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3 years ago

How to make an improper fraction into a proper fraction?

1 answer:

7 0

Divide the numerator by the denominator and any remaining values go back above the denominator.

Example:

17 / 4 is an improper fraction. To turn it into a proper fraction we do 17 divided by 4.

17 / 4 is 4 with a remainder of 4. So we put the 4 on the outside and the 1 back above the denominator, which is 4.

It ends up looking like this: $\frac{17}{4} = 4 \frac{1}{4}$

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A square napkin is folded in half on the diagonal and placed on the diameter of a round plate (see diagram below). If the folded

Crank

Answer:

$A=81(\pi-1)\ in^2$

Step-by-step explanation:

step 1

Find the area of the plate

The area of a circle is given by the formula

$A=\pi r^{2}$

we have

$r=18/2=9\ in$ ---> the radius is half the diameter

substitute

$A=\pi (9)^{2}\\A=81\pi\ in^2$

step 2

Find the area of the square napkin folded (is a half of the area of the square napkin)

we know that

The diagonal of the square is the same that the diameter of the plate

Applying Pythagorean theorem

$D^2=2b^2$

where

b is the length side of the square

we have

$D=18\ in$

substitute

$18^2=2b^2$

solve for b^2

$b^2=162\ in^2$ -----> is the area of the square

Divide by 2

$162/2=81\ in^2$

step 3

Find the area of the space on the plate that is NOT covered by the napkin

we know that

The area of the space on the plate that is NOT covered by the napkin, is equal to subtract the area of the square napkin folded (is a half of the area of the square napkin) from the area of the plate

$A=(81\pi-81)\ in^2$

simplify

$A=81(\pi-1)\ in^2$

8 0

3 years ago

Which expressions are completely factored? Select each correct answer. 32y10−24=8(4y10−3) 18y3−6y=3y(6y2−2) 16y5+12y3=4y3(4y2+3)

laila [671]

Answer:

Option A and Option C

Step-by-step explanation:

Option A: $32y^{10}-24 = 8(4y^{10}-3)$ This is completely factored as 8 is the Highest Common Monomial factor

Option B: $18y^{3}-6y = 3y(6y^{2}-2)$ This is not completely factored as 2 is still a common factor of 6y2 and -2.

Option C: $16y^{5}+12y^{3}=4y^{3}(4y^{2}+3)$ This is completely factored as 4y2 is the Highest Common Monomial factor

Option D: $20y^{7}+10y^{2} = 5y(4y^{6}+2y)$ This is not completely factored as 2y is still a common factor of 4y6 and 2y.

So the options that are completely factored are Option A and Option C

3 0

3 years ago

make m the subject!

Xelga [282]

How to:
a+b-mx=0
a+b=mx
(a+b)/x=m

7 0

2 years ago

A portion of the graph of f(x) = −x2 + 6x − 5 is shown. Which of the following describes all solutions for f(x)? a partial parab

marishachu [46]

Answer:

Step-by-step explanation:

7 0

3 years ago

The cost of renting a moving van for a 26 mile trip is $62.50. the cost of renting the same van for a 38 mile trip is $65.50 The

Darya [45]

The difference between the 26 mile trip and 38 mile trip is 12 miles.
The difference in the price is $3.00 ($65.50 - $62.50)

So those 12 miles cost $3.00 $3.00÷12 = $.25 per mile

We can use either given trip to solve. I will use the 38 mile trip.
The difference between 38 miles and 54 miles is 16 miles. At $.25 a mile those 16 miles will add $4.00 to the price. ($.25 x 16 = $4.00)
Since the 38 mile trip costs $65.50 we add $4.00 and get $69.50 for a 54 mile trip.

5 0

3 years ago