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Math Problems
Algebra 1
Unions and intersections of sets
If
x
2
+
6
x
−
5
=
0
x^{2}+6 x-5=0
x
2
+
6
x
−
5
=
0
, what are the values of
x
x
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
−
14
-3-\sqrt{14}
−
3
−
14
and
−
3
+
14
-3+\sqrt{14}
−
3
+
14
\newline
(B)
3
−
14
3-\sqrt{14}
3
−
14
and
3
+
14
3+\sqrt{14}
3
+
14
\newline
(C)
−
1
-1
−
1
and
−
5
-5
−
5
\newline
(D)
1
1
1
and
5
5
5
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What is the product of
6
,
x
2
−
3
x
6, x^{2}-3 x
6
,
x
2
−
3
x
, and
x
−
10
x-10
x
−
10
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
42
x
+
180
-42 x+180
−
42
x
+
180
\newline
(B)
6
x
2
−
78
x
+
180
6 x^{2}-78 x+180
6
x
2
−
78
x
+
180
\newline
(C)
6
x
3
−
42
x
2
+
180
x
6 x^{3}-42 x^{2}+180 x
6
x
3
−
42
x
2
+
180
x
\newline
(D)
6
x
3
−
78
x
2
+
180
x
6 x^{3}-78 x^{2}+180 x
6
x
3
−
78
x
2
+
180
x
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If
x
+
y
=
−
4
x+y=-4
x
+
y
=
−
4
and
x
−
y
=
2
x-y=2
x
−
y
=
2
, what is the value of
(
x
+
y
)
(
x
2
−
y
2
)
?
(x+y)\left(x^{2}-y^{2}\right) ?
(
x
+
y
)
(
x
2
−
y
2
)
?
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If
f
(
x
)
=
3
x
−
1
f(x)=3 x-1
f
(
x
)
=
3
x
−
1
and
g
(
x
)
=
x
2
+
1
g(x)=x^{2}+1
g
(
x
)
=
x
2
+
1
, what is the value of
g
(
f
(
3
)
)
g(f(3))
g
(
f
(
3
))
?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
8
8
\newline
(B)
10
10
10
\newline
(C)
29
29
29
\newline
(D)
65
65
65
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3
−
m
=
2
(
ℓ
−
4
)
m
=
ℓ
−
4
\begin{array}{c} 3-m=2(\ell-4) \\ m=\ell-4 \end{array}
3
−
m
=
2
(
ℓ
−
4
)
m
=
ℓ
−
4
\newline
Consider the given system of equations. If
(
ℓ
,
m
)
(\ell, m)
(
ℓ
,
m
)
is the solution to the system, then what is the value of
ℓ
⋅
m
\ell \cdot m
ℓ
⋅
m
?
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If
2
+
2
(
8347
−
4783
)
=
−
2
j
2+2(8347-4783)=-2 j
2
+
2
(
8347
−
4783
)
=
−
2
j
, then what is the value of
−
j
-j
−
j
?
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What is the value of
y
2
−
x
4
y^{2}-x^{4}
y
2
−
x
4
when
y
=
8
y=8
y
=
8
and
x
=
2
x=2
x
=
2
?
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What is the value of
y
2
−
x
2
y^{2}-x^{2}
y
2
−
x
2
when
x
=
5
x=5
x
=
5
and
y
=
6
y=6
y
=
6
?
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What is the value of
x
6
+
y
2
x^{6}+y^{2}
x
6
+
y
2
when
x
=
1
x=1
x
=
1
and
y
=
9
y=9
y
=
9
?
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Which of the following expressions is equivalent to
\newline
106
×
3.7
106 \times 3.7
106
×
3.7
?
\newline
Choose
1
1
1
answer:
\newline
(A)
106
×
37
÷
10
106 \times 37 \div 10
106
×
37
÷
10
\newline
(B)
106
×
37
÷
100
106 \times 37 \div 100
106
×
37
÷
100
\newline
(C)
106
×
37
÷
1
,
000
106 \times 37 \div 1,000
106
×
37
÷
1
,
000
\newline
(D)
106
×
37
÷
10
,
000
106 \times 37 \div 10,000
106
×
37
÷
10
,
000
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Let
R
=
{
−
4
,
4
,
14
}
R = \{-4, 4, 14\}
R
=
{
−
4
,
4
,
14
}
and
S
=
{
2
,
12
}
S = \{2, 12\}
S
=
{
2
,
12
}
. What is
R
∪
S
R \cup S
R
∪
S
?
\newline
Choices:
\newline
(A)
{
−
4
,
2
,
4
,
12
,
14
}
\{-4,2,4,12,14\}
{
−
4
,
2
,
4
,
12
,
14
}
\newline
(B)
Φ
\Phi
Φ
\newline
(C)
{
2
,
4
,
12
}
\{2, 4, 12\}
{
2
,
4
,
12
}
\newline
(D)
{
−
4
,
2
}
\{-4, 2\}
{
−
4
,
2
}
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