<h2><u>
Answer:</u></h2>
<u />
<h2><u>
</u></h2><h2><u>
S</u><u>olution Steps: </u></h2><h3>- Graphing -</h3><h3>______________________________
</h3><h3>
</h3><h3>1.) <u>Graph:</u></h3>
- Since we know
, you graph
on the
-axis. And this is an ending, meaning it doesn't go on forever.
- However, we don't know what
is. So because we don't know what
is we still graph it but it'll go on forever.
<em> - You can either graph this like this, OR graph this using desmos.com. </em>
<h3><u /></h3><h3><u>Vertical or Horizontal?</u> </h3>
Horizontal, Left and Right.
- <em />
<em> </em>Vertical, Up and Down.
- So since we know
is, (Horizontal,) we have to graph
, (Vertical.) So to sum this up, this just means whatever variable you don't know yet, that will be the one that you graph as an infinite.
<h3>______________________________
</h3><h3 />
Answer:
See below
Step-by-step explanation:
Using the table of 150 students, we can configure probabilities.
18 students participate in tennis, so the probability of a student participating in tennis is 18/150, or 3/25 simplified.
45 students participate in football, so the probability of a student participating in football is 45/150, or 3/10 simplified.
12 students participate in gymnastics, so the probability of a student participating in gymnastics is 12/150, or 2/25 simplified.
9 students participate in volleyball, so the probability of a student participating in volleyball is 9/150, or 3/50 simplified.
We have to determine the equation of the line passing through the point (2,-5) and parallel to the line ![5x = 6y+7](https://tex.z-dn.net/?f=5x%20%3D%206y%2B7)
When two lines are parallel, then the slopes of the two lines are equal.
Equation of line with point
and slope 'm' is given by:
![(y-y_1) = m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%20%3D%20m%28x-x_1%29)
Since, we have to determine the equation of a line with point (2,-5).
So, the equation of the line is : ![(y-(-5)) = m(x-2)](https://tex.z-dn.net/?f=%28y-%28-5%29%29%20%3D%20m%28x-2%29)
![y+5 = m(x-2)](https://tex.z-dn.net/?f=y%2B5%20%3D%20m%28x-2%29)
Since, the line is parallel to the line ![5x = 6y+ 7](https://tex.z-dn.net/?f=5x%20%3D%206y%2B%207)
So, ![6y +7 = 5x](https://tex.z-dn.net/?f=6y%20%2B7%20%3D%205x)
![6y = 5x - 7](https://tex.z-dn.net/?f=6y%20%3D%205x%20-%207)
![y = \frac{5}{6}x - \frac{7}{6}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5%7D%7B6%7Dx%20-%20%5Cfrac%7B7%7D%7B6%7D)
So, slope of the line 'm' is
.
Therefore, the equation of the line is:
![(y+5) = \frac{5}{6}(x-2)](https://tex.z-dn.net/?f=%28y%2B5%29%20%3D%20%5Cfrac%7B5%7D%7B6%7D%28x-2%29)
![6y + 30 = 5x - 10](https://tex.z-dn.net/?f=6y%20%2B%2030%20%3D%205x%20-%2010)
![6y - 5x = -10-30](https://tex.z-dn.net/?f=6y%20-%205x%20%3D%20-10-30)
![6y - 5x = -40](https://tex.z-dn.net/?f=6y%20-%205x%20%3D%20-40)
Therefore,
is the required equation of the line.
Answer:
f
−
1
(
x
)
=
9
x
−
18
Explanation:
To find the inverse or
f
−
1
(
x
) of a function we solve the equation for x
So in this example, we can start by subtracting
2 from both sides: y
−
2
=
1
9
x
+
2
−
2
Next we multiply
9 to each side to isolate the variable x 9
(
y
−
2
)
=
1
x
9
⋅
9
9
y
−
18
=
x
Since the function of a line is written in terms of y we can simply switch x and y and rewrite the equation to get: y
=
9
x−
18 or f
−
1
(
x
)
=
9
x
−
18
As p and s should occupy the first and last position, the first and last position can be filled in only one way. The remaining 4 positions can be filled in 4! Ways by the remaining words (S,C,E,N,T). hence by rearranging the letters of the word ASCENT we can form 1x4!