Answer:
Step-by-step explanation:
This can be set up like an inequality. Chances are just as likely that you are in ratios and proportions, but since I'm not sure, I'm going with the easier way for this particular situation. The inequality, before reducing, is:
20 < 4x < 40,
which states that a 4 minute shower uses less than 40 gallons but greater than 20 gallons, where x is the number of gallons of water. Therefore,
5 < x < 10 results when you simplify. This puts things in terms of 1 minute now. This states that a 1 minute shower uses less than 10 gallons of water but more than 5 gallons. We got this by dividing everything by 4.
Now that things are in terms of a single minute, all you have to do is multiply the greatest number of gallons by 18 and the least number of gallons by 18 (and the x as well) to get the number of gallons used in an 18 minute shower as a range:
90 < 18x < 180
Answer:
c
Step-by-step explanation:
1 and 3/5 is 8/5
8/5 * 5/8 is 8/5 * 8/5
64/25
25*2 is 50
64-50 is 14
2 and 14/25 or 2 14/25
Answer:
y = g(x) = 1 + x
Now, the range of a function is the set of the possible values of y.
In this function, a linear function, y can be any real number, so the range of this function is { y ∈ ℝ )
y = h(x) = x^2 + 2*x
This is a quadratic function, as the leading coefficient is positive, we know that the arms of the function go up.
For a quadratic function y = a*x^2 + b*x + c
The minimum is at:
x = -b/2a.
In this case, b = 2 and 1 = 1
the minimum is at:
x = -2/2 = -1
The minimum is:
y = h(-1) = 1^2 +2*(-1) = -1
Then the range of this function is
{y ∈ ℝ ≥ -1 )
The composite functions are:
g∘h = g(h(x)) = 1 + x^2 + 2*x
The minimum is still at x = -1
g∘h(-1) = 1 + -1^2 + 2*-1 = 0
Then the range of this function is:
{y ∈ ℝ ≥ 0 )
The other composition is:
h∘g = h(g(x)) = (1 + x)^2 + 2*(1 + x) = 1 + 2*x + x^2 + 2 + 2*x
h∘g = x^2 + 4*x + 3
Here the minimum is at:
x = -4/2*1 = -2
h∘g(-2) = (-2)^2 + 4*-2 + 3 = 4 - 8 + 3 = -1
The range is:
{y ∈ ℝ ≥ -1 )
Answer:
As a fraction:
x | y
________
|
7/3 | 2
3 | 4
11/3 | 6
13/3 | 8
As a mixed fraction:
x | y
________
|
2 ⅓ | 2
3 | 4
3 ⅔ | 6
4 ⅓ | 8
As a decimal:
x | y
___________
|
2.33.. | 2
3 | 4
3.66.. | 6
4.33.. | 8
You should start with x values since the y values will be easier to plot. x's will not be easy to represent.
For example:
x | y
________
|
0 | -5
1 | -2
2 | 1
3 | 4
4 | 7
5 | 10
Hi there
total payments
437.78×12
=5,253.36
If Jocelyn pays off the loan
437.78×5+2,897.95
=5,086.85
she will save
5,253.36−5,086.85
=166.51
Good luck!
