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2 years ago

The table of values represents a function f(x).

Mathematics

1 answer:

NeX [460]2 years ago

5 0

Answer:

The average rate of change over the interval [9,10] is greater than that over the interval [5,8] by 6490.

Step-by-step explanation:

The value of f(x) = 4052 for x = 9 and f(x) = 11014 for x = 10.

Therefore, the average rate of change of f(x) with respect to x over the interval [9,10] is given by

= $\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}$

= $\frac{11014 - 4052}{10 - 9} = 6962$

Now, the value of f(x) = 75 for x = 5 and f(x) = 1491 for x = 8.

Therefore, the average rate of change of f(x) with respect to x over the interval [5,8] is given by

= $\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}$

= $\frac{1491 - 75}{8 - 5} = 472$

Therefore, the average rate of change over the interval [9,10] is greater than that over the interval [5,8] by (6962 - 472) = 6490. (Answer)

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write the equation of the line that passes through the points 7, -4 and -1, 3 first and point-slope form and then in slope inter

anyanavicka [17]

The slope of line is $\frac{-7}{8}$

The point slope form is found when point (7, -4) is used is $y + 4 = \frac{-7}{8}(x - 7)$

The slope intercept form is $y = \frac{-7}{8}x + \frac{17}{8}$

<em><u>Solution:</u></em>

We have to find the equation of the line that passes through the points 7, -4 and -1, 3

<h3><u>Point slope form:</u></h3>

The point slope form is given as:

$y - y_1 = m(x - x_1)$

Where "m" is the slope of line

Given two points are (7, -4) and (-1, 3)

<h3><u>Let us find the slope of line</u></h3>

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting $(x_1 , y_1 ) = (7, -4) \text{ and } (x_2, y_2) = (-1, 3)$

$m=\frac{3-(-4)}{-1-7}=\frac{7}{-8}$

$m=\frac{-7}{8}$

Thus slope of line is found

Substitute value of m and point (7, -4) in eqn 1

$y - (-4) = \frac{-7}{8}(x - 7)\\\\y + 4 = \frac{-7}{8}(x - 7)$

Thus the point slope form is found when point (7, -4) is used

<h3><u>Slope intercept form:</u></h3>

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Substitute m = -7/8 and (x, y) = (7, -4) in eqn 1

$-4 = \frac{-7}{8}(7) + c\\\\-32 = -49 + 8c\\\\8c = 17\\\\c = \frac{17}{8}$

Substitute m = -7/8 and $c = \frac{17}{8}$ in eqn 1

$y = \frac{-7}{8}x + \frac{17}{8}$

Thus the required equation of line is found

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3 years ago

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Which best describes the following sentence?

neonofarm [45]

Answer:

Step-by-step explanation:

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2 years ago

When solving the linear equation, ax + b = 0 where a≠ 0, what is the answer of the equation x = -b/a referred as?

Oksi-84 [34.3K]

In a system of equations ax + b = 0, a≠ 0, the equation x = -b/a is referred as a non-trivial solution.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The system Ax + b = 0 has the following solutions:

The zeros, which is the trivial solution.

x = -b/a, which is the non-trivial solution.

More can be learned about a system of equations at brainly.com/question/24342899

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7 0

1 year ago

Find the interest rate r compounded monthly if the principal P = $4,300 reaches the future value F = $4,720 in t = 6 years. Roun

kirza4 [7]

Answer:

1.55%

Step-by-step explanation:

Fill in the values and solve for the rate using the future value formula.

FV = P(1 +r/n)^(nt)

4720 = 4300(1 +r/12)^(12·6)

(4720/4300)^(1/72) = 1 +r/12

r = 12(4720/4300)^(1/72) -1) ≈ 0.015542

The annual interest rate is about 1.55%.

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2 years ago

4.5<br>-<br>17 - X 8<br><br>I need help! <br>10 pts

sesenic [268]

Answer:

x = -1.5625

Step-by-step explanation:

Solve for x:

-8 x - 12.5 = 0

Add 12.5` to both sides:

(12.5 - 12.5) - 8 x = 12.5

12.5 - 12.5 = 0:

-8 x = 12.5

Divide both sides of -8 x = 12.5 by -8:

(-8 x)/(-8) = 12.5/(-8)

(-8)/(-8) = 1:

x = 12.5/(-8)

12.5/(-8) = -1.5625:

Answer: x = -1.5625

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2 years ago

The table of values represents a function ​f(x).

The table of values represents a function f(x).