The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
Answer:
y=3/2x+11/2
Step-by-step explanation:
Hello! Sorry I just saw this
Anyways, let's continue
first, we need to find the equation of the line with the one that is (-2,-4) and (2,2)
first, we need to find the slope
the equation for slope is y2-y1/x2-x1
so let's label the points
x1=-2
y1=-4
x2=2
y2=2
now plug it in
2-(-4)/2-(-2)=6/4=3/2
now, let's turn it into a line
the point-slope form is y-y1=m(x-x1) (m=slope)
now, plug it in
y-(-4)=3/2(x-(-2))
simplify to
y+4=3/2(x+2)
turn into y=mx+b format
y+4=3/2x+3
subtract 4 on both sides
y=3/2x-1
Now for the line that is parallel.
Parallel lines have the same slopes, so you automatically know that the new line will be y=3/2x+b
To make sure (-3,1) is a solution to the point, put 1 as y and -3 as x
1=3/2(-3)+b
1=-9/2+b
add 9/2 on both sides
b=11/2 or 5.5
now, put it into the equation
y=3/2x+11/2
Hope this helps!
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Answer:
0.66
Step-by-step explanation:
24.95 x 25%=6.23
24.94 - 6.23 = 18.72
25.80 x 30% = 7.74
25.80 - 7.74 = 18.06
18.72 -18 .06 = 0.66
Slope: (y2-y1)/(x2-x1)
(24-(-30))/(12-(-6)) = (24+30)/(12+6)
(54)/(18) = 3
The slope is 3
