Answer:
x=5, x=-1
Step-by-step explanation:
Since both equations are equal to y, we can set them equal to each other
y = -x + 7 and y = 0.5(x - 3)2
-x + 7 = 0.5(x - 3)^2
Distribute the right hand side by Foiling
-x+7 =.5 ( x^2 -3x-3x+9)
Combine like terms
-x+7 = .5( x^2 -6x+9)
Distribute the .5
-x+7 = .5x^2 -3x+4.5
Add x to each side
-x+x+7 = .5x^2 -3x+x+4.5
7 = .5x^2 -2x+4.5
Subtract 7 from each side
7 -7= .5x^2 -2x+4.5-7
0 = .5x^2 -2x-2.5
Multiply by 2 to clear the decimals
0 = x^2 -4x -5
Factor
0 = (x-5) (x+1)
Using the zero product property
x-5=0 x+1 =0
x=5, x=-1
Answer:
The slope would be 1/2.
Step-by-step explanation:
Do rise over run. If you look at the y-intercept, 2, and go up 1 (rise) and over 2 (run) that tells you that the slope is 1/2. The "run" stops at 2 because it intersected into a perfect point on the graph.
Answer:
.9 miles per 5 minutes
dividing .9 by 5
equals .18 miles in 1 minute
Step-by-step explanation:
Answer:
√180 or 5√6
Step-by-step explanation:
Plug in: a^+b^2=c^2
a^2+12^2=18^2
a^2+144=324
subtract 144 from both sides
a=√180
a= 5√6
Answer:
The vertex is at (1, -108).
Step-by-step explanation:
We have the function:
And we want to find its vertex point.
Note that this is in factored form. Hence, our roots/zeros are <em>x</em> = 7 and <em>x</em> = -5.
Since a parabola is symmetric along its vertex, the <em>x-</em>coordinate of the vertex is halfway between the two zeros. Hence:
To find the <em>y-</em>coordinate, substitute this back into the function. Hence:
Therefore, our vertex is at (1, -108).