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 formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.
Step-by-step explanation:
1)Write down the formula for finding the volume of a rectangular prism. The formula is simply V = length * width * height.
2)Find the length.
3)Find the width.
4)Find the height.
5)Multiply the length, the width, and the height.
6)State your answer in cubic units.
Answer:
Step-by-step explanation:
Let p represent cost of each drink.
We have been given that the medium pizza costs two times as much as one drink, so the cost of medium pizza would be 
.
We are also told that the large pizza costs three times as much as one drink, so the cost of la pizza would be 
.
We have been given that Mary wants to buy one large pizza, one medium pizza, and three drinks.
Since the cost of one drink is p, so cost of 3 three drinks would be .
The total cost of one large pizza, one medium pizza, and three drinks would be 
Mary started with $30, so amount left after all of her purchases would be 30 minus total cost of all purchases.
Therefore, Mary will have dollars left after making all of her purchases.
They definitely can be positive they can be negative and they can have an absolute value but I would choose they both can be positive and negative
Answer:
y = -8x -25
Step-by-step explanation:
The 2-point form of the equation of a line is useful when you are given 2 points.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (7 -(-1))/(-4 -(-3))(x -(-3)) +(-1)
y = 8/-1(x +3) -1
y = -8x -25
