Answer:
Option A. These two lines are perpendicular
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are equal
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
step 1
Convert the given equation A in slope intercept form
where
m is the slope
b is the y-intercept
we have
----> equation A
Solve for y
That means----> isolate the variable y
Divide by 3 both sides
so
step 2
Convert the given equation B in slope intercept form
where
m is the slope
b is the y-intercept
we have
----> equation B
Solve for y
That means----> isolate the variable y
subtract 3x both sides
Divide by 2 both sides
so
step 3
Compare the slopes
The slopes are opposite reciprocal (the product is equal to -1)
therefore
These two lines are perpendicular
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Okay so I attatched pictures of my work. I would just graph it by plugging in x-values on either side of the vertex into the equation. For example, the vertex is at (-2,3). So try plugging x=-5 and x=1 into the equation (y=a(x-h)^2 +k).
y=(x+2)^2 +3
y=((1)+2)^2 +3=(3)^2+3= 9+3=
12
Now you can plot the vertex (-2,3), the point (1,12), and (-5,12). From there just connect the dots and you should get a graph that looks similar to the last picture I attached. Hope this all made sense sorry it was so wordy I just wasn't sure how much you knew or didn't know. So, I thought it would be better to explain it all rather than not enough.
x=23
a²+b²=c²
25+144=169
the square root of 169 is 13
add 10 to get x
23
