Answer:
Center: (3,5)
Radius: 2
Step-by-step explanation:
x² + y² - 6x - 10y + 30 = 0
Put equation into center-radius form. First regroup terms:
(x²-6x) + (y²-10y) = -30
Complete the squares:
(x²-6x+3²) + (y²-10y+5²) = -30 + 3² + 5²
(x-3)² + (y-5)² = 4 = 2²
Center: (3,5)
Radius: 2
Cylinder is 10 meters wide, so its diameter is 10 meters. You get radius of it by dividing 10 by 2, which equals 5.
As you count volume of cylinder from that equation
You get an equation to count height:
h≈3.82 meters
Surface area is just the area of all these 4 triangles plus the rectangle.
First we can find the area of the rectangle.

Half of the length is 28 cm, so the full length must be 28 * 2 = 56 cm.


The base for the left and right triangles are 27. The heights would be the net length minus half the length of the rectangle:

Calculate the area:



We have two of these triangles.

Now do the other two pair of triangles. The bases for them are 28 + 28 = 56 cm. The heights would be the net width minus the width of the rectangle:

Now find the area:



We have two of these triangles.

Add all the areas together:
Answer:
3d + 4p = $37.25
5d + 2p = $38.75
Actual Answer:
Bag of popcorn is $5
A drink is $5.75
Step-by-step explanation:
Let drinks = d
Let popcorn = p
Noah: 3d + 4p = $37.25
Other: 5d + 2p = $38.75
Choose a variable to eliminate (We'll choose p)
3d + 4p = $37.25
(5d + 2p = $38.75) -2
Distribute
-10d - 4p = -77.5
The -4p cancels out the 4p, then we combine
-7d = -40.25
Divide both sides by -7
-7d/-7 = -40.25/-7
d = 5.75
Back to 3d + 4p = $37.25
Substitute d with 5.75
3(5.75) + 4p = $37.25
17.25 + 4p = 37.25
Move the constant to the other side
17.25 + 4p = 37.25
-17.25 -17.25
4p = 20
Divide both sides by 4
4p/4 = 20/4
p = 5