Answer:
The Y-intercept changes .
Step-by-step explanation:
Answer:
Option A. True
Step-by-step explanation:
we know that
<u>The Triangle Inequality Theorem</u>, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
we have
4,3 and 6
Applying the triangle inequality theorem
case 1) 4+3 > 6 -----> is true
case 2) 3+6 > 4 ----> is true
therefore
The given segments could form a triangle
Is true
The common factor is 7 so its
7(2x - 3)
When you plot the given points on a coordinate plane, you can see this is an ellipse that is vertical. The equation for this is
![\frac{(x-h) ^{2} }{ b^{2} }+ \frac{(y-k) ^{2} }{ a^{2} }=1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x-h%29%20%5E%7B2%7D%20%7D%7B%20b%5E%7B2%7D%20%7D%2B%20%5Cfrac%7B%28y-k%29%20%5E%7B2%7D%20%7D%7B%20a%5E%7B2%7D%20%7D%3D1%20%20)
. Of the values a and b, a is always greater than b, so it is on our major axis, the y-axis (it's under the y-k). a is the distance from the center to the vertices. When you plotted those given points, you can see that point dead center between the foci and the vertices is the origin (0, 0). That gives us our h and k values of 0 and 0. a is the number of units from the h coordinate of 0 to the y coordinate of the vertex, so a = 12. c is the number of units from the center to the foci, so c = 11. We need to find b now using the formula for the foci which is
![c^{2} = a^{2}- b^{2}](https://tex.z-dn.net/?f=%20c%5E%7B2%7D%20%3D%20a%5E%7B2%7D-%20b%5E%7B2%7D%20%20)
. We have c and a, so
![121=144- b^{2}](https://tex.z-dn.net/?f=121%3D144-%20b%5E%7B2%7D%20)
and
![b= \sqrt{23}](https://tex.z-dn.net/?f=b%3D%20%5Csqrt%7B23%7D%20)
. Now we have all the info we need to rewrite the equation:
![\frac{(x-0) ^{2} }{23} + \frac{(y-0) ^{2} }{144}=1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x-0%29%20%5E%7B2%7D%20%7D%7B23%7D%20%2B%20%5Cfrac%7B%28y-0%29%20%5E%7B2%7D%20%7D%7B144%7D%3D1%20)
or, simplified,