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Math Problems
Algebra 1
Set-builder notation
What does the set
{
x
∣
x
≤
14
or
x
>
17
}
\{x | x \leq 14 \text{ or } x > 17\}
{
x
∣
x
≤
14
or
x
>
17
}
represent?
\newline
Choices:
\newline
(A)all numbers less than or equal to
14
14
14
or less than or equal to
17
17
17
\newline
(B)all numbers greater than or equal to
14
14
14
or greater than or equal to
17
17
17
\newline
(C)all numbers less than or equal to
14
14
14
or greater than
17
17
17
\newline
(D)all numbers greater than or equal to
14
14
14
or less than
17
17
17
Get tutor help
What does the set
{
x
∣
x
>
6
and
x
≤
9
}
\{x | x > 6 \text{ and } x \leq 9\}
{
x
∣
x
>
6
and
x
≤
9
}
represent?
\newline
Choices:
\newline
(A)all numbers less than or equal to
6
6
6
or less than or equal to
9
9
9
\newline
(B)all numbers less than or equal to
6
6
6
and less than or equal to
9
9
9
\newline
(C)all numbers greater than
6
6
6
and less than or equal to
9
9
9
\newline
(D)all numbers less than
6
6
6
or greater than or equal to
9
9
9
Get tutor help
What does the set
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than
0
0
0
\newline
(B)all numbers equal to
0
0
0
\newline
(C)all numbers less than or equal to
0
0
0
\newline
(D)all numbers greater than or equal to
0
0
0
Get tutor help
Which is the set of numbers less than or equal to
4
4
4
or greater than
7
7
7
?
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
4
or
x
>
7
}
\{x | x \leq 4 \text{ or } x > 7\}
{
x
∣
x
≤
4
or
x
>
7
}
\newline
(B)
{
x
∣
x
≤
4
or
x
<
7
}
\{x | x \leq 4 \text{ or } x < 7\}
{
x
∣
x
≤
4
or
x
<
7
}
\newline
(C)
{
x
∣
x
<
4
or
x
≥
7
}
\{x | x < 4 \text{ or } x \geq 7\}
{
x
∣
x
<
4
or
x
≥
7
}
\newline
(D)
{
x
∣
x
<
4
and
x
≥
7
}
\{x | x < 4 \text{ and } x \geq 7\}
{
x
∣
x
<
4
and
x
≥
7
}
Get tutor help
Which is the set of numbers less than or equal to
6
6
6
or greater than or equal to
12
12
12
?
\newline
Choices:
\newline
(A)
{
x
∣
x
<
6
and
x
>
12
}
\{x | x < 6 \text{ and } x > 12\}
{
x
∣
x
<
6
and
x
>
12
}
\newline
(B)
{
x
∣
x
≤
6
and
x
≥
12
}
\{x | x \leq 6 \text{ and } x \geq 12\}
{
x
∣
x
≤
6
and
x
≥
12
}
\newline
(C)
{
x
∣
x
≤
6
or
x
≥
12
}
\{x | x \leq 6 \text{ or } x \geq 12\}
{
x
∣
x
≤
6
or
x
≥
12
}
\newline
(D)
{
x
∣
x
<
6
or
x
>
12
}
\{x | x < 6 \text{ or } x > 12\}
{
x
∣
x
<
6
or
x
>
12
}
Get tutor help
What does the set
{
x
∣
x
>
−
9
and
x
<
1
}
\{x | x > -9 \text{ and } x < 1\}
{
x
∣
x
>
−
9
and
x
<
1
}
represent?
\newline
Choices:
\newline
(A)all numbers less than
−
9
-9
−
9
and greater than
1
1
1
\newline
(B)all numbers greater than
−
9
-9
−
9
and less than
1
1
1
\newline
(C)all numbers greater than
−
9
-9
−
9
and less than or equal to
1
1
1
\newline
(D)all numbers less than
−
9
-9
−
9
and greater than or equal to
1
1
1
Get tutor help
Which is the set of numbers greater than
−
3
-3
−
3
and less than
4
4
4
?
