how do you find the rate of change for a function over a given interval

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

ANSWER

C. lower: 6

middle: 13

upper: 17

EXPLANATION

First we have to order this data from lowest to highest value:

The middle quartyle is the median of the data set. Since this set has 8 values, which is even, the median is the mean of the two middle values: 12 and 14:

Then, the lower quartile is the median of the first half of the data set. Since the median of the whole data set is located between 12 and 14, the first half of the set is:

This is too an even number of values, but since the two middle values are the same the lower quartile is that value: 6.

Then, the upper quartile is the median of the second half of the data set:

For this quartile is the same as the lower quartile, the number of values is even and the two middle values are the same. The upper quartile is 17

Answer:

Approximately 25.5 miles

Step-by-step explanation:

Location of both the cities are \( (25,\: 5)=(x_1, \:y_1) \:\&\: (50,\: 10)=(x_2 , \:y_2) \)

The distance between two cities can be obtained by using distance formula:

Distance between two cities

\( = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2}} \\ \\ = \sqrt{ {(50 - 25)}^{2} + {(10 - 5)}^{2}} \\ \\ = \sqrt{ {(25)}^{2} + {(5)}^{2}} \\ \\ = \sqrt{ 625 + 25} \\ \\ = \sqrt{ 650} \\ \\ = 25.4950976 \\ \\ \approx25.5 \: miles\)

The solution to the equation is x = 2 , x = 1/2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( 2x - 4 ) ( 2x - 1 ) = 0

So , the two values of x are

when ( 2x - 4 ) = 0

Adding 4 on both sides , we get

2x = 4

Divide by 2 on both sides , we get

x = 2

And , when ( 2x - 1 ) = 0

Adding 1 on both sides , we get

2x = 1

Divide by 2 on both sides , we get

x = 1/2

Hence , the solution is x = 2 , 1/2

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Answer:

a. f(-1)=12

b. f(2t)=16t²-6t+5

c. f(t-2)=4t²-19t+27

Step-by-step explanation:

For a, b, c, we are given an input. We plug that into f(x) to find our answers.

a.  f(-1)=12

f(-1)=4(-1)²-3(-1)+5

f(-1)=4+3+5

f(-1)=12

-------------------------------------------------------------------------------------------------------------

b. f(2t)=16t²-6t+5

f(2t)=4(2t)²-3(2t)+5

f(2t)=4(4t²)-6t+5

f(2t)=16t²-6t+5

-------------------------------------------------------------------------------------------------------------

c. f(t-2)=4t²-19t+27

f(t-2)=4(t-2)²-3(t-2)+5

f(t-2)=4(t²-4t+4)-3t+6+5

f(t-2)=4t²-16t+16-3t+6+5

f(t-2)=4t²-19t+27

The correct answer is (1,1) because both of the lines meet together at these numbers

Answer:

12

Step-by-step explanation:

more 3:4:5 triangles lol, x is 3/4 * 16 = 12

The Dividend per Shareholder in 2017 is $20.

As, Dividend per Shareholder = Profit / Number of Shareholders

Since the number of shareholders is assumed to have remained unchanged during the period 2017-2020, we can calculate the dividend per shareholder in 2017 using the profit value for that year.

Based on the given table, the profit for 2017 is $7,000.

Dividend per Shareholder in 2017

7000/x = 15500 / 44.29

7000/x = 349.966

x = 7000/349.966

x= 20.01

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Answer:

b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The mean price of a gallon of gas at the five stations is $3.81. Therefore, option A is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

Given that, Yesterday, the price of a gallon of gas at five gas stations was $3.56, $3.71, $3.62, $3.93, and $3.83, respectively.

Today each gas station raised its price by $0.08

Now, mean =(3.56+3.71+3.62+3.93+3.83+5×0.08)/5

= (18.65+0.4)/5

= 19.05/5

= $3.81

Therefore, option A is the correct answer.

