Answer:

Step-by-step explanation:
![S= \frac{n}{2 [2a + (n - 1)d]}](https://tex.z-dn.net/?f=S%3D%20%5Cfrac%7Bn%7D%7B2%20%5B2a%20%2B%20%28n%20-%201%29d%5D%7D)
Simplifying the fraction by multiplying d into the (n-1) term,
![s=\frac{n}{2 [2a + (n - 1)d] } = \frac{n}{2[2a + dn - d] }](https://tex.z-dn.net/?f=s%3D%5Cfrac%7Bn%7D%7B2%20%5B2a%20%2B%20%28n%20-%201%29d%5D%20%7D%20%3D%20%5Cfrac%7Bn%7D%7B2%5B2a%20%2B%20dn%20-%20d%5D%20%7D)
Simplifying the fraction by multiplying 2 throughout,

Multiply
on both sides

Cancel the
on the right hand side

Multiply s to the terms,

Move
to the right hand side by subtracting
on both sides

On the right hand side of the equation, take out 

Divide Left hand side by
,

Let's take this one at a time starting from the brother's net income because this would be the root basis. We let x be the number of lawns his brother and Tom mowed.
Brother's Net Income = 32x - 12x = 20x
Mitch promises to pay the borrowed money of $500 plus 40% of what his brother earns. The algebraic equation for this is:
Mitch's payment = $500 + 0.4(20x) = $500 +$8x
Answer:
Step-by-step explanation:
The given function is
and we need to graph it.
In order to graph this function, we'll find below things:
Horizontal asymptote:
Since the degree of both numerator and denominator is same. Hence, the horizontal asymptote is the ratio of leading coefficient of numerator to the leading coefficient of denominator.
Horizontal asymptote is y = 1/1 = 1
Vertical asymptote:
Vertical asymptote occurs where the denominator is zero.

x-intercepts:
For x-intercept, y = 0
y-intercepts:
For y-intercept, x= 0
Using these, we can draw the graph of the rational expression.
Answer:the short cut is 55 meters.
Step-by-step explanation:
The park around which the jogger jogged is rectangular in shape. The Short cut that the jogger jogged through to her car is the diagonal of the rectangle. The diagonal becomes the hypotenuse of the rectangle. The sides of the field becomes the opposite side and adjacent side of the triangle. To determine the length of the diagonal, we would apply Pythagoras theorem. It is expressed as
Hypotenuse^2 = opposite side^2 + adjacent side^2
Hypotenuse^2 = 44^2 + 33^2 = 3025
Hypotenuse = √3025
Hypotenuse = 55 meters