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
−
3
and
x
≥
4
}
\{x | x \leq -3 \text{ and } x \geq 4\}
{
x
∣
x
≤
−
3
and
x
≥
4
}
\newline
(B)
{
x
∣
x
≥
−
3
and
x
≤
4
}
\{x | x \geq -3 \text{ and } x \leq 4\}
{
x
∣
x
≥
−
3
and
x
≤
4
}
\newline
(C)
{
x
∣
x
<
−
3
and
x
>
4
}
\{x | x < -3 \text{ and } x > 4\}
{
x
∣
x
<
−
3
and
x
>
4
}
\newline
(D)
{
x
∣
x
>
−
3
and
x
<
4
}
\{x | x > -3 \text{ and } x < 4\}
{
x
∣
x
>
−
3
and
x
<
4
}
Get tutor help
What does the set
{
x
∣
x
≥
4
}
\{x | x \geq 4\}
{
x
∣
x
≥
4
}
represent?
\newline
Choices:
\newline
(A)all numbers less than or equal to
4
4
4
\newline
(B)all numbers less than
4
4
4
\newline
(C)all numbers greater than or equal to
4
4
4
\newline
(D)all numbers equal to
4
4
4
Get tutor help
What does the set
{
x
∣
x
≥
−
3
and
x
≤
7
}
\{x | x \geq -3 \text{ and } x \leq 7\}
{
x
∣
x
≥
−
3
and
x
≤
7
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than or equal to
−
3
-3
−
3
and greater than
7
7
7
\newline
(B)all numbers greater than or equal to
−
3
-3
−
3
and less than
7
7
7
\newline
(C)all numbers greater than or equal to
−
3
-3
−
3
and less than or equal to
7
7
7
\newline
(D)all numbers less than or equal to
−
3
-3
−
3
and greater than or equal to
7
7
7
Get tutor help
Which is the set of numbers greater than
14
14
14
?
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
14
}
\{x | x \geq 14\}
{
x
∣
x
≥
14
}
\newline
(B)
{
x
∣
x
≤
14
}
\{x | x \leq 14\}
{
x
∣
x
≤
14
}
\newline
(C)
{
x
∣
x
<
14
}
\{x | x < 14\}
{
x
∣
x
<
14
}
\newline
(D)
{
x
∣
x
>
14
}
\{x | x > 14\}
{
x
∣
x
>
14
}
Get tutor help
What does the set
{
x
∣
x
<
15
or
x
≥
19
}
\{x | x < 15 \text{ or } x \geq 19\}
{
x
∣
x
<
15
or
x
≥
19
}
represent?
\newline
Choices:
\newline
(A)all numbers less than
15
15
15
or greater than or equal to
19
19
19
\newline
(B)all numbers less than
15
15
15
or greater than
19
19
19
\newline
(C)all numbers greater than or equal to
15
15
15
or less than
19
19
19
\newline
(D)all numbers greater than or equal to
15
15
15
or less than or equal to
19
19
19
Get tutor help
Which is the set of numbers less than
−
12
-12
−
12
or greater than
3
3
3
?
\newline
Choices:
\newline
(A)
{
x
∣
x
<
−
12
or
x
>
3
}
\{x | x < -12 \text{ or } x > 3\}
{
x
∣
x
<
−
12
or
x
>
3
}
\newline
(B)
{
x
∣
x
>
−
12
or
x
<
−
3
}
\{x | x > -12 \text{ or } x < -3\}
{
x
∣
x
>
−
12
or
x
<
−
3
}
\newline
(C)
{
x
∣
x
≥
−
12
or
x
≤
−
3
}
\{x | x \geq -12 \text{ or } x \leq -3\}
{
x
∣
x
≥
−
12
or
x
≤
−
3
}
\newline
(D)
{
x
∣
x
≤
−
12
or
x
≥
−
3
}
\{x | x \leq -12 \text{ or } x \geq -3\}
{
x
∣
x
≤
−
12
or
x
≥
−
3
}
Get tutor help
Which is the set of numbers less than or equal to
4
4
4
or greater than
7
7
7
?
