Answer:
The vertex of this parabola,
, can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
,
where
,
, and
are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at
.
The vertex form can be expanded to obtain:
.
Compare that expression with the given equation of this parabola. The constant term, the coefficient for
, and the coefficient for
should all match accordingly. That is:
.
The first equation implies that
is equal to
. Hence, replace the "
" in the second equation with
to eliminate
:
.
.
Similarly, replace the "
" and the "
" in the third equation with
and
, respectively:
.
.
Therefore,
would be equivalent to
. The vertex of this parabola would thus be:
.
Answer:

Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines will always have the same slope but different y-intercepts.
<u>1) Determine the slope of the parallel line</u>
Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

Switch the sides

Divide both sides by 2 to isolate y

Now that this equation is in slope-intercept form, we can easily identify that
is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope
. Plug this into
:

<u>2) Determine the y-intercept</u>

Plug in the given point, (4,0)

Subtract both sides by 6

Therefore, -6 is the y-intercept of the line. Plug this into
as b:

I hope this helps!
Answer:
5
Step-by-step explanation:
take your price and subtract the monthly price
115-40=75
now you have the price of all your extra devices summed up
75÷15=5 extra devices
2x + y = 10 is y = -2x + 10
4x + 7 = 40
-7 -7
4x = 33
4 4
x = 8.25
y = -2(8.25) + 10
y = -6.5 and x = 8.25
Hope this helps :)
Here is your solution,
(-5)^2 - √25 - 4 x (-14)/2
25 - √ 25 + 56/2
25 - √81/2
(25 - 9)/2 = 16/2 = 8
or
25 + √25 +56/2
25 + √81/2
(25 + 9)/2 = 34/2 = 17
So m = 8,17