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3 years ago

9

A rancher has 2 comma 200 feet of fencing to enclose a rectangular pig pen. However, one side of the pen lies along a river and

requires no fencing. Express the area of the pen, A, as a function of x.

1 answer:

DiKsa [7]3 years ago

7 0

Answer:

$A = 2200x - 2x^2$

Step-by-step explanation:

Let's x be the length of the side that is NOT the same as the side along the river (or in opposite). From the fencing perimeter of 2200ft we can calculate the other side y of the rectangular:

y = 2200 - 2x

The area A of the pen would be the product of the 2 sides

$A = xy = x(2200 - 2x) = 2200x - 2x^2$

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And animals weight change from 12 pounds to 16 pounds what was the percent increase to the nearest whole number

amm1812

That's a 33% increase.

I calculated this using the formula:

$\frac{|n-o|}{o} * 100$

Where n = the new value (16 in your question), o = the old value (12 in your question) and the result is outputted as a percent increase. You can check that this is correct by finding 33% of 12, adding the result to 12, and checking that the result equals your "new" number.

Note that 33% is only an approximation as your question requires a number rounded to the nearest whole.

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3 years ago

What is 1/7+2/3 fractions

cricket20 [7]

Answer:

$\frac{17}{21}$

Step-by-step explanation:

$\frac{1}{7}$ + $\frac{2}{3}$ ( multiply $\frac{1}{7}$ by 3 and $\frac{2}{3}$ by 7 to get a common denominator)

$\frac{3}{21}$ + $\frac{14}{21}$ = $\frac{17}{21}$

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3 years ago

Why does the highest percent profit occur with the smallest annual interest rate?

anzhelika [568]

Answer:

This is so because the higher the interest rate the lower the profit and the higher the total expenses and the percentage profit = (Profit/Expenses) × 100

Step-by-step explanation:

Question;

It is desired to find out the monthly percentage profit made to help decide the best loan option

Part A

Given that the monthly operating cost of the gym is 5,000 and the monthly sales is 7,500

Let 'I' represent the monthly interest paid on the loan, we have;

The percentage profit = Profit/(Total expenses) × 100

The total expenses = I + 5000

Profit = Sales - The total expenses

∴ Profit = 7,500 - (I + 5,000) = 2,500 - I

The percentage profit, P = (2,500 - I)/(5,000 + I) × 100

Therefore, as the interest rate becomes smaller, the numerator of the function for the percentage profit approaches its maximum value of 2,500 and the denominator approaches the minimum value of 5,000 and the percentage profit therefore, approaches the maximum value

Therefore;

The highest percentage profit occurs at the smallest interest rate.

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3 years ago

Which statement best describes the area of Triangle ABC shown below? A triangle ABC is shown on a grid. The vertex A is on order

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Answer:

It is one-half the area of a rectangle of length 4 units and width 5 units.

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2 years ago

Find the sides of a rectangle having area 125 square units if the sides are in the ratio 5:3.

tatiyna

For this case we have the following data:

Area of the rectangle, $A = 125$

Relationship of the sides 5: 3

By definition, the area of a rectangle is given by:

$A = a * b$

Where

a: is the longest side.

b: it is the side of least length.

If the sides have a 5: 3 ratio, it means:

$\frac{a}{b}=\frac{5}{3}$

$a=\frac{5}{3}b$

Substituting in the formula of the area, we have:

$125 =a * b\\$

$125=\frac{5}{3}b*b$

Clearing b:

$3 * 125 = 5 * b ^ 2$

$\frac{375}{5}= b ^ 2$

$75 = b ^ 2$

$b =\sqrt{75}b = 8.7$ units

Substituting and clearing:

$125 = a * 8.7$

$a =\frac{125}{8.7}$

$a = 14.4$ units

So, the sides are:

$a = 14.4$ units

$b = 8.7$ units

Answer:

$a = 14.4$ units

$b = 8.7$ units

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3 years ago