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3 years ago

The length of a rectangle is 8 feet more than it’s worth. The area of the rectangle is 84 ft.². Find its Length and width.

Mathematics

1 answer:

Furkat [3]3 years ago

5 0

Answer: 100 i think, but am not sure.

Step-by-step explanation:

The formula for area of a rectangle is A=l*w. Since the area is 84, then you can use the A=l*w formula. 84 = x(x+8) would be the equation to solve for x.

Now, you need to put the equation in standard form. So, x2 + 8x - 84 = 0.

Since you can't solve this quadratic using factoring, you need to complete the square.

To complete the square you need to add 84 to both sides. Now you have x2 + 8x = 84. Take the coefficient for the x term (8) and divide by 2. Now square it. That would be 42, so 16. Now you have x2 +8x +16 = 100.

Factor x2 +8x +16, so (x+4)2 = 100

If you use the square root property, you have x+4 = 10. Therefore, x = 6 (the short side) and 14 is the long side.

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$40

Step-by-step explanation:

30% = .30

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A triangle has a 90° angle. What type of triangle is it?

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A right triangle has one angle equal to 90 degrees. A right triangle can also be an isosceles triangle--which means that it has two sides that are equal. A right isosceles triangle has a 90-degree angle and two 45-degree angles. This is the only right triangle that is an isosceles triangle. But the answer is right triangle

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Find the sum and difference (first mixed number minus the second mixed number) for the following pair of mixed numbers. The answ

xz_007 [3.2K]

Answer:

Sum = 15 8/15, Difference = 1 2/15

Step-by-step explanation:

8⅓, 71/5

A. Sum

8⅓ + 7 1/5

Convert to improper fraction

25/3 + 36/5

Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:

[(25×5) + (36×3)] / 15

[125 + 108] / 15

233 / 15

Convert to mixed fraction

15 8/15

B. Difference

8⅓ – 7 1/5

Convert to improper fraction

25/3 – 36/5

Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:

[(25×5) – (36×3)] / 15

[125 – 108] / 15

17 / 15

Convert to mixed fraction

1 2/15

SUMMARY:

Sum = 15 8/15, Difference = 1 2/15

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2 years ago

The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

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2 years ago

What is the solution to x ? <br><br> 7/3x + 1/3x = 3x + 6/3 + 5/3x

nignag [31]

7/3x+1/3x=3x+6/3+5/3x
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3 years ago