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3 years ago

Can the average rate of change of a function be constant ? Explain

Mathematics

1 answer:

Marianna [84]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

The average rate of change of any linear function is a constant. That fact is what makes it a linear function.

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Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

Answer

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

2 years ago

The product of a number and -7/10 is 1/2 What is the number?

kirza4 [7]

1/2*5
5/10+-7/10
-2/10

4 0

3 years ago

Pls answer the question in the picture.

mr_godi [17]

Answer:

5:2

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Chloe kicks a soccer ball across a field. The height of the ball above the ground is given by the equation

Reika [66]

Answer:

It takes 3.5 seconds for the ball to hit the ground

Step-by-step explanation:

By finding the x intercepts you can determine when the ball hits the ground.

the second x intercept is (3.5,0), which means the ball hits the ground at 3.5 seconds

4 0

3 years ago

In AGHI, the measure of ZI=90°, GH = 96 feet, and IG = 25 feet. Find the measure of ZH to the nearest tenth of a degree.

iVinArrow [24]

Answer:

15.1

Step-by-step explanation:

4 0

2 years ago