Answer:
P'(7,0)Q'(2,1) R'(12,-6)
Step-by-step explanation:
P(3,5)------>P'(3+4,5-5)
P'(7,0)
Q(-2,6)----->Q'(-2+4,6-5)
Q'(2,1)
R(8,-1)------>R'(8+4,-1-5)
R'(12,-6)
The standard form of a parabola is y=ax²+bx+c
use the three given points to find the three unknown constants a, b, and c:
-2=a+b+c............1
-2=4a+2b+c......... 2
-4=9a+3b+c...........3
equation 2 minus equation 1: 3a+b=0..........4
equation 3 minus equation 2: 5a+b=-2.........5
equation 5 minus equation 4: 2a=-2, so a=-1
plug a=-1 in equation 4: -3+b=0, so b=3
Plug a=-1, b=3 in equation 1: -2=-1+3+c, so c=-4
the parabola is y=-x²+3x-4
double check: when x=1, y=-1+3-4=-2
when x=2, y=-4+6-4=-2
when x=3, y=-9+9-4=-4
Yes.
Incomplete Question the complete Qs is
Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m = 1/2?
a: y=1/2x+2
b: y=-2x+1/2
c: x-2y=-4
d: y-1=1/2(x+2)
Answer:
The Correct option is c. x-2y=-4
Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

Step-by-step explanation:
Given:

point A(x₁, y₁)=(-2,1)
To Find:
Equation of Line =?
Solution:
Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,
i.e equation in point - slope form
Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2 , 1) we get
As required
Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

First take the amount of drinks and popcorn needed then multiply the amount by the price then see if she has enough money when you finish the multiplying.
Answer:
sine 23 = x/21
Multiply both sides by 21
21 x sine 23 = x
Now, use a calculator and find the answer of the 21 times the sine of 23:
x = -17.7706284876