1: If AB = 8ft, and BC = 113ft, find 4C =

Mrs miller sells a hoouse for 179000 if she earns a commission of 6%, how much money does she earn?

Ivenika [448]

$10740

This is because that amount multiplied times .06 is equal to the answer.

8 0

4 years ago

ol McDonald would like to build a pin for his favorite pig horse and cow he needs to enclose a rectangular plot of land into thr

garri49 [273]

The area of the pen is the products of its dimensions

The dimension of the pen is 300 by 120 feet
The maximum area of the pen is 36000 square feet.

Let the dimension of the fence be x by y.

So, we have:

$\mathbf{2x + 5y = 1200}$ --- perimeter

$\mathbf{Area =xy}$ -- area

Subtract 5y from both sides of $\mathbf{2x + 5y = 1200}$

$\mathbf{2x = 1200 - 5y}$

Divide both sides by 2

$\mathbf{x = \frac{1200 - 5y}{2}}$

Substitute $\mathbf{x = \frac{1200 - 5y}{2}}$ in $\mathbf{Area =xy}$

$\mathbf{Area = \frac{1200 - 5y}{2} \times y}$

$\mathbf{Area = \frac{1200y - 5y^2}{2}}$

Split

$\mathbf{Area = 600y - \frac{5}{2}y^2}$

Differentiate

$\mathbf{A' = 600 -5y}$

Set to 0

$\mathbf{600 -5y = 0}$

Add 5y to both sides

$\mathbf{5y = 600}$

Divide both sides by 5

$\mathbf{y = 120}$

Substitute $\mathbf{y = 120}$ in $\mathbf{x = \frac{1200 - 5y}{2}}$

$\mathbf{x = \frac{1200 - 5 \times 120}{2}}$

$\mathbf{x = \frac{1200 - 600}{2}}$

$\mathbf{x = \frac{600}{2}}$

$\mathbf{x = 300}$

Recall that:

$\mathbf{Area =xy}$

So, we have:

$\mathbf{Area = 300 \times 120}$

$\mathbf{Area = 36000}$

Hence, the maximum area of the pen is 36000 square feet.

Read more about maximum areas at:

brainly.com/question/11906003

7 0

3 years ago

Emily cuts two circles from a sheet of colored paper measuring 8" x 12". One circle

allsm [11]

Answer:

a. 48.1 square inches

b. yes

c. 2.51 in

Step-by-step explanation:

a. How many square inches of paper are left over?

To know this, we need to calculate the area of the sheet of colored paper and then subtract the are of the circle from it.

So, A = area of colored paper = 8" x 12" = 96 in²

A'= Area of 3 inch radius circle = πr²

= π(3)²

= 9π in²

A" = Area of 5 inch diameter circle = πd²/4

= π(5)²/4

= 25π/4 in²

= 6.25π in²

A₀ = area of circles = 9π in² + 6.25π in²

= 15.25π in²

= 47.91 in²

So, there are left A₁ = A - A₀

= 96 in² - 47.91 in²

= 48.09 in²

≅ 48.1 in²

So there are 48.1 square inches left over.

b. Is it possible to cut another circle with a 3 inch radius from the paper?

To know this, we calculate the area of a 3 inch radius paper and see if it is less or more than the remaining area of paper. If it is less, it can be cut.

So, A₂ = Area of 3 inch radius circle = πr²

= π(3)²

= 9π in²

= 28.3 in²

Since A₂ = 28.3 in² < A₁ = 48.1 in² (the rest of the colored paper area), it can be cut. So the answer is yes, another circle with a 3 inch radius can be cut from the paper.

c. If the 3 inch circle fits what is the largest circle (What is its radius) you can draw that will still fit on your paper.

We find the area of the remaining colored paper by subtracting the area of the 3 inch circle from the remaining area. So.

A₃ = A₁ - A₂

= 48.1 in² - 28.3 in²

= 19.8 in²

This is the area of the remaining colored paper. We then find the radius, r of the circle with area A₃ = 19.8 in² that would fit into the area.

So, A₃ = πr²

r = √(A₃/π)

= √(19.8 in²/π)

= √(6.302 in²)

= 2.51 in

4 0

3 years ago

Replace? with =, >, or < to make the statement true. 4 ∙ 16 – 16? 4 ∙ [24 – 2 ∙ (4 + 8)]

wel

$4 \times 16 - 16 = \ \ \ \ |\hbox{multiplication before subtraction} \\
64-16= \\
48 \\ \\
4 \times [24 -2 \times (4+8)]= \ \ \ \ \ |\hbox{parentheses first} \\
4 \times [24 - 2 \times 12]= \ \ \ \ \ \ \ \ \ \ \ |\hbox{multiplication before subtraction} \\
4 \times [24 - 24]= \\
4 \times 0= \\
0 \\ \\
48 \ \textgreater \ 0 \\ \Downarrow \\
4 \times 16 - 16 \ \textgreater \ 4 \times [24- 2 \times (4+8)]
$

The answer is c. >.

8 0

3 years ago

Can you write the equation of a quadratic function knowing its zeros and its non-zero y-intercept? If so, describe the process

valkas [14]

Yes, if you know where the y-intercept is, and your zeros, the line is fixed, and you have a curve that is already fixed based on the y-intercept. However without the y-intercept, your zero's would be useless.

4 0

2 years ago