The flat fee that the store charges is $14 and the cost for 7 hours is $56
A linear equation is on the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
let f for the total rental cost of a vacuum cleaner for x hours
Using the points (1, 20) and (3, 32) from the table:
The flat fee that the store charges is $14
The reasonable domain is 1 ≤ x ≤ 12
The cost for 7 hours is:
f(7) = 6(7) + 14 = 46
Find out more on linear equation at: brainly.com/question/14323743
<h3>
Answer: -2</h3>
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Explanation:
We use the remainder theorem. This is the idea where if we divide P(x) over (x-k), then the remainder is P(k).
Comparing x+1 to x-k shows that k = -1
It might help to rewrite x+1 as x-(-1) to get it into the form x-k better.
Plug this k value into the function
f(x) = 2x^6 + 3x^5 - 1
f(-1) = 2(-1)^2 + 3(-1)^5 - 1
f(-1) = 2(1) + 3(-1) - 1
f(-1) = 2 - 3 - 1
f(-1) = -1 - 1
f(-1) =-2
The remainder is -2
We can confirm this through synthetic division or polynomial long division.
You have to make sure that whatever you do to one side, you also do to the other.
2x + 37 = 8x + 7
2x + 37 - 2x = 8x + 7 - 2x
37 = 6x + 7
37 - 7 = 6x + 7 - 7
30 = 6x
30 / 6 = 6x / 6
5 = x
x = 5
Hope this helps! :)
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Step-by-step explanation:
The slope intercept form for a line is y = mx + b.
↑ <span>↑
m is the slope of the line or how steep it is. b is where the line runs into the y axis at one point. x and y are the values you plug in when you have a specific point you want to use (x, y).
For the first picture, you can see that the line "intercepts" or collides with the y axis at 1. Thus we know the b value.
To find the slope, you just pick 2 points on the line and plug them into a little equation (try to memorize this equation, it helps to find slope):
m = (y</span>₂ - y₁)/(x₂ - x₁)
The two points we'll use are (1, 0) and (0, 1) since x goes through both of
those points. ↑ ↑ ↑ ↑
x₁ y₁ x₂ y<span>₂
m = (1 - 0)/(0 - 1)
m = 1 / -1
m = -1
This makes sense - since the slope is going downward, the slope is negative.
So the equation is:
y = -x + 1
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For the second problem, We can see the line intercepts the y-axis at -5. That is our b value.
The the slope of this line is 0 since it is not going up or down, so that is our m value:
y = 0(x) - 5 = -5
The equation of the line is y = -5</span>
