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madam [21]
2 years ago
5

Emily knows that the area of a rectangle is 54x9y8 square yards and that it’s length 6x3y4 yards. If she divides the area by the

length to find the width, then which expression represents the width of her rectangle in yards?
A 9x3y2 B 48x6y4 C 9x6y4 D 60x12y12
Mathematics
1 answer:
Furkat [3]2 years ago
6 0

Answer:

Width of the rectangle is: \mathbf{Width= 9x^6 y^4}

Option C is correct.

Step-by-step explanation:

Area of rectangle = 54x^9y^8

Length of rectangle = 6x ^ 3y^4

We need to find width of rectangle.

The formula used is:

Area\:of\:rectangle=Length\times Width\\Width=\frac{Area\:of\:rectangle}{Length}

Putting values in the formula to find Width of rectangle

Width=\frac{Area\:of\:rectangle}{Length}\\Width=\frac{54x^9y^8}{6x^ 3y^4}

Using the exponent rule: \frac{a^m}{a^n}=a^{m-n}

and simplifying the terms we get

Width=\frac{54x^9y^8}{6x^3y^4}\\Width=9x^{9-3} \: y^{8-4}\\Width=9x^6 y^{4}

So, Width of the rectangle is: \mathbf{Width= 9x^6 y^4}

Option C is correct.

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The pipe leaks 1.5 cups each day, so in one week, or 7 days, the cup leaks 1.5 times 7 cups, which equates to 10.5 cups per week.
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3 years ago
You bought your car for $12500 and it is depreciating at 13% per year. How long until it is only worth half of what you paid for
il63 [147K]

Answer:

5 years

Step-by-step explanation:

We are given;

  • Initial value of the car = $12,500
  • Rate of Depreciation = 13% per year
  • New value (after depreciation) = $6,250 (half the initial value)

We are required to determine the time taken for the value of the car to depreciate to half the original value.

  • We need to know the depreciation formula;
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Therefore;

$6,250 = $12,500(1 - r/100)^n

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0.5 = 0.87^n

Introducing log on both sides;

log 0.5 = n log 0.87

Therefore;

n = log 0.5 ÷ log 0.87

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Therefore, it takes 5 years for the value of the car to depreciate to half the initial value.

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