\newline
Choices:
\newline
(A)
{
x
∣
x
<
4
or
x
≥
7
}
\{x | x < 4 \text{ or } x \geq 7\}
{
x
∣
x
<
4
or
x
≥
7
}
\newline
(B)
{
x
∣
x
<
4
and
x
≥
7
}
\{x | x < 4 \text{ and } x \geq 7\}
{
x
∣
x
<
4
and
x
≥
7
}
\newline
(C)
{
x
∣
x
≤
4
or
x
>
7
}
\{x | x \leq 4 \text{ or } x > 7\}
{
x
∣
x
≤
4
or
x
>
7
}
\newline
(D)
{
x
∣
x
≤
4
or
x
<
7
}
\{x | x \leq 4 \text{ or } x < 7\}
{
x
∣
x
≤
4
or
x
<
7
}
Get tutor help
x
2
+
8
x
+
6
=
0
x^{2}+8 x+6=0
x
2
+
8
x
+
6
=
0
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
x
=
−
8
−
10
and
x
=
−
8
+
10
\begin{array}{l} x=-8-\sqrt{10} \text { and } \\ x=-8+\sqrt{10} \end{array}
x
=
−
8
−
10
and
x
=
−
8
+
10
\newline
(B)
\newline
x
=
−
8
−
7
and
x
=
−
8
+
7
\begin{array}{l} x=-8-\sqrt{7} \text { and } \\ x=-8+\sqrt{7} \end{array}
x
=
−
8
−
7
and
x
=
−
8
+
7
\newline
(C)
\newline
x
=
−
4
−
10
and
x
=
−
4
+
10
\begin{array}{l} x=-4-\sqrt{10} \text { and } \\ x=-4+\sqrt{10} \end{array}
x
=
−
4
−
10
and
x
=
−
4
+
10
\newline
(D)
\newline
x
=
−
4
−
7
and
x
=
−
4
+
7
\begin{array}{l} x=-4-\sqrt{7} \text { and } \\ x=-4+\sqrt{7} \end{array}
x
=
−
4
−
7
and
x
=
−
4
+
7
Get tutor help
z
=
−
24
−
12.7
i
z=-24-12.7 i
z
=
−
24
−
12.7
i
\newline
What are the real and imaginary parts of
z
z
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
Re
(
z
)
=
−
24
and
Im
(
z
)
=
−
12.7
\begin{array}{l} \operatorname{Re}(z)=-24 \text { and } \\ \operatorname{Im}(z)=-12.7 \end{array}
Re
(
z
)
=
−
24
and
Im
(
z
)
=
−
12.7
\newline
(B)
\newline
Re
(
z
)
=
−
24
and
Im
(
z
)
=
−
12.7
i
\begin{array}{l} \operatorname{Re}(z)=-24 \text { and } \\ \operatorname{Im}(z)=-12.7 i \end{array}
Re
(
z
)
=
−
24
and
Im
(
z
)
=
−
12.7
i
\newline
(C)
\newline
Re
(
z
)
=
−
12.7
and
Im
(
z
)
=
−
24
\begin{array}{l} \operatorname{Re}(z)=-12.7 \text { and } \\ \operatorname{Im}(z)=-24 \end{array}
Re
(
z
)
=
−
12.7
and
Im
(
z
)
=
−
24
\newline
(D)
\newline
Re
(
z
)
=
−
12.7
i
and
Im
(
z
)
=
−
24
\begin{array}{l} \operatorname{Re}(z)=-12.7 i \text { and } \\ \operatorname{Im}(z)=-24 \end{array}
Re
(
z
)
=
−
12.7
i
and
Im
(
z
)
=
−
24
Get tutor help
z
=
77
−
27.8
i
z=77-27.8 i
z
=
77
−
27.8
i
\newline
What are the real and imaginary parts of
z
z
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
Re
(
z
)
=
77
and
Im
(
z
)
=
−
27.8
\begin{array}{l} \operatorname{Re}(z)=77 \text { and } \\ \operatorname{Im}(z)=-27.8 \end{array}
Re
(
z
)
=
77
and
Im
(
z
)
=
−
27.8
\newline
(B)
\newline
Re
(
z
)
=
−
27.8
i
and
Im
(
z
)
=
77
\begin{array}{l} \operatorname{Re}(z)=-27.8 i \text { and } \\ \operatorname{Im}(z)=77 \end{array}
Re
(
z
)
=
−
27.8
i
and
Im
(
z
)
=
77
\newline
(C)
\newline
Re
(
z
)
=
−
27.8
and
Im
(
z
