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Math Problems
Grade 6
Powers with fractional bases
Determine if the following ordered pairs are
s
s
s
Show the math below and write
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x
+
4
5
=
12
\frac{x+4}{5}=12
5
x
+
4
=
12
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3
3
3
Write each number as a power of
5
5
5
.
\newline
a
0
0
0
.
2
2
2
\newline
b
25
25
25
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Write each number as a power of
5
5
5
.
\newline
a
0
0
0
.
2
2
2
\newline
b
25
25
25
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2
y
+
4
=
x
+
y
+
6
2 y+4=x+y+6
2
y
+
4
=
x
+
y
+
6
\newline
Which of the following is the graph of the given equation in the
x
y
x y
x
y
-plane?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
(B)
\newline
(C)
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Suppose that one selects some subset of integers from the set
{
0
,
1
,
2
,
…
,
44
}
\{0,1,2, \ldots, 44\}
{
0
,
1
,
2
,
…
,
44
}
. What is the smallest number to select to guarantee that two of the selected numbers sum to
44
44
44
?
\newline
Answer:
\newline
23
23
23
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10
10
10
)
3
4
=
10
k
\frac{3}{4}=\frac{10}{k}
4
3
=
k
10
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31
b
\frac{31}{b}
b
31
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Find the value of
b
b
b
and simplify your answer.
\newline
4
3
b
=
10
\frac{4}{3}b=10
3
4
b
=
10
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w
=
3.1
+
l
2
w=3.1+\frac{l}{2}
w
=
3.1
+
2
l
\newline
The weight,
w
w
w
, in ounces, of a glass soda bottle design with a side length of
l
l
l
inches is given by the equation. By how many ounces does the weight of the bottle increase for every inch of increase in the side length?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.5
0.5
0.5
\newline
(B)
2
2
2
\newline
(C)
3.1
3.1
3.1
\newline
(D)
3.6
3.6
3.6
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(
0
0
0
)
\newline
y
=
5
3
x
y=\frac{5}{3}x
y
=
3
5
x
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Solve the equation. Check your solution.
\newline
−
5
(
5
n
−
5
)
=
30
-5(5 n-5)=30
−
5
(
5
n
−
5
)
=
30
\newline
The solution set is (Type an integer or a simplified fract
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1
3
\frac{1}{3}
3
1
of
3
3
3
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a
7
=
5
\frac{a}{7}=5
7
a
=
5
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
5
2
−
3
\frac{\frac{5}{2}}{-3}
−
3
2
5
\newline
Answer:
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Solve for
n
n
n
and simplify your answer.
\newline
3
5
n
=
−
10
\frac{3}{5} n=-10
5
3
n
=
−
10
\newline
Answer:
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Solve for
w
w
w
and simplify your answer.
\newline
4
3
w
=
−
2
\frac{4}{3} w=-2
3
4
w
=
−
2
\newline
Answer:
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Solve for
a
a
a
and simplify your answer.
\newline
2
5
a
=
10
\frac{2}{5} a=10
5
2
a
=
10
\newline
Answer:
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A landscaping company sells bags that hold up to
2.3
cubic feet
(
ft
3
)
2.3 \text{ cubic feet } (\text{ft}^{3})
2.3
cubic feet
(
ft
3
)
of mulch. The company guarantees that there is at least
2
ft
3
2\text{ft}^{3}
2
ft
3
of mulch inside each bag. Which of the following functions gives the nonnegative difference between the maximum and minimum mulch volumes, in cubic feet, that could be contained in
b
b
b
bags purchased from the landscaping company?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
b
)
=
0.3
b
f(b)=0.3b
f
(
b
)
=
0.3
b
\newline
(B)
f
(
b
)
=
2
b
f(b)=2b
f
(
b
)
=
2
b
\newline
(C)
f
(
b
)
=
2.3
b
f(b)=2.3b
f
(
b
)
=
2.3
b
\newline
(D)
f
(
b
)
=
4.3
b
f(b)=4.3b
f
(
b
)
=
4.3
b
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Ari thinks the perfect milkshake has
5
5
5
scoops of ice cream for every
3
3
3
spoonfuls of caramel. Freeze Zone makes batches of milkshakes with
10
10
10
scoops of ice cream and
7
7
7
spoonfuls of caramel.
\newline
What will Ari think about the amount of caramel in Freeze Zone's milkshakes?
\newline
Choose
1
1
1
answer:
\newline
(A) Freeze Zone's milkshakes have too much caramel.
\newline
(B) Freeze Zone's milkshakes have too little caramel.
\newline
(C) Freeze Zone's milkshakes are just right.
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