1. Slope = Yb - Ya / Xb - Xa
= 7-3/2-(-2)
= 7-3/2+2
= 4/4
= 1
2. Y-intercept
Y = mx + b
7 = (1)(2) + b
7 = 2 + b
7 - 2 = 2-2 + b (two’s cancel out and we are just left with our b on the right side)
5 = B
Therefore, the equation is: Y = 1x + 5 which is also the same thing as: Y= X +5.
the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.
it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.
check the picture below.
so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bparabola%20vertex%20form%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cleftarrow%20%5Ctextit%7Busing%20this%20one%7D%5C%5C%5C%5C%20x%3Da%28y-%20k%29%5E2%2B%20h%20%5Cend%7Barray%7D%20%5Cqquad%5Cqquad%20vertex~~%28%5Cstackrel%7B%7D%7B%20h%7D%2C%5Cstackrel%7B%7D%7B%20k%7D%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-5%5C%5C%20k%3D9%20%5Cend%7Bcases%7D%5Cimplies%20y%3Da%5Bx-%28-5%29%5D%5E2%2B9%5Cimplies%20y%3Da%28x%2B5%29%5E2%2B9)
![\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bwe%20also%20know%20that%20%7D%20%5Cbegin%7Bcases%7D%20x%3D-7%5C%5C%20y%3D1%20%5Cend%7Bcases%7D%5Cimplies%201%3Da%28-7%2B5%29%5E2%2B9%20%5C%5C%5C%5C%5C%5C%20-8%3Da%28-2%29%5E2%5Cimplies%20-8%3D4a%5Cimplies%20%5Ccfrac%7B-8%7D%7B4%7D%3Da%5Cimplies%20-2%3Da%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20y%3D-2%28x%2B5%29%5E2%2B9~%5Chfill)
Answer:
Yes because the answer to both of them is 1
Step-by-step explanation:
Let's solve your equation step-by-step.
−2x+9=7
Step 1: Subtract 9 from both sides.
−2x+9−9=7−9
−2x=−2
Step 2: Divide both sides by -2.
−2x
−2
=
−2
−2
x=1
Answer:
x=1
Let's solve your equation step-by-step.
2x=2
Step 1: Divide both sides by 2.
2x
2
=
2
2
x=1
Answer:
x=1
For this problem, all you need to do is find the three #'s that add up to 156.
So, lets look at the answers and add them up.
A. 50, 52, 54
50 + 52 + 54 = 156
B. 51,52,53
51 + 52 + 53 = 156
C. 49,50,51
49 + 50 + 51 = 150
D. 49,51,53
49 + 51 + 53 = 153
We get the answers (50,52,54) and (51,52,53)
Now, consecutive numbers are numbers that in order, like 1,2,3.
Therefore, the answer is (51,52,53)
Answer:
100
Step-by-step explanation:
Just so you know, there is a thing called calculator
You should really get one if you are asking such questions
Or maybe, IDK maybe DON'T BE LAZY AND LEARN TO DO SIMPLE CALCULATIONS
