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)
The GCF of 33c and 55cd is
33c/11c = 3
55cd/11c = 5d
the greatest common factor is 11c
hope this helps
Answer:
8x² - 15y² + xy
Step-by-step explanation:
(4x + 5y) (2x - 3y) + 3xy
multiplying the terms in brackets
(4x) (2x - 3y) + (5y) (2x - 3y) + 3 xy
multiplying with each terms inside the bracket
(4x)(2x) - (4x) (3y) + (5y) (2x) - (5y) (3y) + 3xy
doing the product each of the pair of terms
8x² - 12xy + 10xy - 15y² + 3xy
taking the sum of terms with coefficient "xy"
8x² - 15y² -2xy + 3xy
8x² - 15y² + xy
Answer:
Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope
So the easiest way to do so is to put the said equation in <u>y-intercept </u>form
y=mx +b
m= slope
b= y intercept
so 1. 3x + 4y = 12
=
4y = 12-3x
divide that by 4 to get only y
y=3-3/4x
-3/4 is our slope
y=-3/4x+b
than we have a point -2, -2
if we put -2 for y
-2=-3/4x+b
and then we put our -2 for x
-2 = -3/4 * -2 + b
=
-2 = -1.5 +b
b=-0.5
Answer : y=-3/4x-0.5
Net Income: I=$1,240.00
Food: F=$150.00
Car payment: C=$244.00
Rent: R=$300.00
Saving: S=$50.00
Other things: O=?
F+C+R+S+O=I
$150.00+$244.00+$300.00+$50.00+O=$1240.00
Solving for O:
$744.00+O=$1240.00
$744.00+O-$744.00=$1240.00-$744.00
O=$496.00
Percent of his net income Victor can spend on other things: P=?
P=(O/I)*100%
P=($496.00/$1240.00)*100%
P=(0.40)*100%
P=40%
Answer: 40% of his net income Victor can spend on other things.
