Answer:
n=288
Step-by-step explanation:
Rewrite the equation as
√
n
=
18
√
8
−
8
√
18
.
√
n
=
18
√
8
−
8
√
18
To remove the radical on the left side of the equation, square both sides of the equation.
√n
2
=
(
18
√
8
−
8
√
18
)
2
Simplify each side of the equation.
Use
n
√
a
x
=
a
x
n
to rewrite
√
n as n
1
2
.
(
n
1
2
)
2
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
n
1
2
)
2
.
Multiply the exponents in
(
n
1
2
)
2
.
Apply the power rule and multiply exponents,
(
a
m)n
=
a
m
n
.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Cancel the common factor of 2
Cancel the common factor.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Rewrite the expression.
n
1
=
(
18
√
8
−
8
√
18
)
2
Simplify.
n
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
18
√
8
−
8
√
18
)
2
Simplify each term.
Rewrite
8 as 2
2
⋅
2
.
Factor
4 out of 8
n
=
(
18
√
4
(
2
)
−
8
√
18
)
2
Rewrite
4 as 2
2
n
=
(
18√
2
2
2
−
8
√
18
)
2
Pull terms out from under the radical.
n
=
(
18
(
2
√
2
)
−
8
√
18
)
2
Multiply
2 by 18
n
=
(
36
√
2
−
8
√
18
)
2
Rewrite
18
as
3
2
⋅
2
.
Factor
9
out of
18
.
n
=
(
36
√
2
−
8
√
9
(
2
)
)
2
Rewrite
9
as
3
2
.
n
=
(
36
√
2
−
8
√
3
2
⋅
2
)
2
Pull terms out from under the radical.
n
=
(
36
√
2
−
8
(
3
√
2
)
)
2
Multiply
3
by
−
8
.
n
=
(
36
√
2
−
24
√
2
)
2
Simplify terms.
Subtract
24
√
2
from
36
√
2
.
n
=
(
12
√
2
)
2
Simplify the expression.
Apply the product rule to
12
√
2
.
n
=
12
2
√
2
2
Raise
12
to the power of
2
.
n
=
144
√
2
2
Rewrite
√
2
2
as
2
.
Use
n
√
a
x
=
a
x
n
to rewrite
√
2
as
2
1
2
.
n
=
144
(
2
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
n
=
144
⋅
2
1
2
⋅
2
Combine
1
2
and
2
.
n
=
144
⋅
2
2
2
Cancel the common factor of
2
.
Cancel the common factor.
n
=
144
⋅
2
2
2
Rewrite the expression.
n
=
144
⋅
2
1
Evaluate the exponent.
n
=
144
⋅
2
Multiply
144
by
2
.
n
=
288
Answer:
He made approximately 32 free throws.
Step-by-step explanation:
Assuming that there's a typo in the question and that he made 57% of his attempted free throws, then we can solve it as shown below:
We can apply a rule of three in order to calculate the number of free throws he made. This is done as follows:
56 free throws -> 100%
x free throws -> 57%
56/x = 100/57
100*x = 57*56
x = 57*56/100 = 31.92
It can also be solved by transforming the percentage in a fraction such as 57% = 57/100 and then multiplying it by the total attempts.
free throws made = 56*57/100 = 31.92
He made approximately 32 free throws.
Answer:
The correct answer is B. The rate of change is about 3 feet per minute
I hope this helped!