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To solve for x, first, we add 3 to the given equation:

Dividing by 2, we get:

Therefore:

Finally, subtracting 5 we get:

Answer:

Answer: look up the answer

Step-by-step explanation:

Subtract 9 from both sides then divide by 3 on both sides

X=-2

Answer:

1023/4

Step-by-step explanation:

shown in the picture

Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

Answer:

add me as a friend and give me thanks

Step-by-step explanation:

the answer is A for sure

Answer:

The equation of the line in slope-intercept form is:

\(\:y=-\frac{1}{6}x\:+\:4\)

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where  

Given the points on the line graph  

Determining the slope between (0, 4) and (3, 3.5)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{3.5-4}{3-0}\)

\(m=\frac{\frac{7}{2}-4}{3-0}\)

\(m=-\frac{1}{6}\)

Thus, the slope of the line = m = -1/6

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 4

Thus, the y-intercept b = 4

now substituting b = 4 and m = -1/6 in the slope-intercept form

\(y = mx + b\)

\(\:y=-\frac{1}{6}x\:+\:4\)

Therefore, the equation of the line in slope-intercept form is:

\(\:y=-\frac{1}{6}x\:+\:4\)

Answer:

-2

Step-by-step explanation:

Slope if rise / run

So what you want to do is look for two points that are close to each other on the vertical (y axis). This case i'm going with the 7 and the 5

This would give you a rise of -2: since as it move downwards as it goes to the right. (y2 - y1, y2 = 5, y1 = 7 so 5-7 = -2)

Next take the same points but look at them on the horizontal (x axis) and see how long it takes for it to get to the same points.

it starts at -1 and ends at 0.

so run = 1: since it moves to the left (x2 - x1, x2=0, x1=-1, 0-(-1) = 1)

This makes your slope

-2 as you have (-2/1)

The sale price of the sweater is $2.7

From the question, we have the following parameters that can be used in our computation:

Markdown rate = 85% off

Original price of the sweater = $18

The retail price of the coat can be calculated using the following equation

Retail price = original price * (1 - Markdown rate)

Substitute the known values in the above equation, so, we have the following representation

Retail price = 18 * (1 - 85%)

Evaluate the products

Retail price = 2.7

Hence, the sales price is $2.7

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Answer:

1/4.

Step-by-step explanation:

1/4 is the answer because 25 x 4 = 100. Lets say you had 50/100. That would be equivalent to 2/4 , because 50 x 2 = 100.

25 is often reffered to as a quarter, but if someone says it is lets say a quarter past 5:00, they are trying to say is is 5:15, because 15 x 4 = 60, and 60 minutes is an hour.

When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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Answer:

Incomplete question, but I gave a guide to solve using the Empirical Rule.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

It is also important to note that the normal distribution is symmetric. This means of the 68% of the measures are within 1 standard deviation of the mean, for example, 68/2 = 34% are between 1 standard deviation below the mean and the mean, and 34% are between the mean and 1 standard deviation above the mean.

In this question:

You take the mean and the standard deviation. Then you take both bounds that the percentage asks, and see how many standard deviations each are from the mean, and you then use the empirical rule to solve.

The correct option that can be used to prove that ∠ABC = ∠FDE is option (A). It is done using rules of congruency.

What is meant by congruency?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

For the construction of the congruent angle, the compass measurement used is the same for both figures.

Now we draw a line through points A and C and another line through points F and E.

We can then say that

AB = FD

BC = DE

CA = EF

These are the sides of the triangles ΔABC and ΔFDE

As all sides are equal, we can say that

ΔABC ≅ ΔFDE by SSS congruency rule.

Now CPCTC rule says that "corresponding parts of congruent triangles are congruent". This means that the corresponding angles and sides of two or more triangles must also be identical in order for them to be considered congruent.

So ∠ABC ≅ ∠FDE by CPCTC as they are corresponding angles.

Therefore the correct congruency rules that can be used to prove that

∠ABC = ∠FDE is option (A).

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Answer:

Equation of the parabola:

The height of the arch 18 meters from the center is 6.75m

Explanation:

The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0

Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9

Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.

With all this, we can try to find the general form of a parabola. The general form is:

c is the y-intercept. We know that c = 9

We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:

SInce the x-coordinate of the vertex is x = 0

If we solve:

So far we have:

Finally, to find a, we can use the point (36, 0) (one of the roots)

And solve:

Thus, the equation of the arch is:

Evaluating this equation for x = 18, we can find the height of the arch:

Answer:

0

Step-by-step explanation:

20 - 2x, if x = 10

First, plug in 10 for each value of x.

20 - 2(10) = ?

Next, multiply 2 and 10 due to PEMDAS. (parentheses/exponents, multiplication/division, addition/subtraction)

20 - 20 = ?

Now, subtract.

= 0

Hope this helps!