Determine which elements of S satisfy the inequality

Mathematics

1 answer:

kumpel [21]2 years ago

4 0

Answer:

The elements of S-block elements are 14, so therefore to create an inequality model we declare S to be the unknown variable.

therefore since we have 14 elements we use an inclusive class interval from 1-14. the model is given as

1≤S≥14

Step-by-step explanation:

you have to declare variables before for the unknowns.

you also declare the class interval to be inclusive class interval or exclusive class interval.

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Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula [ BLANK ] The value of f(-1) is [BLANK

lesantik [10]

Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2

==============================================

Explanation:

For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval

In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank

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To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.

-------------------------------------------

Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4

This is why f(-4) = -3

-------------------------------------------

We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.

From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]

We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3

Doing those replacements and simplifying leads to...

[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2

So the average rate of change is 2

Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.

6 0

2 years ago

Samantha sends her son, Barry, to a preschool center on certain days. The cost of preschool is $45 per day along with a fixed mo

Travka [436]

Answer: Option D

D. $880 = 45d + 70$ ; $18\ days$