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konstantin123 [22]
3 years ago
11

3. Find the dimensions of the

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
4 0

Answer:

16 ft, 8 ft

Step-by-step explanation:

Area of rectangle = 128 Sq ft

(x + 7)(x - 1) = 128 \\  \\  {x}^{2}  - x + 7x - 7 = 128 \\  \\  {x}^{2}  + 6x - 7 - 128 = 0 \\  \\  {x}^{2}  + 6x - 135 = 0 \\  \\  {x}^{2}  + 15x - 9x - 135 = 0 \\  \\ x(x + 15) - 9(x + 15) = 0 \\  \\ (x + 15)(x - 9) = 0 \\  \\ x + 15 = 0 \:  \: or \:  \: x - 9 = 0 \\  \\ x =  - 15 \: or \:  \: x = 9 \\  \\  \because \: side \:  of \: a \: rectangle \: can \: not \:  \\ be \: negative \\  \\  \implies \: x \neq   - 15 \\  \\  \implies \: x = 9 \\  \\  \red{ \bold{x + 7 = 9 + 7 = 16}} \\  \\ \purple{ \bold{ x - 1 = 9 - 1 = 8}}

Thus, the dimensions of the rectangle are 16 ft and 8 ft.

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Answer: Choice A

g(x) = sqrt(2x)

====================================================

Explanation:

"sqrt(x)" is shorthand for "square root of x"

f(x) = 3x^2 is given

g( f(x) ) = x*sqrt(6) is also given

One way to find the answer is through trial and error. This would only apply of course if we're given a list of multiple choice answers.

------------------

Let's start with choice A

g(x) = sqrt(2x)

g( f(x) ) = sqrt(2 * f(x) ) .... replace every x with f(x)

g( f(x) ) = sqrt(2 * 3x^2 ) .... plug in f(x) = 3x^2

g( f(x) ) = sqrt(6x^2 )

g( f(x) ) = sqrt(x^2 * 6)

g( f(x) ) = sqrt(x^2)*sqrt(6)

g( f(x) ) = x*sqrt(6)

We found the answer on the first try. So we don't need to check the others.

------------------

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