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Step2247 [10]
3 years ago
7

If a pizza with a diameter of 12 inches costs $10.99, based on area, about how much should a 15-inch pizza cost?

Mathematics
1 answer:
Dafna1 [17]3 years ago
5 0

Answer:

Area of a circle=πr^2

12 inch pizza

π(6^2)≈113.04in^2

15 inch pizza

π(7.5^2)≈176.625in^2

Now we turn this into a fraction, and solve the problem:

113.04/10.99=176.625/x

113.04x=1941.10875 <-------Division property of equality

x=17.171875.

The cost of a 15 inch diameter pizza is $17.17

Hope this helped.

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The length of a rectangle is 5 more than the width. Find the length and width of a rectangle if the area of the rectangle is 36
harkovskaia [24]

Answer:

width = 4 in

length = 9 in

Step-by-step explanation:

To solve this problem, write an expression for the length and use the area of a rectangle formula.

The formula for area of a triangle is A = lw

"A" is the area.

"l" is the length.

"w" is the width.

"The length of a rectangle is 5 more than the width". It is represented in an expression:

l = w + 5     The width plus 5 is the length.

We also know the area is 36 in². Using information we know, replace variables in the formula for area of a rectangle.

Substitute l = w + 5 and A = 36

A = lw

36 = (w + 5)w     Expand by multiplying w by the terms in the brackets.

36 = w² + 5w      Since the equation is quadratic, make it equate to 0.

36 - 36 = w² + 5w - 36   Subtract 36 from both sides

0 = w² + 5w - 36      Factor this. Use group factoring, which is when you replace the middle term (5w) with two terms that add to make 5w, and multiply to get the last term (-36).

0 = w² + 9w - 4w - 36      9w times -4w is -36. They also add to get 5w.

0 = (w² + 9w) + (-4w - 36)  Group the factors

0 = w(w + 9) + -4(w + 9)   Take out the common factor in each group.

0 = w(w + 9) + -4(w + 9)   Take out the new common factor binomial w+9

0 = (w + 9) (w - 4)    Fully factored equation.

w + 9 = 0       w - 4 = 0    Set each binomial to equal 0.

     w = -9            w = 4   Chose what makes sense to be the width.

The width cannot be a negative number, so the width is 4.

Since we know the width, we can find the length because the length is 5 more than the width.

l = w + 5

l = 4 + 5

l = 9      Length of the rectangle

Don't forget to include the units, inches.

Therefore the length is 9 inches and the width is 4 inches.

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2 years ago
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Answer:

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Step-by-step explanation:

The solution is where the lines intersect which is at the point (3,2).

So the answer is Option D.

The point (3,2) satisfies both equations.

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