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Math Problems
Algebra 1
Negative exponents
Find the average value of the function
f
(
x
)
=
3
9
−
4
x
f(x)=\frac{3}{9-4 x}
f
(
x
)
=
9
−
4
x
3
from
x
=
3
x=3
x
=
3
to
x
=
6
x=6
x
=
6
. Express your answer as a constant times
ln
5
\ln 5
ln
5
.
\newline
Answer:
□
ln
5
\square\ln 5
□
ln
5
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Write the expression
−
ln
2
+
3
-\ln 2+3
−
ln
2
+
3
as a single logarithm in simplest form without any negative exponents.
\newline
Answer:
ln
(
□
)
\ln (\square)
ln
(
□
)
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A baby mango tree stands
2
2
2
.
6
6
6
meters above the ground. Its roots extend
7
5
\frac{7}{5}
5
7
meters below the ground.
\newline
Which
2
2
2
of the following expressions represents the vertical distance between the top of the mango tree and the tips of its roots?
\newline
Choose
2
2
2
answers:
\newline
(A)
∣
−
7
5
−
2.6
∣
\left|-\frac{7}{5}-2.6\right|
∣
∣
−
5
7
−
2.6
∣
∣
\newline
(B)
∣
2.6
+
7
5
∣
\left|2.6+\frac{7}{5}\right|
∣
∣
2.6
+
5
7
∣
∣
\newline
(C)
∣
2.6
−
7
5
∣
\left|2.6-\frac{7}{5}\right|
∣
∣
2.6
−
5
7
∣
∣
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Jonael dropped a sandbag from a hot air balloon at a target that is
250
250
250
meters below the balloon. At this moment, the sandbag is
75
75
75
meters below the balloon.
\newline
Which
2
2
2
of the following expressions represents the distance between the sandbag and the target?
\newline
Choose
2
2
2
answers:
\newline
(A)
∣
−
250
+
75
∣
|-250+75|
∣
−
250
+
75∣
\newline
(B)
∣
250
+
75
∣
|250+75|
∣250
+
75∣
\newline
(C)
∣
−
75
+
250
∣
|-75+250|
∣
−
75
+
250∣
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Order the following numbers from least to greatest.
\newline
Put the least number on the left.
\newline
1
−
8
4
−
4.5
4
8
1 \quad -\frac{8}{4} \quad -4.5 \quad \frac{4}{8}
1
−
4
8
−
4.5
8
4
Get tutor help
Evaluate the expression.
\newline
Do not round your answer.
\newline
(
2
⋅
3
)
2
−
5
2
=
(2 \cdot 3)^{2}-5^{2}=
(
2
⋅
3
)
2
−
5
2
=
Get tutor help
Evaluate the expression.
\newline
Do not round your answer.
\newline
2
(
1
3
2
)
=
2\left(\frac{1}{3^{2}}\right)=
2
(
3
2
1
)
=
Get tutor help
Evaluate the expression.
\newline
Do not round your answer.
\newline
1
2
(
4
⋅
5
)
−
2
3
=
\frac{1}{2}(4 \cdot 5)-2^{3}=
2
1
(
4
⋅
5
)
−
2
3
=
Get tutor help
Evaluate the expression. Do not round your answer.
\newline
(
1
9
−
2
)
2
=
\left(\frac{1}{9-2}\right)^{2}=
(
9
−
2
1
)
2
=
Get tutor help
Evaluate the expression.
\newline
Do not round your answer.
\newline
5
−
3
2
2
=
5-\frac{3^{2}}{2}=
5
−
2
3
2
=
Get tutor help
Evaluate the expression.
\newline
Do not round your answer.
\newline
1
4
(
2
3
+
4
2
)
=
\frac{1}{4}\left(2^{3}+4^{2}\right)=
4
1
(
2
3
+
4
2
)
=
Get tutor help
Evaluate the expression. Do not round your answer.
\newline
1
4
(
6
+
3
+
1
)
2
=
\frac{1}{4}(6+3+1)^{2}=
4
1
(
6
+
3
+
1
)
2
=
Get tutor help
Evaluate the expression. Do not round your answer.
\newline
(
2
⋅
3
)
2
+
5
2
=
(2 \cdot 3)^{2}+5^{2}=
(
2
⋅
3
)
2
+
5
2
=
Get tutor help
Evaluate the expression. Do not round your answer.
\newline
1
3
(
4
⋅
3
)
+
2
3
=
\frac{1}{3}(4 \cdot 3)+2^{3}=
3
1
(
4
⋅
3
)
+
2
3
=
Get tutor help
Evaluate the expression.
\newline
Do not round your answer.
\newline
2
(
3
2
+
4
2
)
=
2\left(3^{2}+4^{2}\right)=
2
(
3
2
+
4
2
)
=
Get tutor help
Evaluate the expression. Do not round your answer.
