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vichka [17]
2 years ago
11

Find the average rate of change of each function on the interval specified.

Mathematics
1 answer:
ExtremeBDS [4]2 years ago
4 0

The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by

f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}

So for f(x) = x² on [1, 5], the AROC of f is

f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}

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Solve a) 2(x+3)=x-4 b) 4(5x-2)=2(9x+3)
Nat2105 [25]

Answer:

a) -10 b) 7

Step-by-step explanation:

a) 2(x+ 3) = x - 4

2x + 6 = x - 4

2x - x = -6 - 4

x = -10

b) 4(5x - 2) = 2(9x + 3)

20x - 8 = 18x + 6

20x - 18x = 6 + 8

2x = 14

x = 14/2

x = 7

5 0
3 years ago
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-8(6+X) + 4(2x + 7) = 0
Talja [164]

Answer:

-20 = 0

Step-by-step explanation:

-8 (6 + x) + 4 (2x + 7) = 0

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-20 = 0

3 0
2 years ago
The scores of the first two football games were 28 and
butalik [34]

Answer:

35+28=63

Step-by-step explanation:

hope this helps

4 0
3 years ago
CAN SOMEONE JUST PLEASE ANSWER THIS ASAP FOR BRAINLIEST!!!!
gizmo_the_mogwai [7]

Answer:

When the ball hit the ground, the height of the ball will be zero. So using the value of h(x) as zero in the given equation, we can find the time in which the ball will hit the ground.


0 = -(x-2)^2 + 16


(x-2)^2 = 16


x-2 = 16


x-2 = 4


x = 6


This means the ball will hit the ground 6 seconds after Amir threw it.



Step-by-step explanation:


7 0
3 years ago
Dawn has been using two bank accounts to save money for a car. the difference between account 1 and account 2 is $100. if she us
asambeis [7]
1) name the variables:

 - amount in account 1 "a"
 - amount in account 2 "b"

2) trtanslate the statements into equations:

<span>- the difference between account 1 and account 2 is $100.

=> a - b = 100

-  if she uses 3/8 of account 1 and 7/8 of account 2, Dawn will have a down payment of $2,000.

=> (3/8)a + (7/8)b = 2000

3) solve the system of equations

(1) a - b = 100
(2) (3/8)a + (7/8b) = 2000

Steps:

- multiply equation (1) by 7 and equaton (2) by 8

=>

(1) 7a - 7b = 700
(2) 3a + 7b = 16,000

- add the two equations

=>

7a + 3a - 7b + 7b = 700 + 16,000

- combine like terms:

10a = 16,700

- divide by 10:

a = 16,700 / 10 = 1670

- use equation (1) to find b:

a - b = 100 => b = a - 100 = 1670 - 100 = 1570

Answer: Dawn has $ 1670 in account 1 and $ 1570 in account 2. </span>
8 0
3 years ago
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