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3 years ago

12

Felix surrounds a 12 in. by 8 in. photo with a frame that is x inches wide. which quadratic function represents the combined are

a A of the picture and the frame?
A. A(x)=x^2+20x+96
B. A(x)=x^2+40x+96
C. A(x)=4x^2+20x+96
D. A(x)=4x^2+40x+96

1 answer:

Montano1993 [528]3 years ago

5 0

Answer:

Step-by-step explanation:

Total dimensions = (12+2x) inches by (8+2x) inches

A = (12+2x)(8+2x) = 4x² + 40x + 96

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Simplify the number into simplest radical form. Use the factor tree to help determine the factors. StartRoot 96 Endroot StartRoo

NikAS [45]

Answer:

$[tex]4608\sqrt{3}$ [/tex]

Step-by-step explanation:

1. $\sqrt{96} *\sqrt{6}* 2*\sqrt{6}*4 *\sqrt{6} *4*\sqrt{3}$

2. $\sqrt{2^{5} *3} \sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}$ <em>factoring 96</em>

<em>since $\sqrt{2^{5}*3 } = \sqrt{2^{5} } \sqrt{3}$ </em>

3. $\sqrt{2^{5} } \sqrt{3}\sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}$

<em>using exponent rule - $(a^{b}) ^{c} = a^{bc}$ </em>

<em> $\sqrt{2^{5} } = 2^{5/2}$ </em>

4. $2^{5/2}\sqrt{3}\sqrt{2*3} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}$

<em>doing some simple simplification and $4=2^{2}$ and 6=2*3</em>

5. $2^{5/2} \sqrt{3} \sqrt{2} \sqrt{3} *2\sqrt{2} \sqrt{3} *2^{2}\sqrt{2} \sqrt{3}*4\sqrt{3}$

<em>collecting the roots on one side and applying exponent rule</em>

6. $\sqrt{3} \sqrt{3}\sqrt{3} \sqrt{3}\sqrt{2} \sqrt{2}\sqrt{2} *2^{5/2+1+2+2} \sqrt{3}$

<em>Applying exponents rule on all $\sqrt{3}$ and $\sqrt{2}$ </em>

<em>7. $2^{1/2+1/2+1/2} *2^{5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}$ </em>

<em>combining all powers of 2</em>

8. $2^{1/2+1/2+1/2+5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}$

<em>Simplifying</em>

9. $2^{9} *3^{2}\sqrt{3}$

10. $512*9\sqrt{3}$

11. $4608\sqrt{3}$

3 0

3 years ago

Read 2 more answers

What is the average rate of change of the function over the interval x = 0 to x = 8?

Hatshy [7]

Answer:

if f(x) = 3x+4, the rate of change is 4.

if f(x) = 2x+7, the rate of change is 2.

Step-by-step explanation:

We know that the average rate of change over the interval x=0 to x=8 is:

(f(x2) - f(x1))/x2-x1

Where:

x2 = 8

x1 = 0

if f(x) = 3x+4

so f(8)=3(8)+4 = 28

f(0)=3(0)+4 = 4

Then: (f(x2) - f(x1))/x2-x1 = (28 - 4)/8-0 = 24/8 = 3

On the other hand, if f(x) = 2x+7

f(8) = 2(8)+7 = 23

f(0) = 2(0)+7 = 7

Then: (f(x2) - f(x1))/x2-x1 = Then: 23 - 7/8-0 = 16/8 = 2

8 0

3 years ago

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asambeis [7]

The answer is 24.10!!!

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3 years ago