline
−
3.999
-3.999
−
3.999
\newline
−
12
-12
−
12
0
0
0
\newline
−
12
-12
−
12
1
1
1
\newline
−
12
-12
−
12
2
2
2
\newline
−
12
-12
−
12
3
3
3
\newline
−
12
-12
−
12
4
4
4
\newline
−
12
-12
−
12
5
5
5
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(
x
−
3
)
(
a
x
+
4
)
=
0
(x-3)(ax+4)=0
(
x
−
3
)
(
a
x
+
4
)
=
0
in the given equation
a
a
a
is a constant if the equation has the solutions
x
=
3
x=3
x
=
3
and
x
=
−
2
x=-2
x
=
−
2
what is the value of
a
a
a
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Given the functions
f
(
x
)
=
x
4
f(x)=x^{4}
f
(
x
)
=
x
4
and
g
(
x
)
=
12
⋅
2
x
g(x)=12 \cdot 2^{x}
g
(
x
)
=
12
⋅
2
x
, which of the following statements is true?
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
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Given the functions
f
(
x
)
=
4
x
5
f(x)=4 x^{5}
f
(
x
)
=
4
x
5
and
g
(
x
)
=
3
⋅
6
x
g(x)=3 \cdot 6^{x}
g
(
x
)
=
3
⋅
6
x
, which of the following statements is true?
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
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Given the functions
f
(
x
)
=
3
x
2
f(x)=3 x^{2}
f
(
x
)
=
3
x
2
and
g
(
x
)
=
3
⋅
2
x
g(x)=3 \cdot 2^{x}
g
(
x
)
=
3
⋅
2
x
, which of the following statements is true?
\newline
f
(
4
)
>
g
(
4
)
f(4)>g(4)
f
(
4
)
>
g
(
4
)
\newline
f
(
4
)
=
g
(
4
)
f(4)=g(4)
f
(
4
)
=
g
(
4
)
\newline
f
(
4
)
<
g
(
4
)
f(4)<g(4)
f
(
4
)
<
g
(
4
)
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Given the functions
f
(
x
)
=
4
x
5
f(x)=4 x^{5}
f
(
x
)
=
4
x
5
and
g
(
x
)
=
3
x
g(x)=3^{x}
g
(
x
)
=
3
x
, which of the following statements is true?
\newline
f
(
14
)
=
g
(
14
)
f(14)=g(14)
f
(
14
)
=
g
(
14
)
\newline
f
(
14
)
<
g
(
14
)
f(14)<g(14)
f
(
14
)
<
g
(
14
)
\newline
f
(
14
)
>
g
(
14
)
f(14)>g(14)
f
(
14
)
>
g
(
14
)
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Given the functions
f
(
x
)
=
2
x
4
f(x)=2 x^{4}
f
(
x
)
=
2
x
4
and
g
(
x
)
=
8
⋅
3
x
g(x)=8 \cdot 3^{x}
g
(
x
)
=
8
⋅
3
x
, which of the following statements is true?
\newline
f
(
6
)
<
g
(
6
)
f(6)<g(6)
f
(
6
)
<
g
(
6
)
\newline
f
(
6
)
>
g
(
6
)
f(6)>g(6)
f
(
6
)
>
g
(
6
)
\newline
f
(
6
)
=
g
(
6
)
f(6)=g(6)
f
(
6
)
=
g
(
6
)
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Given the functions
f
(
x
)
=
x
4
f(x)=x^{4}
f
(
x
)
=
x
4
and
g
(
x
)
=
2
⋅
3
x
g(x)=2 \cdot 3^{x}
g
(
x
)
=
2
⋅
3
x
, which of the following statements is true?
\newline
f
(
8
)
=
g
(
8
)
f(8)=g(8)
f
(
8
)
=
g
(
8
)
\newline
f
(
8
)
>
g
(
8
)
f(8)>g(8)
f
(
8
)
>
g
(
8
)
\newline
f
(
8
)
<
g
(
8
)
f(8)<g(8)
f
(
8
)
<
g
(
8
)
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Given the functions
f
(
x
)
=
3
x
3
f(x)=3 x^{3}
f
(
x
)
=
3
x
3
and
g
(
x
)
=
3
⋅
3
x
g(x)=3 \cdot 3^{x}
g
(
x
)
=
3
⋅
3
x
, which of the following statements is true?
