PLEASE HELP!!!!!!!!!!!!!!!
1 answer:
You might be interested in
<u>Step-by-step explanation:</u>
The ellipse is vertical so y has the biggest radius.
Major axis (y) = 20 so the y-radius is 20/2 = 10
Minor axis (x) = 14 so the x-radius is 14/2 = 7
The equation of an ellipse is: where
- (h, k) is the center of the ellipse
- a is the x-radius
- b is the y-radius
Given: a = 7, b = 10
Assume: (h, k) = (0, 0)
Answers:
- b = -19
- b = -11
- b = -9
- b = 19
- b = 11
- b = 9
====================================================
Explanation:
Here are all the ways to multiply to 18 when using integers only:
- -1*(-18) = 18
- -2*(-9) = 18
- -3*(-6) = 18
- 1*18 = 18
- 2*9 = 18
- 3*6 = 18
Sum each pair of factors to find out a possible value of b.
- -1 + (-18) = -19
- -2 + (-9) = -11
- -3 + (-6) = -9
- 1 + 18 = 19
- 2 + 9 = 11
- 3 + 6 = 9
Therefore, the possible values of b are
- b = -19
- b = -11
- b = -9
- b = 19
- b = 11
- b = 9
which are the final answers.
----------------------
An example:
Let's say b = 11. This would mean becomes
It would factor to since it was stated earlier that:
2+9 = 11
2 * 9 = 18
You can use the FOIL rule, distributive property, or the box method to confirm that is a true equation for all real numbers x.
This same idea applies for the other values of b.
----------------------
If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)
Use the FOIL rule to get
The middle term has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).