A parabola is a quadratic function, and a quadratic can be expressed in vertex form, which is:
y=a(x-h)^2+k, where (h,k) is the vertex (absolute maximum or minimum point of the quadratic)
In this case we are given that (h,k) is (-5,80) so we have so far:
y=a(x--5)^2+80
y=a(x+5)^2+80, we are also told that it passes through the point (0,-45) so:
-45=a(0+5)^2+80
-45=25a+80 subtract 80 from both sides
-125=25a divide both sides by 25
-5=a, so now we know the complete vertex form is:
y=-5(x+5)^2+80
The x-intercepts occur when y=0 so:
0=-5(x+5)^2+80 add 5(x+5)^2 to both sides
5(x+5)^2=80 divide both sides by 5
(x+5)^2=16 take the square root of both sides
x+5=±√16 which is
x+5=±4 subtract 5 from both sides
x=-5±4 so the x-intercepts are:
x=-1 and -9
Answer:
≈9.64 gallons
Step-by-step explanation:
To solve, we can figure out how many quarts are in a minute and use that to figure out how many quarts are in an hour. Then, we can convert quarts to gallons.
4.5 quarts = 7 minutes
First, we can find how many quarts equal 1 minute. To do this, we can divide both sides by 7 because anything divided by itself equals 1
4.5/7 quarts = 1 minute
Next, we want to figure out how many quarts go into 60 minutes, or 1 hour. To do this, we can multiply both sides by 60 because 1 * 60 = 60
4.5 * 60 / 7 quarts = 60 minutes = 1 hour
We now know how many quarts are in an hour, so we can now convert quarts to gallons
4 quarts = 1 gallon
divide both sides by 4
1 quart = 1/4 gallons
To get from quarts to gallons, we can divide by 4, so we have
(4.5 * 60 / 7)/4 = 4.5 * 60 / 28
≈9.64 gallons
Triangles JFE and JLK are similar provided that line segments FE and LK are parallel. This means that corresponding parts of these triangles occur proportionally to one another. In particular,
From this relation we get
Now we can solve for :
Answer:
Step-by-step explanation:
Split the shape up into two rectangles
(1) rectangle would be 2 x 10 = 20
(2) rectangle would be 4 x 7 = 28
Add them up =
Rounded up, it would be 7,540