)
=
77
\begin{array}{l} \operatorname{Re}(z)=-27.8 \text { and } \\ \operatorname{Im}(z)=77 \end{array}
Re
(
z
)
=
−
27.8
and
Im
(
z
)
=
77
\newline
(D)
\newline
Re
(
z
)
=
77
and
Im
(
z
)
=
−
27.8
i
\begin{array}{l} \operatorname{Re}(z)=77 \text { and } \\ \operatorname{Im}(z)=-27.8 i \end{array}
Re
(
z
)
=
77
and
Im
(
z
)
=
−
27.8
i
Get tutor help
z
=
−
16
i
−
92.3
z=-16 i-92.3
z
=
−
16
i
−
92.3
\newline
What are the real and imaginary parts of
z
z
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
Re
(
z
)
=
−
92.3
and
Im
(
z
)
=
−
16
i
\begin{array}{l} \operatorname{Re}(z)=-92.3 \text { and } \\ \operatorname{Im}(z)=-16 i \end{array}
Re
(
z
)
=
−
92.3
and
Im
(
z
)
=
−
16
i
\newline
(B)
\newline
Re
(
z
)
=
−
92.3
and
Im
(
z
)
=
−
16
\begin{array}{l} \operatorname{Re}(z)=-92.3 \text { and } \\ \operatorname{Im}(z)=-16 \end{array}
Re
(
z
)
=
−
92.3
and
Im
(
z
)
=
−
16
\newline
(C)
\newline
Re
(
z
)
=
−
16
i
and
Im
(
z
)
=
−
92.3
\begin{array}{l} \operatorname{Re}(z)=-16 i \text { and } \\ \operatorname{Im}(z)=-92.3 \end{array}
Re
(
z
)
=
−
16
i
and
Im
(
z
)
=
−
92.3
\newline
(D)
\newline
Re
(
z
)
=
−
16
and
Im
(
z
)
=
−
92.3
\begin{array}{l} \operatorname{Re}(z)=-16 \text { and } \\ \operatorname{Im}(z)=-92.3 \end{array}
Re
(
z
)
=
−
16
and
Im
(
z
)
=
−
92.3
Get tutor help
A physicist measures the energies of atoms
A
A
A
and
B
B
B
to be the positive values
a
a
a
and
b
b
b
respectively. He determines that the energy of atom
B
B
B
is between one percent more than and one percent less than twice the energy of atom
A
A
A
. Which of the following systems of inequalities best models the possible range of values for the energies of atoms
A
A
A
and
B
B
B
?
\newline
Choose
1
1
1
answer:
\newline
(A)
{
a
<
2.02
b
a
>
1.98
b
\left\{\begin{array}{l}a<2.02 b \\ a>1.98 b\end{array}\right.
{
a
<
2.02
b
a
>
1.98
b
\newline
(B)
{
a
<
2
b
+
0.02
a
>
2
b
−
0.02
\left\{\begin{array}{l}a<2 b+0.02 \\ a>2 b-0.02\end{array}\right.
{
a
<
2
b
+
0.02
a
>
2
b
−
0.02
\newline
(C)
{
b
<
2.02
a
b
>
1.98
a
\left\{\begin{array}{l}b<2.02 a \\ b>1.98 a\end{array}\right.
{
b
<
2.02
a
b
>
1.98
a
\newline
(D)
{
b
<
2
a
+
0.02
b
>
2
a
−
0.02
\left\{\begin{array}{l}b<2 a+0.02 \\ b>2 a-0.02\end{array}\right.
{
b
<
2
a
+
0.02
b
>
2
a
−
0.02
Get tutor help
Which is the set of numbers less than
−
13
-13
−
13
?
\newline
Choices:
\newline
(A)
{
x
∣
x
=
−
13
}
\{x|x = -13\}
{
x
∣
x
=
−
13
}
\newline
(B)
{
x
∣
x
<
−
13
}
\{x|x < -13\}
{
x
∣
x
<
−
13
}
\newline
(C)
{
x
∣
x
>
−
13
}
\{x|x > -13\}
{
x
∣
x
>
−
13
}
\newline
(D)
{
x
∣
x
≤
−
13
}
\{x|x \leq -13\}
{
x
∣
x
≤
−
13
}
Get tutor help
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