X = 71 degrees
And here is a sentence to fill the minimum word rule
Answer:
A is 1/2 and the answer for B is 2/3
step-by-step explanation:
since it tells you the equation 'y = 20x' and y is the number of gallons where as x is minutes
the independent variable = number of gallons
the dependent variable = minutes
and the number(s) to fill in the table
x , y
( 0, 0 )
( 1, 20 )
( 2, 40 )
( 3, 60 )
( 4, 80 )
and the relationship between x and y is linear because you can clearly see the graph having especially a straight line that is not interfering with itself
hope this helps you! :)
For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.
The standard equation of an ellipse is given below:
![\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%2B%5Cfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%3D1)
Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.
The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:
![\begin{gathered} \frac{(x+2)^2}{3^2}+\frac{(y-2)^2}{2^2}=1 \\ \frac{(x+2)^2}{9}+\frac{(y-2)^2}{4}=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%28x%2B2%29%5E2%7D%7B3%5E2%7D%2B%5Cfrac%7B%28y-2%29%5E2%7D%7B2%5E2%7D%3D1%20%5C%5C%20%5Cfrac%7B%28x%2B2%29%5E2%7D%7B9%7D%2B%5Cfrac%7B%28y-2%29%5E2%7D%7B4%7D%3D1%20%5Cend%7Bgathered%7D)
In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:
![\begin{gathered} e=\sqrt{a^2-b^2} \\ e=\sqrt{3^2-2^2} \\ e=\sqrt{9-4}=\sqrt{5} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20e%3D%5Csqrt%7Ba%5E2-b%5E2%7D%20%5C%5C%20e%3D%5Csqrt%7B3%5E2-2%5E2%7D%20%5C%5C%20e%3D%5Csqrt%7B9-4%7D%3D%5Csqrt%7B5%7D%20%5Cend%7Bgathered%7D)
The coordinates of the foci are given by:
![\begin{gathered} F(h+e,k)=(-2-\sqrt{5},2) \\ F^{\prime}(h-e,k)=(-2+\sqrt{5},2) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20F%28h%2Be%2Ck%29%3D%28-2-%5Csqrt%7B5%7D%2C2%29%20%5C%5C%20F%5E%7B%5Cprime%7D%28h-e%2Ck%29%3D%28-2%2B%5Csqrt%7B5%7D%2C2%29%20%5Cend%7Bgathered%7D)
The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).
Answer:
Axioms are generally statements made about real numbers. ... Sometimes they are called algebraic postulates. Often what they say about real numbers holds true for geometric figures, and since real numbers are an important part of geometry when it comes to measuring figures, axioms are very useful