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
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Given the functions
f
(
x
)
=
4
x
f(x)=4 x
f
(
x
)
=
4
x
and
g
(
x
)
=
9
⋅
2
x
g(x)=9 \cdot 2^{x}
g
(
x
)
=
9
⋅
2
x
, which of the following statements is true?
\newline
f
(
2
)
<
g
(
2
)
f(2)<g(2)
f
(
2
)
<
g
(
2
)
\newline
f
(
2
)
=
g
(
2
)
f(2)=g(2)
f
(
2
)
=
g
(
2
)
\newline
f
(
2
)
>
g
(
2
)
f(2)>g(2)
f
(
2
)
>
g
(
2
)
Get tutor help
Given the functions
f
(
x
)
=
4
x
4
f(x)=4 x^{4}
f
(
x
)
=
4
x
4
and
g
(
x
)
=
9
⋅
3
x
g(x)=9 \cdot 3^{x}
g
(
x
)
=
9
⋅
3
x
, which of the following statements is true?
\newline
f
(
5
)
<
g
(
5
)
f(5)<g(5)
f
(
5
)
<
g
(
5
)
\newline
f
(
5
)
=
g
(
5
)
f(5)=g(5)
f
(
5
)
=
g
(
5
)
\newline
f
(
5
)
>
g
(
5
)
f(5)>g(5)
f
(
5
)
>
g
(
5
)
Get tutor help
Given the functions
f
(
x
)
=
5
x
5
f(x)=5 x^{5}
f
(
x
)
=
5
x
5
and
g
(
x
)
=
9
⋅
6
x
g(x)=9 \cdot 6^{x}
g
(
x
)
=
9
⋅
6
x
, which of the following statements is true?
\newline
f
(
4
)
<
g
(
4
)
f(4)<g(4)
f
(
4
)
<
g
(
4
)
\newline
f
(
4
)
>
g
(
4
)
f(4)>g(4)
f
(
4
)
>
g
(
4
)
\newline
f
(
4
)
=
g
(
4
)
f(4)=g(4)
f
(
4
)
=
g
(
4
)
Get tutor help
Consider the system of equations. If
(
x
,
y
)
(x,y)
(
x
,
y
)
is the solution to the system, then what is the value of
y
+
x
y+x
y
+
x
?
\newline
24
−
6
y
=
2
x
24-6y=2x
24
−
6
y
=
2
x
\newline
6
(
y
−
2
)
=
3
+
x
6(y-2)=3+x
6
(
y
−
2
)
=
3
+
x
Get tutor help
x
2
≥
10
\frac{x}{2} \geq 10
2
x
≥
10
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Select the graph of the given inequality
\newline
x
≥
7
x \geq 7
x
≥
7
\newline
Choose the correct answer below
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Select the graph of the given inequality.
\newline
x
≥
7
x \geq 7
x
≥
7
\newline
Choose the correct answer below
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Nath question
4
4
4
\newline
y
<
−
4
x
+
4
y<-4 x+4
y
<
−
4
x
+
4
\newline
Which point
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the given inequality in the
x
y
x y
x
y
-plane?
\newline
A)
(
2
,
−
1
)
(2,-1)
(
2
,
−
1
)
\newline
B)
(
2
,
1
)
(2,1)
(
2
,
1
)
\newline
C)
(
0
,
5
)
(0,5)
(
0
,
5
)
\newline
D)
(
−
4
,
0
)
(-4,0)
(
−
4
,
0
)
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b.
