Answer:
(7,5)
Step-by-step explanation:
the rule for y=x is (a, b)... (b, a)
(5,7).... (7,5)
Answer:
y = 1
Step-by-step explanation:
Given:
- equation of the parabola:
![y=a(x-1)^2+q](https://tex.z-dn.net/?f=y%3Da%28x-1%29%5E2%2Bq)
- points on the parabola: (-1, -9) and (1, 1)
Substitute point (1, 1) into the given equation of the parabola to find q:
![\begin{aligned}\textsf{At}\:(1,1)\implies a(1-1)^2+q &=1\\a(0)^2+q &=1\\q &=1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BAt%7D%5C%3A%281%2C1%29%5Cimplies%20a%281-1%29%5E2%2Bq%20%26%3D1%5C%5Ca%280%29%5E2%2Bq%20%26%3D1%5C%5Cq%20%26%3D1%5Cend%7Baligned%7D)
Substitute the found value of q and point (-1, -9) into the given equation of the parabola to find a:
![\begin{aligned}\textsf{At}\:(-1,-9)\implies a(-1-1)^2+1 &=-9\\a(-2)^2+1 &=-9\\4a+1 &=-9\\4a &=-10\\a &=-\dfrac{5}{2}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BAt%7D%5C%3A%28-1%2C-9%29%5Cimplies%20a%28-1-1%29%5E2%2B1%20%26%3D-9%5C%5Ca%28-2%29%5E2%2B1%20%26%3D-9%5C%5C4a%2B1%20%26%3D-9%5C%5C4a%20%26%3D-10%5C%5Ca%20%26%3D-%5Cdfrac%7B5%7D%7B2%7D%5Cend%7Baligned%7D)
Therefore, the equation of the parabola is:
![y=-\dfrac{5}{2}(x-1)^2+1](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B5%7D%7B2%7D%28x-1%29%5E2%2B1)
The maximum or minimum point on a parabola is the vertex.
Vertex form of a parabola:
where (h, k) is the vertex.
Therefore, the vertex of the parabola is (1, 1) and so the maximum value of y = 1
Answer:
x=15
Step-by-step explanation:
Well, you have 2 numbers that sum up to 90 (the angle) so you can first minus the one you know, making your number from 90-30=60. Now all thats left is the 4x=60, which you can do 60/4=15 to get your answer that x=15.
Answer:
(A) 2 3/10
(B) 1 7/15
Step-by-step explanation:
(A) Add the gallons he collected together to get the total amount of milk he started with: 4/5 + 6/8 + 3/4 = 2 3/10 gallons of milk.
(B) Take that number, 2 3/10, and subtract the amount of milk he has left to get the amount of milk he used. 2 3/10 - 5/6 = 1 7/15