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sergejj [24]
3 years ago
12

The average rate of change of f from 2 to 3

Mathematics
1 answer:
ella [17]3 years ago
3 0

For a function of f, the average rate of change can be found as follows:


ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}


So, this problem asks for the Average Rate of Change of f from x_{1}=2 to x_{2}=3. In this way, we need to find f(x_{1}) \ and \ f(x_{2}). As you can see above, we have the graph of f(x), so we can find these values. Thus, from the graph:


f(x_{1})=4 \\ f(x_{2})=1


Therefore:


ARC=\frac{1-4}{3-2} \\ \\ \therefore \boxed{ARC=-3}

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URGENT WILL GIVE YOU 100 POINTS PLEASE ANSWER CORRECTLY
wariber [46]

Answer:

1. x = 18.4

2. x = -1.25

3. x = \frac{5}{12}

4. x = 12.3

5. x = 6.4

6. z = 5.8

7. x = \frac{1}{12}

8. x = -\frac{1}{4}

9. x = \frac{1}{3}

10. x = -9

11. z = 18

12. x = 7

13. x = -9

14. x = -36

15. x = -7

16. x = 8

17. z = -1.5

18. x = -\frac{45}{7}

19. x = 16

20. x = -12

21. x = \frac{8}{3}

22. x = -1.6

23. x = 1.8

24. x = -8.2

Step-by-step explanation:

1. x - 3.5 = 14.9 (add 3.5 to each side)

x = 18.4

2. x + 2.25 = 1 (subtract 2.25 from each side)

x = -1.25

3. -\frac{1}{3} = x - \frac{3}{4} (add \frac{3}{4} to each side)

\frac{3}{4} - \frac{1}{3}  = x (multiply \frac{3}{4} by \frac{3}{3} and \frac{1}{3} by \frac{4}{4} to get a common denominator)

\frac{9}{12} - \frac{4}{12} = x

\frac{5}{12} = x

4. x - 2.8 = 9.5 (add 2.8 to each side)

x = 12.3

5. x - 8.5 = -2.1 (add 8.5 to each side)

x = 6.4

6. z - 9.4 = -3.6 (add 9.4 to each side)

z = 5.8

7. x + \frac{5}{6} = \frac{11}{12} (subtract \frac{5}{6} from each side)

x = \frac{11}{12} - \frac{5}{6} (multiply \frac{5}{6} by \frac{2}{2} to get a common denominator)

x = \frac{11}{12} - \frac{10}{12}

x = \frac{1}{12}

8. -\frac{5}{6} + x = -\frac{13}{12} (add \frac{5}{6} to each side)

x = \frac{5}{6} - \frac{13}{12} (multiply \frac{5}{6} by \frac{2}{2} to get a common denominator)

x = \frac{10}{12} - \frac{13}{12}

x = -\frac{3}{12} = -\frac{1}{4}

9. x - \frac{1}{9} = \frac{5}{18} (add \frac{1}{9} to each side)

x = \frac{1}{9} + \frac{5}{18} (multiply \frac{1}{9} by \frac{2}{2} to get a common denominator)

x = \frac{2}{18} + \frac{5}{18}

x = \frac{6}{18} = \frac{3}{9} = \frac{1}{3}

10. x + 6 = -3 (subtract 6 from each side)

x = -9

11. z - 7 = 11 (add 7 to each side)

z = 18

12. -1 = x - 8 (add 8 to each side)

7 = x

13. -4x = 36 (divide each side by -4)

x = -9

14. -\frac{x}{3} = 12 (multiply each side by -3)

x = -36

15. 63 = -9x (divide each side by -9)

-7 = x

16. 6.4 = 0.8x (divide each side by 0.8)

8 = x

17. -2.8z = 4.2 (divide each side by -2.8)

z = -1.5

18. -\frac{7}{9}x = 5 (divide each side by -\frac{7}{9})

x = \frac{5}{1} ÷ -\frac{7}{9}

x = \frac{5}{1} (times) -\frac{9}{7}

x = -\frac{45}{7}

19. \frac{1}{2}x = 8 (divide each side by \frac{1}{2})

x = 16

20. -\frac{3}{4}x = 9 (divide each side by -\frac{3}{4})

x = -12

21. -\frac{7}{8}x = -\frac{21}{64} (divide each side by -\frac{7}{8})

x = -\frac{7}{8} ÷ -\frac{21}{64}

x = -\frac{7}{8} (times) -\frac{64}{21}

x = \frac{448}{168} = \frac{56}{21} = \frac{8}{3}

22. 1.6x = -3.2 (divide each side by 1.6)

x = -1.6

23. -\frac{1}{2} = -\frac{5}{18}x (divide each side by -\frac{5}{18})

1.8 = x

24. -2.5x = 20.5 (divide each side by -2.5)

x = -8.2

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madreJ [45]
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