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.
Answer:
5x +3
Step-by-step explanation:
f(x) = 2x-6
g(x) = 3x+9
(f+g) (x) = 2x-6+ 3x+9
Combine like terms
= 5x +3
Let us take 'a' in the place of 'y' so the equation becomes
(y+x) (ax+b)
Step-by-step explanation:
<u>Step 1:</u>
(a + x) (ax + b)
<u>Step 2: Proof</u>
Checking polynomial identity.
(ax+b )(x+a) = FOIL
(ax+b)(x+a)
ax^2+a^2x is the First Term in the FOIL
ax^2 + a^2x + bx + ab
(ax+b)(x+a)+bx+ab is the Second Term in the FOIL
Add both expressions together from First and Second Term
= ax^2 + a^2x + bx + ab
<u>Step 3: Proof
</u>
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
Identity is Found
.
Trying with numbers now
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)
((10)+8)(7) =(2*25)+(4*5)+(40)+(16)
(18)(7) =(50)+(20)+(56)
126 =126
Answer:
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