y
=
x
−
7
4
y=\sqrt[4]{x-7}
y
=
4
x
−
7
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Answer:
\newline
(b)
(
h
−
1
)
2
+
(
h
−
2
)
3
=
3
\frac{(h-1)}{2}+\frac{(h-2)}{3}=3
2
(
h
−
1
)
+
3
(
h
−
2
)
=
3
Get tutor help
State all integer values of
x
x
x
in the interval
−
2
≤
x
≤
5
-2 \leq x \leq 5
−
2
≤
x
≤
5
that satisfy the following inequality:
\newline
5
x
−
5
≥
−
10
5 x-5 \geq-10
5
x
−
5
≥
−
10
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
[
−
6
,
1
]
[-6,1]
[
−
6
,
1
]
that satisfy the following inequality:
\newline
−
3
x
−
10
>
3
-3 x-10>3
−
3
x
−
10
>
3
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
−
2
≤
x
≤
4
-2 \leq x \leq 4
−
2
≤
x
≤
4
that satisfy the following inequality:
\newline
4
x
−
9
≥
−
13
4 x-9 \geq-13
4
x
−
9
≥
−
13
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
−
1
≤
x
≤
4
-1 \leq x \leq 4
−
1
≤
x
≤
4
that satisfy the following inequality:
\newline
3
x
+
4
≤
4
3 x+4 \leq 4
3
x
+
4
≤
4
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
[
−
8
,
−
3
]
[-8,-3]
[
−
8
,
−
3
]
that satisfy the following inequality:
\newline
4
x
+
8
≥
−
18
4 x+8 \geq-18
4
x
+
8
≥
−
18
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
[
−
2
,
4
]
[-2,4]
[
−
2
,
4
]
that satisfy the following inequality:
\newline
5
x
+
4
≥
3
5 x+4 \geq 3
5
x
+
4
≥
3
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
4
≤
x
≤
10
4 \leq x \leq 10
4
≤
x
≤
10
that satisfy the following inequality:
\newline
−
4
x
+
6
≤
−
16
-4 x+6 \leq-16
−
4
x
+
6
≤
−
16
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
2
≤
x
≤
7
2 \leq x \leq 7
2
≤
x
≤
7
that satisfy the following inequality:
\newline
2
x
−
2
>
4
2 x-2>4
2
x
−
2
>
4
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
[
4
,
9
]
[4,9]
[
4
,
9
]
that satisfy the following inequality:
\newline
−
2
x
+
8
≤
−
3
-2 x+8 \leq-3
−
2
x
+
8
≤
−
3
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
[
1
,
6
]
[1,6]
[
1
,
6
]
that satisfy the following inequality:
\newline
5
x
−
10
>
4
5 x-10>4
5
x
−
10
>
4
\newline
Answer:
x
=
x=
x
=
Get tutor help
State all integer values of
x
x
x
in the interval
−
3
≤
x
≤
4
-3 \leq x \leq 4
−
3
≤
x
≤
4
that satisfy the following inequality:
\newline
3
x
+
10
≥
4
3 x+10 \geq 4
3
x
+
10
≥
4
\newline
Answer:
x
=
x=
x
=
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c
(
n
)
=
−
6
+
5
(
n
−
1
)
c(n) = -6 + 5(n - 1)
c
(
n
)
=
−
6
+
5
(
n
−
1
)
\newline
Find the
8
th
8^{\text{th}}
8
th
term in the sequence.
\newline
□
\square
□
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y
−
4
=
−
2
(
x
+
3
)
y-4=-2(x+3)
y
−
4
=
−
2
(
x
+
3
)
\newline
Complete the missing value in the solution to the equation
\newline
(
−
3
,
□
)
(-3,\square)
(
−
3
,
□
)
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−
(
a
−
1
)
(
b
−
1
)
(
c
−
1
)
- (a - 1)(b - 1)(c - 1)
−
(
a
−
1
)
(
b
−
1
)
(
c
−
1
)
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
1
−
a
)
(
b
−
1
)
(
1
−
c
)
(1 - a)(b - 1)(1 - c)
(
1
−
a
)
(
b
−
1
)
(
1
−
c
)
\newline
(B)
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
(1 - a)(1 - b)(1 - c)
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
\newline
(C)
(
a
−
1
)
(
1
−
b
)
(
1
−
c
)
(a - 1)(1 - b)(1 - c)
(
a
−
1
)
(
1
−
b
)
(
1
−
c
)
\newline
(D)
(
1
−
a
)
(
1
−
b
)
(
c
−
1
)
(1 - a)(1 - b)(c - 1)
(
1
−
a
)
(
1
−
b
)
(
c
−
1
)
Get tutor help
Which value of
x
x
x
satisfies the equation
4
3
(
x
+
5
4
)
=
11
\frac{4}{3}\left(x+\frac{5}{4}\right)=11
3
4
(
x
+
4
5
)
=
11
?
