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3 years ago

Use the product property of exponents to justify that (9^1/2)^2=9

Mathematics

1 answer:

WARRIOR [948]3 years ago

6 0

The rule states that

$(a^b)^c = a^{bc}$

So, in your case, you have

$(9^{\frac{1}{2}})^2=9^{\frac{1}{2}\cdot 2}=9^1=9$

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The triangles at right are similar what is the value of x

Ilya [14]

Answer:

must remember triangle interior angle is 180.

and they said the triangle is similar so they have similar angle

180-95-58=27

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3 years ago

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3 years ago

Did I do this correctly?

butalik [34]

6/x= -2/18

Cross multiply. ( Multiply the numerators together ) . ( Multiply the denominators together (.

6*18= - 2*x

108= -2x

Divide by -2 for 108 and -2x

108/-2= -2x/2

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3 years ago

2. The rectangular floor of a garage has an area of 198 square feet. Andy knows that the floor is 7

Charra [1.4K]

Answer:

length = 18 ft

Step-by-step explanation:

Let w = width

L = w+7

Area = l*w

198 = (w+7) (w)

Distribute

198 = w^2 +7w

Subtract 198 from each side

0 = w^2 +7w -198

Factor

What 2 numbers multiply to -198 and add to 7

18* -11 = -198

18+-11 = 7

0=(w+18) (w-11)

Using the zero product property

w+18 =0 w-11=0

w= -18 w=11

We cannot have negative width so w=11

We want the length

l = w+7

l = 11+7 = 18

6 0

3 years ago

Conplete the square to solve the quadratic equation. x<br><img src="https://tex.z-dn.net/?f=1%20%7Bx%7D%5E%7B2%7D%20%20-%206x%20

o-na [289]

Answer:

$\large\boxed{x=4\pm2\sqrt6}$

Step-by-step explanation:

$x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm\sqrt{24}\\\\x-4=\pm\sqrt{4\cdot6}\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6$

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3 years ago