Please help me!!! Will give 100 points. Will give BRAINILEST
2 answers:
Step-by-step explanation:
The shape of the new pizza must meet the conditions:
- Be an irregular polygon (different sides and/or angles).
- Have at least five sides.
- Have the approximately the same area as a 14" diameter circle.
- Fit in a 14⅛" × 14⅛" square.
- Be divisible into 8-12 equal pieces.
For simplicity, I will choose a polygon with 5 sides (a pentagon), and I will use 2 right angles (a "house" shape).
Split the pentagon into a rectangle on bottom and triangle on top. If we cut the rectangle into 8 pieces like a regular pizza, and the triangle in half, we get 10 triangles.
Now we just need to figure out the dimensions. The area of a 14" circular pizza is:
A = πr²
A = π (7 in)²
A ≈ 154 in²
That means the area of each triangle slice needs to be 15.4 in². If we make the total width of the pentagon 14", then the width of each triangle is 7", and the height of each triangle is:
A = ½ bh
15.4 in² = ½ (7 in) h
h = 4.4 in
Which makes the total height of the pentagon 3h = 13.2 in.
So, our 13.2" × 14" pentagon has at least 5 sides, is irregular, has the same area as a 14" diameter circle, fits in a 14⅛" × 14⅛" square, and can be divided into 8-12 equal pieces.
Of course, there are many possible solutions. This is just one way.
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Answer:
Step-by-step explanation:
…………………………
f(y) = x
⇔ 5y = x
We can make a proportion to represent the woods used. On the top is cedar, and on the bottom is the redwood. On the left is what was used the first time, on the right is the current problem.
Before making the proportion, let's do a preliminary step and write all the fractions as improper fractions. We do this because we can't directly multiply or divide mixed numbers, but we can with fractions.
<-- Multiply denominator times whole number and add the leftover fraction.
Now we set up the proportion. We solve it by cross multiplying.
It may seem right to simplify the right side, but let's leave it alone. We divide both sides by 19/2.
Dividing by a fraction means multiplying by its reciprocal. Thus,
Here's where not simplifying really pays off. We can simplify NOW and the terms go away more easily. The 19s go away and simplify to 1, and the 2 and 4 simplify to 1 and 2. All this happens by dividing out common numbers.
Now we multiply all the tops and all the bottoms.
R = 23 * 1 * 1 / 3 * 2 * 1
R = 23 / 6
While R is 23/6, we need to make it a mixed number. The way we made mixed numbers as improper fractions happens here, except in reverse.
23 ÷ 6 = 3 with a remainder of 5, as 3 × 6 + 5 = 23. Thus, .
As a result, feet of redwood is needed.