\newline
−
6
-6
−
6
\newline
7
7
7
\newline
6
6
6
\newline
−
7
-7
−
7
Get tutor help
Find the value of
x
x
x
in the equation below.
\newline
x
6
=
9
\frac{x}{6}=9
6
x
=
9
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
y
\mathrm{y}
y
.
\newline
y
6
=
−
9
\frac{y}{6}=-9
6
y
=
−
9
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
a
3
b
c
2
<
0
a^3bc^2 < 0
a
3
b
c
2
<
0
, which of the following must be correct?
\newline
(A)
a
<
0
&
c
<
0
a < 0 \& c < 0
a
<
0&
c
<
0
\newline
(B)
b
<
0
&
c
<
0
b < 0 \& c < 0
b
<
0&
c
<
0
\newline
(C)
a
<
0
&
b
>
0
a < 0 \& b > 0
a
<
0&
b
>
0
\newline
(D)
a
<
0
&
b
>
0
a < 0 \& b > 0
a
<
0&
b
>
0
or
a
>
0
&
b
<
0
a > 0 \& b < 0
a
>
0&
b
<
0
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If
a
3
b
c
2
<
0
a^3bc^2 < 0
a
3
b
c
2
<
0
, which of the following must be correct?
\newline
(A)
a
<
0
&
c
<
0
a < 0 \& c < 0
a
<
0&
c
<
0
\newline
(B)
b
<
0
&
c
<
0
b < 0 \& c < 0
b
<
0&
c
<
0
\newline
(C)
a
<
0
&
b
>
0
a < 0 \& b > 0
a
<
0&
b
>
0
\newline
(D)
a
<
0
&
b
>
0
a < 0 \& b > 0
a
<
0&
b
>
0
or
a
>
0
&
b
<
0
a > 0 \& b < 0
a
>
0&
b
<
0
Get tutor help
If
x
+
7
x+7
x
+
7
is a factor of the polynomial function
g
g
g
, what is the value of
g
(
7
)
g(7)
g
(
7
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
7
-7
−
7
\newline
(B)
0
0
0
\newline
(C)
14
14
14
\newline
(D) Cannot be determined from the given information
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If
x
−
9
x-9
x
−
9
is a factor of the polynomial function
f
f
f
, what is the value of
f
(
9
)
f(9)
f
(
9
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
9
-9
−
9
\newline
(B)
0
0
0
\newline
(C)
9
9
9
\newline
(D) Cannot be determined from the given information
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Let
f
(
x
)
=
−
4
x
3
+
6
x
2
−
5
f(x)=-4 x^{3}+6 x^{2}-5
f
(
x
)
=
−
4
x
3
+
6
x
2
−
5
.
\newline
The absolute minimum value of
f
f
f
over the closed interval
−
2
≤
x
≤
3
-2 \leq x \leq 3
−
2
≤
x
≤
3
occurs at what
x
x
x
value?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
-2
−
2
\newline
(B)
1
1
1
\newline
(C)
3
3
3
\newline
(D)
0
0
0
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Let
g
(
x
)
=
x
3
+
1
g(x)=x^{3}+1
g
(
x
)
=
x
3
+
1
.
\newline
The absolute minimum value of
g
g
g
over the closed interval
−
2
≤
x
≤
3
-2 \leq x \leq 3
−
2
≤
x
≤
3
occurs at what
x
x
x
value?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
-2
−
2
\newline
(B)
0
0
0
\newline
(C)
3
3
3
\newline
(D)
−
7
-7
−
7
Get tutor help
Let
f
(
x
)
=
−
4
x
3
+
6
x
2
−
5
f(x)=-4 x^{3}+6 x^{2}-5
f
(
x
)
=
−
4
x
3
+
6
x
2
−
5
.
\newline
The absolute minimum value of
f
f
f
over the closed interval
−
2
≤
x
≤
3
-2 \leq x \leq 3
−
2
≤
x
≤
3
occurs at what
x
x
x
value?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
-2
−
2
\newline
(B)
3
3
3
\newline
(C)
0
0
0
\newline
(D)
1
1
1
Get tutor help
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