In a room there are a mixture of people and dogs. there are 72 heads, and 200 legs. how many dogs are in the room?

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.Tiles

Ugo [173]

By definition, the average rate of change is given by:

$AVR = \frac{f(x2)-f(x1)}{x2-x1}$

We evaluate each of the functions in the given interval.

We have then:

For f (x) = x ^ 2 + 3x:

Evaluating for x = -2:

$f (-2) = (-2) ^ 2 + 3 (-2)\\f (-2) = 4 - 6\\f (-2) = - 2$

Evaluating for x = 3:

$f (3) = (3) ^ 2 + 3 (3)\\f (3) = 9 + 9\\f (3) = 18$

Then, the AVR is:

$AVR = \frac{18-(-2)}{3-(-2)}$

$AVR = \frac{18+2}{3+2}$

$AVR = \frac{20}{5}$

$AVR = 4$

For f (x) = 3x - 8:

Evaluating for x =4:

$f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4$

Evaluating for x = 5:

$f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7$

Then, the AVR is:

$AVR = \frac{7-4}{5-4}$

$AVR = \frac{3}{1}$

$AVR = 3$

For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

$f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15$

Evaluating for x = 4:

$f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8$

Then, the AVR is:

$AVR = \frac{8-15}{4-(-3)}$

$AVR = \frac{-7}{4+3}$

$AVR = \frac{-7}{7}$

$AVR = -1$

For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

$f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4$

Evaluating for x = 1:

$f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4$

Then, the AVR is:

$AVR = \frac{-4-(-4)}{1-(-1)}$

$AVR = \frac{-4+4}{1+1}$

$AVR = \frac{0}{2}$

$AVR = 0$

Answer:

from the greatest to the least value based on the average rate of change in the specified interval:

f(x) = x^2 + 3x interval: [-2, 3]

f(x) = 3x - 8 interval: [4, 5]

f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]

4 0

1 year ago

If two lines are perpendicular describe the relationship between their slopes

Aloiza [94]

Perpendicular lines have slopes that are negative reciprocals. example: line a has a slope of 2/3, line b has a slope if -3/2 if they are perpendicular.

7 0

2 years ago

The local pizza shop sells several special items.

Anna35 [415]

Answer:

Tax for Italian Salad=$0.20

Tax for Lasagna= $0.43

Tax for Spaghetti =$0.21

Tax for Fettuccini Alfredo =$0.36

Step-by-step explanation:

Hi, to answer this question we have to multiple the price of each item by the tax percentage in decimal form (divided by 100):

Italian Salad =$3.99

Tax for Italian Salad= 3.99 x (5/100) = 3.99 x 0.05 =$0.20

Lasagna =$8.50

Tax for Lasagna= 8.50 x (5/100) = 8.50 x 0.05 =$0.43

Spaghetti =$4.29

Tax for Spaghetti = 4.29x (5/100) = 4.29 x 0.05 =$0.21

Fettuccini Alfredo =$7.17

Tax for Fettuccini Alfredo = 7.17 x (5/100) = 7.17 x 0.05 =$0.36

Feel free to ask for more if needed or if you did not understand something.

6 0

2 years ago

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A partial proof was constructed given that MNOP is a parallelogram. Parallelogram M N O P is shown. By the definition of a paral

viva [34]

Answer: last notation is right N =~ P

Step-by-step explanation: this is because any angle equals 180° but not less than 90° are regarded as supplementary angles. This means N<= 180°, P<= 180°

6 0

2 years ago

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Rebeckah answered 42 of the 60 questions correctly on a test. Which method should she use to find the percent of questions she a

Nataly_w [17]

Answer:

D.

Step-by-step explanation:

42/60=70% so the only option that also equals 70% is letter D.

3 0

1 year ago

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