y = 3(x + 4)^2 + 31
Step-by-step explanation:
We can convert the given quadratic equation into its vertex form by completing the square:
y = 3x^2 + 24x + 43
= 3(x^2 + 8x) + 43
= 3(x^2 + 8x + 4) + 31
= 3(x + 4)^2 + 31
This is the vertex form of the given quadratic equation with (-4, 31) as its vertex
Answer:
The graph of the equation 40.51x+12.45y=666.64 is attached with the answer where the horizontal axis represents the X axis and the vertical axis represents Y axis.
To plot the graph physically just find two points lying on the line. Mark the points on the graph sheet and then join them. This will give you the line represented by the equation.
To find points on the line assume the value of any one variable, substitute it in the equation, then solve the equation to find the value of other variable. For example : assume y = 1; substitute the value of y in the equation;
⇒ 40.51x + 12.45×1 = 666.64
⇒ 40.51x = 666.64 - 12.45
⇒ 40.51x = 654.19
⇒ x = 
⇒ x ≈ 16.149
Therefore point ( 16.149 , 1 ) lie on the graph of the equation.
***Only two points are required to plot this graph just because it represents a straight line, that we can conclude just by observing the equation. If in an equation the power of x is 1 or 0 and power of y is 1 or 0 then only it will represent a straight line in 2-D plane.***
Answer:
multiply the first equation by 2
Step-by-step explanation:
24x + 36y = 72
-16x + 8y = 80
48x + 72y = 144
-48x + 24y = 240
96y = 384
y = 4
24x + 36(4) = 72
24x + 144 = 72
24x = -72
x = -3
(-3, 4)
140 degrees !!!!!.?.?.?)273)!343;(43
I actually believe that the slope is -1/2. This is because you have to go up 1 and left 2. since going left means it is negative the answer would be -1/2.