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:
(3,-5)
Step-by-step explanation:
We first cal ulate the distance
Answer:
84,375 m^2
Step-by-step explanation:
We need to find the surface area of the pyramid. The pyramid can be divided into 4 triangles and one square (the bottom).
Area of a triangle is 1/2*b*h where b is the base of the triangle and h is the height.
Area of a square is length times width.
Total area = 
Answer:
37°
Step-by-step explanation:
(4x + 2)° = 150° [Vertically Opposite Angles]
=> 4x = 150 - 2
=> 4x = 148
=><u> x = 37° (Ans)</u>
<h3>Answer:</h3>
A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°
<h3>Explanation:</h3>
The sum of angles in ∆ABC is 180°, so ...
... (2x -2) + (2x +2) + (5x) = 180
... 9x = 180
... x = 20
and the angles of ∆ABC are ∠A = 38°, ∠B = 42°, ∠C = 100°.
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The sum of angles of ∆A'B'C' is 180°, so ...
... (58 -x) +(3x -18) +(120 -x) = 180
... x +160 = 180
... x = 20
and ∠A' = 38°, ∠B' = 42°, ∠C' = 100°.
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The values of angle measures of ∆ABC match those of ∆A'B'C', so we can conclude ...
... A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°
