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natta225 [31]
3 years ago
10

A rectangular garden measures 16 feet by 12 feet. a path of uniform width is to be added so as to surround the entire garden. th

e landscape artist doing the work wants the garden and path to cover an area of 320 square feet. how wide should the path be?

Mathematics
1 answer:
kotegsom [21]3 years ago
3 0
For this problem, please see the attached picture to illustrate the problem. The garden is represented by the inner rectangle having dimensions of 16×12 feet. A path is added that surrounds the garden. The path creates a uniform margin around the garden with equal spacing denoted as x feet. To determine x, we use the total area of the outer rectangle which is equal to 320 square feet.

We know that the area of a rectangle is equal to length times width. The length to be used here is 16 feet subtracted with two x feet of path accounting for the two corners. The same applies for the width. Therefore, the equation for the area is

A = (16 - 2x)(12 - 2x)

Finally, we equate area to 320 to solve for x:

320 = (16 - 2x)(12 - 2x)
320 = 192 - 124x - 32x + 4x²
320 = 4x² - 56x + 192

Dividing the whole equation by 4,
x² - 14x + 48 = 80
x² - 14x + 48 - 80 = 0
x² - 14x - 32 = 0

Factoring the polynomial,
(x-16)(x+2) = 0
x = 16, -2

From the two roots, we choose the positive root as our solution. Therefore, the path should be 16 ft.

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Brrunno [24]

We have to solve this quadratic equation n^{2}+n=56 for n to get <em>which figure has 56 blocks</em>.

n^{2}+n=56\\n^{2}+n-56=0

For middle term factorization, we need <em>two numbers that multiplied gives us -56 and added gives us 1 (coefficient of n).</em>

<em>Such two numbers are </em><em>8</em><em> and </em><em>-7</em><em>. We can now write,</em>

<em>n^{2}+n-56=0\\(n+8)(n-7)=0\\n=-8, 7</em>

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3 0
3 years ago
Read 2 more answers
2.
Gnesinka [82]

Answer:

C. –x + 8y = 56

Step-by-step explanation:

Write in standard form.

x  −  8 y  =  − 56

This is a linear function in the slope - intercept form:

y = m x + b and we need a standard form:

a x + b y = c

y = 1/8 x + 7   / * 8 ( we will multiply both sides of equation by 8 )

8 y = x + 56

- x + 8 y = 56  / * ( - 1 )

x - 8 y = - 56

The equation is  y = 1/8x + 7

Standard form equation is Ax + By = C,  where A > = 0.

First eliminate the fractions by multiplying the equation by 8

8y = x + 56

Subtract x from each side

-x + 8y = 56

SInce x coeficient can't be negative multiply the equation by negative one.

x - 8y = -56

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3 years ago
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Answer:

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Step-by-step explanation:

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