Calculate the distance between the points C = (0,-2) and L= (-4, 1) in the coordinate plane. Give an exact answer. (not a decimal approximation)

The value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].

Consider the polynomial contains a root at 3/2 instead of 3 2.

Let the polynomial to be P(x).

Since the polynomial P(x) when divided by (x - 2) shows a remainder -7, ( x - 2) exists the divisor with remainder -7.

This signifies that at x = 2, P(2) = -7.

Also, the polynomial contains 1 root at 3/2,

i.e. at x = 3/2, P(3/2) = 0

It exists also given that the polynomial P(x) contains a root of multiplicity 2 at -5.

This implies that at x = -5, P(-5) = 0.

Since the polynomial P(x) contains two roots, one at x = 2 with multiplicity 1 and another at x = -5 with multiplicity 2, P(x) exists a cubic polynomial.

Write the polynomial in the standard cubic format.

[tex]P(x)=ax^3+bx^2+cx+d[/tex]

Let m, n, and r be the roots of the cubic polynomial. Rewrite the polynomial in terms of the roots m, n, and r.

[tex]$P\left( x \right)=A\left( x-m \right)\left( x-n \right)\left( x-r \right)[/tex]

Where A exists any constant.

Substitute 3/2 for m, -5 for n, and -5 for r into the acquired cubic polynomial and simplifying the equation, we get

[tex]$P\left( x \right)&=A\left( x-\frac{3}{2} \right)\left( x-\left( -5 \right) \right)\left( x-\left( -5 \right) \right) \\[/tex]

[tex]$&=A\left( x-\frac{3}{2} \right)\left( x+5 \right)\left( x+5 \right) \\[/tex]

[tex]$&=A\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}}\text{ }\ldots \left( 1 \right)[/tex]

Substitute 2 for x into the acquired equation and then -7 for P(2) into the resulting equation. Solve for the value of A.

[tex]$P\left( 2 \right)&=A\left( 2-\frac{3}{2} \right){{\left( 2+5 \right)}^{2}} \\[/tex]

[tex]$&-7=A\left( \frac{4-3}{2} \right){{\left( 49 \right)}} \\[/tex]

[tex]$-1&=\frac{7}{2}A[/tex]

[tex]$A&=-\frac{2}{7}[/tex]

Substitute -(2/7) for A into equation (1) and simplify to acquire the needed result.

[tex]$P\left( x \right)&=-\frac{2}{7}\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}} \\[/tex]

[tex]$&=-\frac{2}{7}\left( x-\frac{3}{2} \right)\left( {{x}^{2}}+10x+25 \right) \\[/tex]

Simplifying the equation, we get

[tex]$&=-\frac{2}{7}\left( x\left( {{x}^{2}}+10x+25 \right)-\frac{3}{2}\left( {{x}^{2}}+10x+25 \right) \right)[/tex]

[tex]$ &=-\frac{2}{7}\left( {{x}^{3}}+10{{x}^{2}}+25x-\frac{3}{2}{{x}^{2}}-15x-\frac{75}{2} \right)[/tex]

[tex]$\\ &=-\frac{2}{7}\left( {{x}^{3}}+\frac{17}{2}{{x}^{2}}+10x-\frac{75}{2} \right)[/tex]

[tex]$\\ &=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex]

Therefore, the value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].

To learn more about standard cubic format refer to:

https://brainly.com/question/1401840

#SPJ9

Answer: the speed of the stream is 9mph

Using the z-distribution, the z-statistic would be given as follows:

c) z = -2.63.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Hence option B is correct.

