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4 years ago

5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of

Mathematics

1 answer:

devlian [24]4 years ago

5 0

Answer:

The angle of the slice is 63.64 degrees

Step-by-step explanation:

Here in this question, we are concerned with calculating the angle of the slice.

What we should know are as follows;

1. A pizza is a perfect circular shape

2. A 12-inch pizza means the diameter of the pizza is 12 inches and consequently its radius will be 12/2 = 6 inches

3. A slice of a pizza represents a sector of the circle( a sector is part of a circle bounded by 2 radii and an arc)

Mathematically, to calculate the angle of the slice, we simply use the formula for the area of a sector.

Area of sector = theta/360 * pi * r^2

where Area of sector = 20 square inches

theta is the center angle we are looking for

r is the radius of the pizza which is 6 inches

Plugging these values into the area of sector equation, we have

20 = theta/360 * 22/7 * 6^2

20 = theta/10 * 22/7

22 theta = 10 * 20 * 7

theta = 1400/22

theta = 63.64 degrees which is approximately 64 degrees to the nearest degree

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The order in which the tiles are chosen is not important, hence the <em>combination formula</em> is used to solve this question.

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2 years ago

A store has a pair of pants marked $39.99 with a 40% off tag. What is the sale price of the pants?

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3 years ago

-3x - 3y = 3, -5x + y =13<br> System of Equations

Nataliya [291]

Answer:

( $\frac{-7}{3}$ , $\frac{4}{3}$ )

Step-by-step explanation:

Hi there!

We are given the following system of equations:

-3x-3y=3

-5x+y=13

and we need to find the solution (the point at which the 2 lines intersect)

let's solve this by substitution, where we will set one variable equal to an expression containing the other variable, and then substitute that expression into the other equation to solve for the variable that the expression from earlier contains, and then use the value of the solved variable to find the value of the first variable

in the second equation, add 5x to both sides to isolate y by itself

y=5x+13

now substitute 5x+13 as y in -3x-3y=3

-3x-3(5x+13)=3

do the distributive property

-3x-15x-39=3

combine like terms

-18x-39=3

add 39 to both sides

-18x=42

divide both sides by -18

x= $\frac{-7}{3}$

now we need to find y

remember: y=5x+13

substitute $\frac{-7}{3}$ as x in y=5x+13

y=5( $\frac{-7}{3}$ )+13

multiply

y= $\frac{-35}{3}$ +13

add

y= $\frac{4}{3}$

So the answer is x= $\frac{-7}{3}$ , y= $\frac{4}{3}$ . As a point, it's ( $\frac{-7}{3}$ , $\frac{4}{3}$ )

Hope this helps! :)

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3 years ago