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3 years ago

What is the width of a rug that is 36 1/4 square feet and 8 3/4 wide

Mathematics

1 answer:

blondinia [14]3 years ago

8 0

Answer: $4\frac{1}{7} ft$

<u>Step-by-step explanation:</u>

Area (A): $36\frac{1}{4} = \frac{4(36)+1}{4} = \frac{144+1}{4} = \frac{145}{4}$

Length (L): $8\frac{3}{4} = \frac{4(8)+3}{4} = \frac{32+3}{4} = \frac{35}{4}$

width (w): W

A = L x W

$\frac{145}{4}$ = $\frac{35}{4}$ x W

$(\frac{4}{35})$ $\frac{145}{4}$ = $(\frac{4}{35})$ $\frac{35}{4}$ x W

$\frac{4(145)}{35(4)} = \frac{145}{35} = \frac{5(29)}{5(7)} = \frac{29}{7} = W$

$\frac{29}{7} = \frac{7(4) + 1}{7} = 4\frac{1}{7}$

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1.How much taller Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall. 2.How many times as tall

EleoNora [17]

Answer:

Porter is $n-m$ inches taller than Henry.

Porter is $\frac{n}{m}$ times taller than henry.

Step-by-step explanation:

The difference in height can be found using subtraction.

Since Porter is taller than Henry, we'll subtract away Henry's height from Porter's height. This will leave us with only the difference between the heights.

n = Porter's height

m = Henry's height

Difference in height is thus:

$n-m$

Answer: Porter is $n-m$ inches taller than Henry.

To find out how many times taller Porter is than Henry, we can use division.

An example: if Porter was 200cm, and Henry was 100cm, Porter is obviously 2 times as tall.

If we divide Porter's height by Henry's height...

$\frac{200}{100}=2$

..we'll get 2. This is because Henry's height "fits in twice" in Porter's height. 100 fits twice in 200.

Using our values, n and m, we'll divide n by m.

$\frac{n}{m}$

Answer: Porter is $\frac{n}{m}$ times taller than henry.

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3 years ago

Work out the area of the shaded region.

Makovka662 [10]

Answer: Area of the shaded region is 6.867 square cm

Step-by-step explanation:

The shaded area corresponds to the difference of the area of the rectangle and the area of the semicircle.

Area of the rectangle = 4 times 8 = 32 cm^2

Area of the semicircle = 0.5 * pi * r^2 (where r is the radius, i.e., half of the diameters, i.e., 4 cm). So Area = 0.5*pi*4^2 = 25.133 cm^2

The difference: 32 - 25.133 = 6.867 cm^2 (area of the shaded region)

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Step-by-step explanation:

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