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3 years ago

What is the average rate of change for this quadratic function for the interval

Mathematics

1 answer:

Zina [86]3 years ago

4 0

Answer:

-6

Step-by-step explanation:

The average rate of a function f(x) on the interval from x=a to x=b is $\frac{f(b)-f(a)}{b-a}$ .

So in the problem you have from $x=2$ to $x=4$ .

The average rate of the function from x=2 to x=4 is

$\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}$ .

Now we need to find f(4) and f(2).

f(4) means what is the y-coordinate that corresponds to x=4 on the curve.

f(4)=-15 since the ordered pair at x=4 is (4,-15).

f(2) means what is the y-coordinate that corresponds to x=2 on the curve.

f(2)=-3 since the ordered pair at x=2 is (2,-3).

So let's plug in those values:

$\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}$ .

Now we just simplify:

$\frac{-15+3}{2}$

$\frac{-12}{2}$

$-6$

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What is the probability that a normal random variable has an outcome within 2.5 standard deviations of the mean?

zvonat [6]

I used a calculator ----> 0.9876

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3 years ago

Which expression is equivalent to −1/ 12x−1 /3?

alexandr402 [8]

Answer:

$\frac{1}{12} (-x-4)$

Step-by-step explanation:

the expression we have is:

$-\frac{1}{12} x-\frac{1}{3}$

To find an equivalent expression, it would be helpful to express 1/3 so that it has a 12 in the denominator:

$\frac{1}{3}=\frac{4}{12}$

so we substitute this:

$-\frac{1}{12} x-\frac{4}{12}$

and now we have 1/12 in both terms :

$-\frac{1}{12}x-\frac{1*4}{12}$

so we can factor it (we take it out of each term: in the first we are left with -x and in the second with -4):

$\frac{1}{12} (-x-4)$

the equivalent expression is: $\frac{1}{12} (-x-4)$

5 0

4 years ago

If sin theta=-1/4 and theta terminates in the third quadrant, find the exact value of sin2 theta.

DIA [1.3K]

Answer:

$sin(2\theta)=\frac{\sqrt{15}}{8}$

Step-by-step explanation:

We are given

$sin(\theta)=-\frac{1}{4}$

Firstly, we can draw triangle

angle lies in third quadrant

so, we get

$cos(\theta)=-\frac{\sqrt{15} }{4}$

now, we can use formula

$sin(2\theta)=2sin(\theta)\times cos(\theta)$

now, we can plug values

$sin(2\theta)=2\times -\frac{1}{4}\times -\frac{\sqrt{15} }{4}$

now, we can simplify it

and we get

$sin(2\theta)=\frac{\sqrt{15}}{8}$

7 0

4 years ago

Read 2 more answers

1. How could you figure out the coordinates of a reflection over the x-axis? What would the coordinates of that reflected point

zzz [600]

The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).

If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)

<h3>What is a transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformation are <em>reflection, translation, rotation and dilation.</em>

The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).

If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)

Find out more on transformation at: brainly.com/question/4289712

#SPJ1

7 0

2 years ago

Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the

maria [59]

Answer:

Step-by-step explanation:

given data is:

mean = 7 kg
median = 9 kg
total number of boxes = 3

so since we know that the median is 9 and the total boxes are 3. We already know the weight of one of the three boxes.

so we can think of the sum of the three weights in ascending order as: A+9+B.

here A and B are the unknown weights of the remaining two boxes.

We can first use all of the given data in the mean formula

mean = (sum of all weights)/(number of boxes)

put all the known values in the formula

$7 = \frac{A+9+B}{3}$

and rearrange the formula so one of A and B as the subject.

$A = 21 - (9+B)$

now you can use the given values in the Multiple choices from the question and find the maximum value. try each value to be equal to B, so you can find A.

but you need to be smart about it, and keep in mind that the only one of the value of A and B should be greater than the median i.e. 9, or else that will rearrange the way we have set up our boxes:: A + 9 + B (ascending order).

start from (E), where B = 5

$A = 21 - (9+5)$

$A = 7$

here, no value is greater than the median: 3+9+7 (not ascending)

now check (D), where B = 4.

$A = 21 - (9+4)$

$A = 8$

here no value is greater than the median: 4+9+8 (not ascending)

now check (C), where B = 3

$A = 21 - (9+3)$

$A = 9$

here, one of the boxes is equal to the median: 3+9+9 (ascending)

you see a pattern here, the value of A is increasing, thus B is decreasing.

check (B), where B = 2

$A = 21 - (9+2)$

$A = 10$

here, you can realize that B = 2 is not correct since this is not maximum possible weight of the lightest box: 2+9+10 (ascending, but the weight of the lightest box is not maximum possible)

Since, we want maximum possible weight for the lightest box, that is only possible when B = 3 (maximum possible)

8 0

3 years ago