The fact that the coefficients are pairwise identical (except for sign) tells you that x^2 -1 is a factor (and x-5 is the other factor). Of course, you recognize x^2-1 as a special form (the difference of squares) that is factored as (x +1)(x -1).
The zeros are x = -1, +1, +5.
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A graphing calculator confirms this.
Answer:
10/25, or 2/5
Step-by-step explanation:
This basically asks what 10/25/5/5 is equal to, but we know that 5/5 must equal 1, so this simplifies to 10/25/1, and we know that any number divided by 1 equals itself, so 10/25/1 equals 10/25, and if you reduce the fraction you get 2/5
Answer:
y=−2.984x+112.38
Step-by-step explanation:
Answer:
![y=-\frac{5}{6} + 7](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20%2B%207)
Step-by-step explanation:
Slope-intercept formula requires us to isolate the y variable. We can do this in just a couple of steps.
1) Move 5x from the left to the right side by subtracting 5x from both sides. This cancels out the 5x on the left side, and remember, what we do to one side we must do to the other to keep the equation balanced.
![6y=-5x+42](https://tex.z-dn.net/?f=6y%3D-5x%2B42)
2) Divide both sides by 6. Again, we are cancelling out the 6 on the left but we must also divide on the right. This would mean dividing -5 and 42 by 6 to get:
![y=-\frac{5}{6} + 7](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20%2B%207)
For this case we have that by definition, the general equation of the circle is given by:
![(x-h) ^ 2 + (y-k) ^ 2 = r ^ 2](https://tex.z-dn.net/?f=%28x-h%29%20%5E%202%20%2B%20%28y-k%29%20%5E%202%20%3D%20r%20%5E%202)
Where,
- <em>(h, k): it is the center of the circle
</em>
- <em>r: radius of the circle
</em>
We then have the following equation:
![(x-11) ^ 2 + (y + 15) ^ 2 = 144](https://tex.z-dn.net/?f=%28x-11%29%20%5E%202%20%2B%20%28y%20%2B%2015%29%20%5E%202%20%3D%20144)
Comparing values we have:
For the center of the circle
:
![(h, k) :( 11, -15)](https://tex.z-dn.net/?f=%28h%2C%20k%29%20%3A%28%2011%2C%20-15%29)
For the radius:
![r ^ 2 = 144\\r = \sqrt {144}\\r = 12](https://tex.z-dn.net/?f=r%20%5E%202%20%3D%20144%5C%5Cr%20%3D%20%5Csqrt%20%7B144%7D%5C%5Cr%20%3D%2012)
Then, the diameter is given by:
![d = 2r\\d = 2 (12)\\d = 24](https://tex.z-dn.net/?f=d%20%3D%202r%5C%5Cd%20%3D%202%20%2812%29%5C%5Cd%20%3D%2024)
Answer:
Johnny is wrong:
The center of the circle is (11, -15)
Joyce is wrong:
The diameter of the circle is 24