The set of numbers 1, 5, 13, and 24 contains values for m. What values of m makes the equation below true?
1 answer:
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Answer:
Step-by-step explanation:
In order to solve all of these problems, you have to first create an equation. The typical format for an equation looks like this: y = mx + b
m is the slope and b is the y-intercept.
In order to create an equation, you have to find the slope and y-intercept of the function. You can find the slope using this expression: To find the y-intercept, you use a known point and the slope in the equation to solve for b.
Now that we know this, we can solve the problems.
1a.
To create the equation, let's find the slope using points (1, 15) and (2, 30)
= 15/1 = 15
The equation now looks like this: h = 15w + b
Let's use the point (1, 15) from the table to find b
15 = 15(1) + b
15 = 15 + b
subtract 15 from both sides the isolate the b
0 = b
There is no y-intercept for this equation, so the equation looks like this:
h = 15w
1b. We know the equation is h = 15w, so all we have to do is input the 9 into the equation.
h = 15(9)
h = 135
2a. We'll use the points (1, 8) and (2, 16) to find the slope
= 8/1 = 8
The slope is 8.
Since it's impossible to sell any houses in 0 months, we already know that there is no y-intercept, so the equation looks like this:
h = 8m
2b. Put the value of 15 inside the equation and solve.
h = 8(15)
h = 120
3a. We'll use the points (1, 35) and (2, 70) to find the slope.
= 35/1 = 35
The slope is 35.
It's impossible to see any movies in 0 months, so there is no y-intercept. The equation looks like this:
c = 35m
3b. We know that there are 12 months in a year, so put 12 into the equation and solve.
c = 35(12)
c = 420
4a. We'll use the points (1, 8) and (2, 16) to find the slope
= 8/1 = 8
The slope is 8.
It's impossible for there to be a cost if there are no hats, so the y-intercept must be 0. The equation looks like this:
c = 8h
4b. Put the 30 hats into the equation and solve.
c = 8(30)
c = 240
Answer:
Step-by-step explanation:
I really hope you know how to use your calculator to find regression equations, because in this forum it is impossible to teach you how to do that. I ran the data through my calculator and got the exponential equation as
which means at 4 hours, we started with 1963 bacteria and it is growing at a rate of 114% each hour. Since we started out with an x value of 0, and that value represents the number of bacteria after 4 hours, then time 0 is 4 hours, which means that time 12 is 16 hours. We replace the x in the equation with a 12 and do the math:
which gives us, in the end,
y = 9460