A) since the ratio of green peppers to pureed tomatoes is 1:4, the tomatoes have 4 times the amount of mL as the peppers, so there are 20mL of green peppers he should mix with 80 mL of pureed tomatoes.
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
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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.
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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
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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.
Answer:
The first thing you do is:
Step-by-step explanation:
How to calculate 60 divided by 19
Here we will show you step-by-step with detailed explanation how to calculate 60 divided by 19 using long division.
Before you continue, note that in the problem 60 divided by 19, the numbers are defined as follows:
60 = dividend
19 = divisor
Step 1:
Start by setting it up with the divisor 19 on the left side and the dividend 60 on the right side like this:
1 9 ⟌ 6 0
Step 2:
The divisor (19) goes into the first digit of the dividend (6), 0 time(s). Therefore, put 0 on top:
0
1 9 ⟌ 6 0
Step 3:
Multiply the divisor by the result in the previous step (19 x 0 = 0) and write that answer below the dividend.
0
1 9 ⟌ 6 0
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (6 - 0 = 6) and write the answer below.
0
1 9 ⟌ 6 0
- 0
6
Step 5:
Move down the 2nd digit of the dividend (0) like this:
0
1 9 ⟌ 6 0
- 0
6 0
Step 6:
The divisor (19) goes into the bottom number (60), 3 time(s). Therefore, put 3 on top:
0 3
1 9 ⟌ 6 0
- 0
6 0
Step 7:
Multiply the divisor by the result in the previous step (19 x 3 = 57) and write that answer at the bottom:
0 3
1 9 ⟌ 6 0
- 0
6 0
5 7
Step 8:
Subtract the result in the previous step from the number written above it. (60 - 57 = 3) and write the answer at the bottom.
0 3
1 9 ⟌ 6 0
- 0
6 0
- 5 7
3
