What is the square footage of a 13 foot by 14 foot circle?

can someone help me!! Use algebraic rules of equations to predict the solution type to the system of equations. Include all of y

xz_007 [3.2K]

Answer:

x + y = 4 Equation 1

y = 2x -1 Equation 2

-2x + y = -1

x + y = 4

Subtract

You will get

- 3x = -5

Divide by -3

-3x / -3 = - 5 /-3

x = 5/3

Substitute x into equation 1

x + y = 4

x = 5/3

5/3 + y = 4

y = 4 - 5/3

y = 7/3

x = 5/3 y = 7/3

Hope this helps.

4 0

3 years ago

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

I don't get how to do this, can someone help?

Marianna [84]

Google helps to so try that

4 0

3 years ago

John has a rectangular picture which is 43 inches long and 27 inches wide. He wants to build a wooden gram for the picture but s

Dvinal [7]

Answer:

The border will be 18.6 inches wide

Step-by-step explanation:

Let the width be w

The length = 43 inches

Total wood = 800 square inches

Formula for area of rectangle = length x width

800 = 43 x w

w = 800/43

w = 18.6 inches

Therefore, the border will be 18.6 inches wide.

!!

5 0

2 years ago

Read 2 more answers

What is the slope of the line that passes through the points (3, -2) and (9, -2)?

ICE Princess25 [194]

m=(-2+2)/(9-6)=0/3=0

m=0

7 0

3 years ago