To calculate the distance between two points on the coordinate system you have to use the following formula:
![d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%5B%5D%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D)
Where
d represents the distance between both points.
(x₁,y₁) are the coordinates of one of the points.
(x₂,y₂) are the coordinates of the second point.
To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph
C(2,-1)
D(-1,-2)
Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)
![\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B%282-%28-1%29%29%5E2%2B%28%28-1%29-%28-2%29%29%7D%5E2%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B%282%2B1%29%5E2%2B%28-1%2B2%29%5E2%7D%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B3%5E2%2B1%5E2%7D%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B9%2B1%7D%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B10%7D%20%5Cend%7Bgathered%7D)
The length of CD is √10 units ≈ 3.16 units
Use the Pythagorean theorem to find the height.
Height = sqrt(26^2-10^2)
Height = 24 cm
Volume = 20^2 x 24/3
Volume = 7,200 cm^3
9514 1404 393
9514 1404 393
Answer:
1) (1 1/2)(7/5) = g
2) (1 1/2)/(5/7) = g
Step-by-step explanation:
1) Tyler has painted 5/7 of the 7/7 of the fence. So the total amount of the fence is (7/7)/(5/7) = 7/5 as much as what was already painted.
The total amount of paint needed is then 7/5 the amount already used:
g = (7/5)(1 1/2) . . . . . gallons of paint needed for the whole fence
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2) If g gallons are required for the whole fence, the amount used so far for 5/7 of the fence is 5/7 of the quantity required:
(5/7)g = 1 1/2
g = (1 1/2)/(5/7) . . . . division expression for the paint needed
Answer:
4x²×(1+7x)
Step-by-step explanation:
To find 
, you can switch the "x" and "f(x) or y" in the equation.
![f(x) = \sqrt[3]{x-2} +8](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx-2%7D%20%2B8)
![y = \sqrt[3]{x-2}+ 8](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7Bx-2%7D%2B%208)
![x = \sqrt[3]{y-2}+8](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7By-2%7D%2B8)
Now you need to isolate the "y"
Subtract 8 on both sides
![x - 8 = \sqrt[3]{y-2}](https://tex.z-dn.net/?f=x%20-%208%20%3D%20%5Csqrt%5B3%5D%7By-2%7D)
Cube ( ³ ) each side to get rid of the ∛
![(x-8)^{3} = (\sqrt[3]{y-2}) ^{3}](https://tex.z-dn.net/?f=%28x-8%29%5E%7B3%7D%20%3D%20%28%5Csqrt%5B3%5D%7By-2%7D%29%20%5E%7B3%7D)
Add 2 on both sides
