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3 years ago

What is the average rate of change for f (x)=0.5 (-10x + 24)?

Mathematics

1 answer:

xenn [34]3 years ago

5 0

Answer:

The rate of change of the function is -5.

Step-by-step explanation:

Given : Function $f(x)=0.5(-10x+24)$

To find : What is the average rate of change ?

Solution :

Function $f(x)=0.5(-10x+24)$

The rate of change is the first derivative.

$f(x)=-5x+12$

Derivate w.r.t. x,

$f(x)=-5$

Therefore, The rate of change of the function is -5.

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If sin theta= - 5/7, which of the following are possible?

Sphinxa [80]

Answer:

$\large\boxed{\sec\theta=\dfrac{7}{\sqrt{24}},\ and\ \tan\theta=-\dfrac{5}{\sqrt{24}}}\\\boxed{\cos\theta=\dfrac{\sqrt{24}}{7},\ and\ \tan\theta=\dfrac{5}{\sqrt{24}}}$

Step-by-step explanation:

$\text{Use:}\\\\\sin^2\theta+\cos^2\theta=1\to\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\\\\\sec\theta=\dfrac{1}{\cos\theta}\\\\==========================\\\\\sin\theta=-\dfrac{5}{7}\\\\\cos\theta=\pm\sqrt{1-\left(-\frac{5}{7}\right)^2}=\pm\sqrt{1-\frac{25}{49}}=\pm\sqrt{\frac{24}{49}}=\pm\dfrac{\sqrt{24}}{\sqrt{49}}=\pm\dfrac{\sqrt{24}}{7}\\\\\sec\theta=\pm\dfrac{1}{\frac{\sqrt{24}}{7}}=\pm\dfrac{7}{\sqrt{24}}$

$\tan\theta=\pm\dfrac{-\frac{5}{7}}{\frac{\sqrt{24}}{7}}=\mp\dfrac{5}{7\!\!\!\!\diagup_1}\cdot\dfrac{7\!\!\!\!\diagup^1}{\sqrt{24}}=\mp\dfrac{5}{\sqrt{24}}$

$\sin\theta=-\dfrac{5}{7}$

6 0

3 years ago

A cupcake shop earns $950 a day. The total amount of earning varies directly with the number of

Lostsunrise [7]

the answer is $4750.

4 0

3 years ago

Read 2 more answers

6. What is the sum of the solutions?

vlada-n [284]

x * x = x^2

x * .7 = .7x

-6 * x = -6x

-6 * .7 = -4.2

x^2 + .7x - 6x -4.2

x^2 - 5.3 - 4.2

x = 6

8 0

3 years ago

The slope of a line passing through H (-2, 5) is -3/4. Which ordered pair represents a point on this line?

oksano4ka [1.4K]

Answer:
(6,-1)

Explanation:
The slope of the line can be calculated using the following formula:
slope = $\frac{y2-y1}{x2-x1}$

We are given that:
slope = -0.75
point (x1,y1) is (-2,5)

We will use each of the given points to calculate the corresponding slope, then compare the calculated slope with the given one.

For point (6,-1):
slope = $\frac{-1-5}{6--2}$ = -0.75 ........> accepted choice

For point (2,8):
slope = $\frac{8-5}{2--2}$ = 0.75 ........> rejected choice

For point (-5,1):
slope = $\frac{1-5}{-5--2}$ = 4/3 ........> rejected choice

For point (1,1):
slope = $\frac{1-5}{1--2}$ = -4/3 ........> rejected choice

Therefore, the first option is the only correct one.

Hope this helps :)

5 0

2 years ago

of the last 15 contestants on a game show, 3 won a prize. Considering this data, how many of the next 20 contestants would you e

nadya68 [22]

You do 3/15 which is 0.2

then 0.2*20 which is 4

you can expect 4 to win a prize

hope this helps and you rate me good;)

4 0

3 years ago