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3 years ago

What is the distributive property of the GCF of 36 and 45 to rewrite the sum

Mathematics

1 answer:

Nataliya [291]3 years ago

4 0

Answer:

9(4 + 5)

Step-by-step explanation:

The GCF of 36 and 45 is

36: 2 * 2 * 3 * 3

45: 3 * 3 * 5

The GCF of 45 and 36 is 9 (the bolded part)

9(4 + 5) would be how the distributive property would be written. The numbers inside the brackets represent what is not bolded.

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Fynjy0 [20]

Answer:

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Step-by-step explanation:

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3 years ago

8.2<br> 5. In a '70% off' sale, a hat was £33.60.<br> Work out the original price.

Aleks [24]

100% - 70% = 30%

30% of what = £33.60?

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0.30p = 33.60

p = 33.60 ÷ 0.30

p = £112

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3 years ago

Can you solely rely on induction to prove that your conclusion is correct

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3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$