<u>Given</u>:
The sides of the base of the triangle are 8, 15 and 17.
The height of the prism is 15 units.
We need to determine the volume of the right triangular prism.
<u>Area of the base of the triangle:</u>
The area of the base of the triangle can be determined using the Heron's formula.
Substituting a = 8, b = 15 and c = 17. Thus, we have;
Using Heron's formula, we have;
Thus, the area of the base of the right triangular prism is 36 square units.
<u>Volume of the right triangular prism:</u>
The volume of the right triangular prism can be determined using the formula,
where 
is the area of the base of the prism and h is the height of the prism.
Substituting the values, we have;
Thus, the volume of the right triangular prism is 450 cubic units.
Answer:
c+p = 53
2.5c+1.5p = 105.5
p = 27
c= 26
Mrs. Johnson earned 65
Mr Smith earned 40.5
Mrs Johnson earned 24.50 more
Step-by-step explanation:
Let c = cookies sold
p = popcorn sold
The number of items sold is 53
c+p = 53
The total cost of the items sold is 105.50
The number of cookies sold times 2.50 plus the number of popcorn sold times 1.50 = 105.50
2.5c+1.5p = 105.5
System of equations:
c+p = 53
2.5c+1.5p = 105.5
Multiply the second equation by 10 to clear the decimals
10 *(2.5c+1.5p) = 10*105.5
25c+15p = 1055
Divide by 5
25c/5 +15p/5 = 1055/5
5c+3p =211
Multiply equation 1 by -5
-5(c+p)=-5*53
-5c-5p=-265
Add the equations
5c+3p =211
-5c-5p=-265
---------------------
-2p = -54
Divide by -2
-2p/-2 = -54/-2
p = 27
Now we need to find c
c+p = 53
c+27 = 53
Subtract 27 from each side
c+27-27 = 53-27
c= 26
Mrs. Johnson earned the number of cookies times 2.5
c* 2.5
26*2.5 =65
Mr Smith earned the number of popcorn times 1.5
p*1.5
27*1.5
40.5
Mrs Johnson earned 65-40.5 = 24.50 more
Step-by-step explanation:
OH MY GODD I NEED HELP WITH THIS QUESTION TOOOOOO
Answer:
y-1=0
Step-by-step explanation:
I'm going to write into y=mx+b form first.
m is the slope and b is the y-intercept.
First step is to find the slope.
To find the slope given two points you can use m=(y2-y1)/(x2-x1).
Instead, I like to line up the points and subtract vertically. Then put 2nd difference on top of 1st difference.
Let's do that:
(-2,1)
- (2,1)
--------
-4, 0
The slope is 0/-4=0. That means the line is horizontal and is of the form y=a number.
If you look at the points, you see the y-coordinate doesn't change. The y-coordinate is always 1. So the equation for the line is y=1.
If we subtract 1 on both sides we get y-1=0.
So general form is Ax+By+C=0 which is why I decide to move the one on the other side of the equation.
If I had noticed earlier that the y-coordinates were the same I would have stopped and say y=whatever y-coordinate I seen. However, I really didn't take notice of that until after I found the slope.