\newline
(
1
+
3
9
)
2
=
\left(\frac{1+3}{9}\right)^{2}=
(
9
1
+
3
)
2
=
Get tutor help
Order the expressions from least to greatest.
\newline
5
2
4
2
+
2
2
6
2
−
6
5^{2} \quad 4^{2}+2^{2} \quad 6^{2}-6
5
2
4
2
+
2
2
6
2
−
6
Get tutor help
Evaluate the expression. Do not round your answer.
\newline
1
5
(
3
+
2
+
5
)
2
=
\frac{1}{5}(3+2+5)^{2}=
5
1
(
3
+
2
+
5
)
2
=
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6
4
27
3
\sqrt[3]{64^{27}}
3
6
4
27
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
3
4^{3}
4
3
\newline
(B)
6
4
3
64^{3}
6
4
3
\newline
(C)
8
18
8^{18}
8
18
\newline
(D)
6
4
24
64^{24}
6
4
24
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(
x
−
10
)
2
(x-10)^{2}
(
x
−
10
)
2
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
2
+
100
x^{2}+100
x
2
+
100
\newline
(B)
2
x
2
−
20
x
+
100
2 x^{2}-20 x+100
2
x
2
−
20
x
+
100
\newline
(C)
x
2
−
20
x
+
100
x^{2}-20 x+100
x
2
−
20
x
+
100
\newline
(D)
x
2
−
20
x
−
20
x^{2}-20 x-20
x
2
−
20
x
−
20
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What is the value of
tan
(
22
5
∘
)
?
\tan \left(225^{\circ}\right) ?
tan
(
22
5
∘
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
2
2
-\frac{\sqrt{2}}{2}
−
2
2
\newline
(C)
2
2
\frac{\sqrt{2}}{2}
2
2
\newline
(D)
1
1
1
Get tutor help
Which of the following is equal to
x
(
x
2
+
9
)
x\left(x^{2}+9\right)
x
(
x
2
+
9
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
2
+
x
+
9
x^{2}+x+9
x
2
+
x
+
9
\newline
(B)
x
2
+
9
x
x^{2}+9 x
x
2
+
9
x
\newline
(C)
x
3
+
9
x^{3}+9
x
3
+
9
\newline
(D)
x
3
+
9
x
x^{3}+9 x
x
3
+
9
x
Get tutor help
Which of the following is equivalent to
2
x
2
(
x
−
2
)
2 x^{2}(x-2)
2
x
2
(
x
−
2
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
3
−
2
2 x^{3}-2
2
x
3
−
2
\newline
(B)
2
x
3
−
2
x
2
2 x^{3}-2 x^{2}
2
x
3
−
2
x
2
\newline
(C)
2
x
3
−
2
x
2
−
2
2 x^{3}-2 x^{2}-2
2
x
3
−
2
x
2
−
2
\newline
(D)
2
x
3
−
4
x
2
2 x^{3}-4 x^{2}
2
x
3
−
4
x
2
Get tutor help
2
203
+
2
204
2^{203}+2^{204}
2
203
+
2
204
\newline
Which of the following values is equal to the value?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
407
2^{407}
2
407
\newline
(B)
3
(
2
203
)
3\left(2^{203}\right)
3
(
2
203
)
\newline
(C)
3
(
2
204
)
3\left(2^{204}\right)
3
(
2
204
)
\newline
(D)
2
202
+
2
205
2^{202}+2^{205}
2
202
+
2
205
Get tutor help
x
2
−
36
x^{2}-36
x
2
−
36
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
x
−
6
)
2
(x-6)^{2}
(
x
−
6
)
2
\newline
(B)
(
x
+
6
)
2
(x+6)^{2}
(
x
+
6
)
2
\newline
(C)
(
x
−
6
)
(
x
+
6
)
(x-6)(x+6)
(
x
−
6
)
(
x
+
6
)
\newline
(D)
x
(
x
−
36
)
x(x-36)
x
(
x
−
36
)
Get tutor help
(
n
6
k
14
)
5
\left(n^{6} k^{14}\right)^{5}
(
n
6
k
14
)
5
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
n
2
k
5
)
3
\left(n^{2} k^{5}\right)^{3}
(
n
2
k
5
)
3
\newline
(B)
(
n
3
)
10
(
k
2
)
7
\left(n^{3}\right)^{10}\left(k^{2}\right)^{7}
(
n
3
)
10
(
k
2
)
7
\newline
(C)
(
n
15
k
35
)
2
\left(n^{15} k^{35}\right)^{2}
(
n
15
k
35
)
2
\newline
(D)
(
n
5
)
5
(
k
10
)
7
\left(n^{5}\right)^{5}\left(k^{10}\right)^{7}
(
n
5
)
5
(
k
10
)
7
Get tutor help
Which is equal to
9
−
61
9^{-61}
9
−
61
?
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