Answer:
Assume that Sn is valid for n = k and prove that Sn is valid for n = k + 1.
Step-by-step explanation:
This is the second step in the principal of mathematical induction. The three steps in the principals of mathematical induction are:
1. show that something works for the first case (base or anchor step)
2. assume that it works for any particular step (inductive hypothesis), and then
3. show that it works for the next case (inductive step)
p. 621 in textbook
It's weird that they put steps 2 & 3 together, but it was correct on the test so ¯\_(ツ)_/¯
The slope of the line that passes through the points (x1, y1) and (x2,y2) is computed as follows:
In this case, the points are (24, 28) and (8,8), then its slope is:
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Substituting into the general equation with m = 5/4 and the point (24, 28) we get:
Finally, the equation is
y = 5/4x - 2
Answer:
35 hotdogs
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling hotdogs and sodas.
Let the number of hot dogs be represented by x
The number of soda be represented by y
You sold a total of 87 hotdogs and sodas combined
x + y = 87
x = 87 - y
Each hotdog cost $1.50 and each soda cost $0.50. At the end of the night you made a total of $78.50.
Hence we have the equation:
$1.50 × x + $0.50 × y = $78.50
1.50x + 0.50y = 78.50
Substitute 87 - y for x
1.50(87 - y) + 0.50y = 78.50
130.5 - 1.50y + 0.50y = 78.50
Collect like terms
- 1.50y + 0.50y = 78.50 - 130.50
-1.00y = -52
y = -52/-1
y = 52 sodas
How many hotdogs did you sell?
Using the equation:
x = 87 - y
x = 87 - 52
x = 35 hotdogs
Hence, you sold 35 hotdogs
