Answer:
Step-by-step explanation:
You have 3 unknowns: a, b, and c. It's our job to find them algebraically. I'm going to start with the point where x = 0 and y = 7. You'll see why in a minute. Filling in the standard form of a quadratic
using (0, 7):
gives you that c = 7. We will use that value now when we write the next 2 equations. Now the point (-2, 19):
and
so
12 = 4a - 2b
Now for the next point (-1, 12):
and
so
5 = a - b
Now we have a system of equations (the 2 bold font equations) that we will solve by elimination:
12 = 4a - 2b
5 = a - b
Multiply the bottom equation by -4 to get a new system:
12 = 4a - 2b
-20 = -4a + 4b
Add those together to get rid of the a terms and end up with
-8 = 2b so
b = -4
Now we can sub in -4 for b to solve for a. I'm using the second bold type equation to do this:
5 = a - (-4) and
5 = a + 4 so
a = 1 and the equation for the quadratic function is
Answer:
x = 35.5
Step-by-step explanation:
cos 65° = 15/x
cos 65° · x = 15
x = 15/cos 65°
x = 35.5
Answer:
x=3
Step-by-step explanation:
Right triangle so you can use pythagorean theorem
a squared + b squared = c squared
b=x
14^2 + b^2= 17^2
14+b=17
b=3
Answer:
Step-by-step explanation:
Given that the volume of the aquarium is 20m^3.
Volume = Area of Base x height
Area of Base = Volume / height = 20/h
Given that the aquarium has a square base.
Area of square = l^2
Thus, the length of the base of the aquarium is
The frame is to cover 8 sides with the length equal to the length of the base and 4 sides with the length of the height.
Thus, the total perimeter of the frame is given by
Area of the four side faces of the aquarium is 4 times the length of the base times the height =
Total area to be covered by grass is the base and the four side faces and is given by
Cost of the entire metal frame =
Cost of the entire grass =
Therefore, total cost in terms of the height, h, is given by
