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Ymorist [56]
3 years ago
15

Caroline measured the weight of a dog that came into the veterinary clinic. She determined that her measurement had a margin of

error of 0.05 kilogram. Which of the following could be the measured weight of the dog?
A. 27.939 kilograms
B. 27.93 kilograms
C. 27.9 kilograms
D. 27 kilograms
Mathematics
1 answer:
zvonat [6]3 years ago
5 0
27 kilograms is the answer
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The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
Ratling [72]
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3).  The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
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We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
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Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

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It's easier to work with whole numbers, so we will multiply everything by 2:
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We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
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When solving quadratics, we want the equation equal to 0, so we will add 12:
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0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

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y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).
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