Mathematics, 24.01.2021 14:00 karlrey4401

Find the average rate of change for the given function over the indicated values of x. If necessary, round your final answer to two decimal places. y= 4x^2 − 11x − 11, where x goes from 1 to 4.

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Answer from: Rafael01

The rate of change of a function over a given interval is required.

The average rate of change is 18

Rate of change

The given function is

f(x)=x^2+6x

The interval is between x=5 to x=7

Finding the corresponding values

$y=5^2+6\times 5=55$

$y=7^2+6\times 7=91$

The two points are

(5,55),(7,91)

The slope is

$m=\dfrac{\Delta y}{\Delta x}\\\Rightarrow m=\dfrac{91-55}{7-5}\\\Rightarrow m=18$

Learn more about rate of change:

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Answer from: sampurple123

The average rate of change of the function in this interval is of 18.

Step-by-step explanation:

The average rate of change of a function f(x) in an interval from a to b is given by:

$A = \frac{f(b) - f(a)}{b - a}$

In this question:

f(x) = x^2 + 6x

Where x goes from 5 to 7.

This means that b = 7, a = 5 . So

f(7) = 7^2 + 6(7) = 49 + 42 = 91

f(5) = 5^2 + 6(5) = 25 + 30 = 55

The rate of change is:

$A = \frac{f(7) - f(5)}{7 - 5} = \frac{91 - 55}{2} = 18$

The average rate of change of the function in this interval is of 18.

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

Answer from: Quest

You need to show me the graphs so that i can choose one

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