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makvit [3.9K]
3 years ago
13

A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remai

ning lawn will have seen area of 425 feet squared. How wide will the sidewalk be?

Mathematics
1 answer:
levacccp [35]3 years ago
5 0
So the original lawn has an area
24 × 32 = 768 the new lawn will have area 425
this means the area of the sidewalk will be 768-425=343
now the sidewalk is a certain width of we draw it out and label it x we see the lawn has an area of
(32 - 2x)(24 - 2x) = 425 \\ 768 - 64x - 48x + 4 {x}^{2}  = 425 \\ 4 {x}^{2}  - 112x  + 343 = 0
use the quadratic formula to solve. then you will know how wide the sidewalk is. I will attach picture

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V = l * w * h
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Multiply the length and width on the right side of the equation.

470.40 = 62.72 * h
Divide both sides by 62.72
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CHECK
V = l * w * h
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GuDViN [60]

Answer:

(-2, 11) and (2, 3)

Step-by-step explanation:

<u>Given system of equations:</u>

1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3

2) f(x) = -2x + 7 ⇒ y = -2x + 7

Solve Using the Substitution Method:

<u>Step 1:</u> Substitute the the first equation into the second.

⇒ x² - 2x + 3 = -2x + 7

<u>Step 2:</u> Solve for x.

x² - 2x + 3 = -2x + 7 [ Add 2x to both sides. ]

x² - 2x + 2x + 3 = -2x + 2x + 7

⇒ x² + 3 = 7 [ Subtract 3 from both sides. ]

x² + 3 - 3 = 7 - 3

⇒ x² = 4 [ Take the square root of both sides. ]

√x² = √4

x = ± 2

⇒ x = -2, x = 2

<u>Step 3:</u> Solve for y.

<em>Substitute the found x-values into one of the given equations.</em>

y = -2x + 7 ⇒ y = -2(-2) + 7 ⇒ y = 4 + 7 ⇒ y = 11

y = -2x + 7 ⇒ y = -2(2) + 7 ⇒ y = -4 + 7 ⇒ y = 3

The solutions to the system of equations are: (-2, 11) and (2, 3).

Learn more about system of equations here:

brainly.com/question/26094713

brainly.com/question/27850666

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2 years ago
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Answer:

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Which of the following equations is written in standard form?
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