Answer:
ONE-THIRD OF A GALLON DIVIDED BY 3 GALLONS EQUALS ONE-NINTH
Step-by-step explanation:=1/9
20+(-3.05)+(-9.8)=20-3.05-9.8=7.15
Answer:
The graph of the inverse function is the same that the graph of the original function
Step-by-step explanation:
step 1
Find the equation of the function in the graph
Let
f(x) ---> the function in the graph
we know that
Is a linear function
take the points (0,6) and (6,0)
<em>Find the slope of the linear function</em>
![m=(0-6)/(6-0)\\m=-1](https://tex.z-dn.net/?f=m%3D%280-6%29%2F%286-0%29%5C%5Cm%3D-1)
<em>Find the the equation of the linear function in slope intercept form</em>
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
we have
![m=-1](https://tex.z-dn.net/?f=m%3D-1)
---> the y-intercept is given
substitute
![f(x)=-x+6](https://tex.z-dn.net/?f=f%28x%29%3D-x%2B6)
step 2
Find the inverse of the function f(x)
Let
y=f(x)
![y=-x+6](https://tex.z-dn.net/?f=y%3D-x%2B6)
<em>Exchange the variables (x for y and y for x)</em>
![x=-y+6](https://tex.z-dn.net/?f=x%3D-y%2B6)
Isolate the variable y
![y=-x+6](https://tex.z-dn.net/?f=y%3D-x%2B6)
Let
![f^{-1}(x)=y](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3Dy)
![f^{-1}(x)=-x+6](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D-x%2B6)
![f^{-1}(x)=f(x)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3Df%28x%29)
In this problem the graph of the inverse function is the same that the graph of the original function
Answer:
circle area = 1963.495 ft²
Step-by-step explanation:
<u>Given</u>
A rectangle 550 ft by 350 ft packed with circles on a rectangular grid
<u>Find</u>
the area of the largest circle that can be packed this way
<u>Solution</u>
The diameter of the circle must be a factor of both 350 and 550. We want the diameter to be the largest such factor. We can write the factors of 350 and 550 as ...
- 350 = 50 × 7
- 550 = 50 × 11
The largest factor common to both numbers is 50, so that will be the diameter of the largest circle that will fit on a square grid.
The area of a circle is commonly given by the formula ...
A = πr² . . . . . where r represents the radius of the circle.
The radius is half the diameter, so will be (50 ft)/2 = 25 ft. And the area of the circle is ...
A = π(25 ft)² = 625π ft² ≈ 1963.495 ft²
The area of one circle is about 1963.495 square feet.
_____
The total number of circles is 11×7 = 77. Their total area is 77×1963.495 ft² ≈ 151,189 ft². This is 151,189/192,400 ≈ 78.54% of the total area of the rectangle.
Answer:
1 2/4 or 1.5
Explanation:
There are 4 quarts in a gallon, and 2 left over add 1/2 to the full gallon. So, 1 gallon, plus 2 quarts, which is equal to 1/2 gallon, is 1.5 gallons :D
Hope this helped!