#10 Write the equation of the given circle. center (-2, -2) radius of 6

1 answer:

6 0

(x - h)^2 + (y - k)^2 = r^2

h = -2
k = -2
r = 6

(x - (-2))^2 + (y - (-2))^2 = 6^2

(x + 2)^2 + (y + 2)^2 = 6^2

(x + 2)^2 + (y + 2)^2 = 36. your answer

hope this helped, blessings! :)

You might be interested in

REWARD: 50 points + Brainly to the best answer.<br> Check the file.

Debora [2.8K]

Answer:

a) No because the gallons and quarts of oil you and your friend bought is proportional.

b) Yes because the gallons and quarts of oil are no longer proportional.

c) 1 gallon of gasoline = $3.55

1 quart of oil = $5.00

Step-by-step explanation:

Let g = cost per gallon of gasoline

Let q = cost per quart of oil

a) Creating expressions from the given information:

10g + 2q = 45.50

5g + q = 22.75

From inspection, we can see that if we multiply the second equation by 2, it will give us the first equation. Therefore, they are proportional and we cannot determine the variables.

b) Creating expressions from the given information:

10g + 2q = 45.50

5g + q = 22.75

8g + 2q = 38.40

From inspection, we can see that the third equation is not proportional to equations 1 and 2. Therefore, we can use this equation with either of the other equations to determine the variables.

Using equations 2 and 3 from the previous part (b):

5g + q = 22.75

8g + 2q = 38.40

Rewrite 5g + q = 22.75 to make q the subject:

⇒ q = 22.75 - 5g

Substitute into 8g + 2q = 38.40 and solve for g:

⇒ 8g + 2(22.75 - 5g) = 38.40

⇒ 8g + 45.5 - 10g = 38.40

⇒ 2g = 7.1

⇒ g = 3.55

Substitute found value for g into q = 22.75 - 5g and solve for q:

⇒ q = 22.75 - (5 x 3.55)

⇒ q = 5

3 0

2 years ago

The length of a rectangle is 59 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the

melamori03 [73]

The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width

Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!

5 0

3 years ago

Determine whether the polynomial below can be factored into perfect squares. If so, factor the polynomial. Otherwise, select tha

kkurt [141]

Answer:

A. $=(9x-12)^2$

Step-by-step explanation:

We need to determine whether the polynomial $81x^2-216x+144$ can be factored into perfect squares. If so, factor the polynomial. Otherwise, select that it cannot be factored into a perfect square.