2 boxes per minute. 1/3 of a minute, is 20 seconds. so 2/3 of a box is made every 20 sec. Now, if there are 3, 20 sec periods in a minute, so multiply 2/3 (0.666667) boxes by 3 =2 boxes
Slope intercept form is y=mx+b, one way we can solve is by putting the two points into point slope form, y2-y1 / x2-x1 | 3-0 / -2+3 | The slope is 3, next we pull a pair from any of those two points, For example I'll use (3,0) y-0=3(x+3) | y=3x+9 | Y=3X+9 is the final answer
Step-by-step explanation:
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Answer:
2
Step-by-step explanation:
The average rate of change from x=1 to x=2 is the same as finding the slope of a line at x=1 and x=2.
So we are going to need to corresponding y coordinates.
What y corresponds to x=1? y=3
What y corresponds to x=2? y=5
So we have the ordered pairs (1,3) and (2,5).
Line the points up vertically and subtract vertically then put 2nd difference over 1st difference.
(2 , 5)
-(1 , 3)
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1 2
The average rate of change is 2/1 or just 2.
Now since we were asked to find the average rate of change given the function was a line, it really didn't matter what two points you used on that line.
Answer:f(x) = 2x³ - x² - 9x + 6
0 = 2x³ - x² - 9x + 6
0 = 2x³ + 3x² - 4x² - 3x - 6x + 6
0 = 2x³ + 3x² - 3x - 4x² - 6x + 6
0 = x(2x²) + x(3x) - x(3) - 2(2x²) - 2(3x) + 2(3)
0 = x(2x² + 3x - 3) - 2(2x² + 3x - 3)
0 = (x - 2)(2x² + 3x - 3)
0 = x - 2 or 0 = 2x² + 3x - 3
+ 2 + 2 x = -3 ± √(3)² - 4(2)(-3)
2 = x 2(2)
x = -3 ± √9 - 4(-6)
4
x = -3 ± √9 + 24
4
x = -3 ± √33
4
x ≈ -3 ± 5.74
4
x ≈ -3 + 5.74 or x ≈ -3 - 5.74
4 4
x ≈ 2.74 or x ≈ -8.74
4 4
x ≈ 0.685 or x ≈ -2.185
Step-by-step explanation:
