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BlackZzzverrR [31]
2 years ago
13

How do you find the average rate of change for f(x)=9-x^2 between two points: x=0 to x=3?

Mathematics
1 answer:
ICE Princess25 [194]2 years ago
3 0

Answer:

The average rate of change is -3.

Step-by-step explanation:

We are given the function:

f(x)=9-x^2

And we want to find the average rate of change from <em>x </em>= 0 to <em>x </em>= 3.

In other words, we will compute the function at the two endpoints, and then find the slope of the line that crosses the two points.

For our first endpoint at <em>x</em> = 0, our function evaluates to:

f(0)=9-(0)^2=9

So, our first point is (0, 9).

For our second endpoint at <em>x</em> = 3, our function evaluates to :

f(x)=9-(3)^2=0

So, our second point is (3, 0).

Then by the slope formula, our average rate of change will be:

\displaystyle m=\frac{0-9}{3-0}=\frac{-9}{3}=-3

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What is the equation of the line that passes through the points (−2, 1) and (1, 10)?
Viktor [21]

Answer:

3x - y = -7

Step-by-step explanation:

y = mx + b

m = deltay/deltax

m = (10 - 1)/[( 1 - (-2)]

m = 9/3 = 3

y = 3x + b

From (-2 | 1) we see that when x = -2, y = 1

Placing into the equation, in order to find b (y-intercept)

y = 3x + b

1 = 3(-2) + b

b = 7

y = 3x + 7 or 3x - y = -7

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2 years ago
Simplify (-a2b3)2(c2)0
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A student is saving money to buy a microscope. The student currently has $50 and plans to save $15 every month. Write a function
Evgen [1.6K]

Answer:

Step-by-step explanation:

The student currently has $50 and plans to save $15 every month.

Let x represent the number of months that the student will save enough money to buy the microscope.

Let y represent the amount that the student saves after x months.

The function that represents the amount y (in dollars) of money that the student saves after x months will be

y = 50 + 15x

The 50 remains constant because she has already saved it

5 0
3 years ago
Juana threw five darts at a dartboard. The possible scores on the target were 2, 4, 6, 8, and 10. Each dart hit the target. Whic
Salsk061 [2.6K]

Answer:

Not possible scores: 6, 15, 23, 31 and 58.

Step-by-step explanation:

We have been given that Juana threw five darts at a dartboard. The possible scores on the target were 2, 4, 6, 8, and 10. Each dart hit the target. We are asked to choose the total scores that can be quickly identified as "not possible".

Given scores: 38, 23, 58, 30, 42, 31, 26, 6, 14, or 15.

Since the maximum score is 10 and number of hits are 5, therefore, the maximum score can be hitting 10 each of the 5 times.

10\times 5=50

Since the maximum score is 50, therefore, 58 is an impossible score.

Since the minimum score is 2 and number of hits are 5, therefore, the minimum score can be hitting 2 each of the 5 times.

2\times 5=10

Since the minimum score is 10, therefore, 6 is an impossible score.

Since all scores on board are even, so the sum of 5 hits must be even, therefore, odd numbers like 15, 23, 31 are not possible scores.  

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2 years ago
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