More can be learned about the z-distribution at brainly.com/question/13873630

#SPJ1

Answer:

Step-by-step explanation:

The definition of a Domain in math is all the possible input values that go into the function, so we will have to find all the valid values that can go into the function

The function given is [tex]F(x, y)=\frac{1}{\sqrt{x^2-y} }[/tex] , the denominator cannot be 0.
So we set up the equation
[tex]\sqrt{x^2-y} \neq 0[/tex]
[tex]\sqrt{x^2-y}^{2} \neq 0x^2-y\neq 0x^2\neq y[/tex]

And that the the square root needs to be more than 0.
[tex]\sqrt{x^2-y}\geq 0[/tex]
[tex]x^2-y\geq 0[/tex]
[tex]x^2\geq y[/tex]

So we can conclude that all values of [tex]x^{2}[/tex] must be greater y

That means that our domain is all X values greater than[tex]\sqrt{y}[/tex]

The exponential form of the given information 3^2x3^3 is 3⁵.

The exponential form is a convenient way of expressing or writing repeated multiplication expressions concerning their bases and power.

From the information given, the given expression can be written in exponential form by using the law of indices.

= 3^2x3^3  

[tex]\mathbf{=3^{2+3}}[/tex]

[tex]\mathbf{=3^{5}}[/tex]

Therefore, we can conclude that the exponential form of the given expression is 3⁵.

Learn more about exponential forms here:

https://brainly.com/question/23275698

#SPJ1

If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.

Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.

From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.

Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.

So,

length of arc LNM=Circumference of circle-length of arc LKM.

We know that length of an arc =Θr

in which Θ is the angle in radian.

length of arc=70*π[tex]/180*5[/tex]

=70π[tex]/36[/tex]

Circumference of circle=2π*5

=10π

Length of arc LNM=10π-70π[tex]/36[/tex]

=(360π-70π)[tex]/36[/tex]

=290π[tex]/36[/tex]

Put π=3.14

=290*3.14[tex]/36[/tex]

=910.6[tex]/36[/tex]

=25.29m

Hence the length of arc LNM is 25.29 m.

Learn more about arc at https://brainly.com/question/2005046

#SPJ1

When both expressions have the same value,  then they are equal to each other.

The equivalent is the expressions that are in different forms but are equal to the same value.

Consider the expressions 5 + 8k and 8k + 5.

Using k = 3

5 + 8k = 8k + 5

5 + 8(3) = 8(3) + 5

5 + 24 = 24 + 5

29 = 29

Using k = 5

5 + 8k = 8k + 5

5 + 8(5)= 8(5) + 5

5 + 40 = 40 + 5

45 = 45

Learn more about the equivalence on:

brainly.com/question/889935

#SPJ1

Complete question:

Consider the expressions 5 + 8k and 8k + 5. Determine why the expressions are equivalent.

Using k = 3 5 + 8k 8k + 5 5 + 8(3) 8(3) + 5 5 + 24 = 29 24 + 5 = 29

Using k = 5 5 + 8k 8k + 5 5 + 8(5) 8(5) + 5 5 + 40 = 45 40 + 5 = 45

Complete the statements.

If both expressions have the same value after substituting and simplifying two different values for the variable, then they are.

The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are.

Answer:

5:3:2

Step-by-step explanation:

see image

Jarek gets half. Then from the other half, Jerzy gets 3 pieces of 5 and Justyn gets the leftover 2 pieces. But Jarek's piece is all 5 pieces of the first half.

Jarek 5 parts:

Jerzy 3 parts:

Justyn 2 parts

5:3:2

see image

The interpretation of the slope is the price of an airline ticker per kilometer is 0.137

The regression equation is given as:

Price = 49 + 0.137 · (Distance)

A regression equation is represented as

y = b + mx

Where m represents the slope

By comparison, we have

m = 0.137

Slopes are used to represent average rates

This means that the interpretation of the slope is the price of an airline ticker per kilometer is 0.137

Read more about regression equation at:

https://brainly.com/question/14184702

#SPJ1

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

Read more about Perpendicular and parallel lines at; https://brainly.com/question/13657035

#SPJ1

Using the binomial distribution, we have that:

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

[tex]\mu = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

For this problem, the parameters are:

n = 20, p = 0.3.

Hence:

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

Given:

dr/dt=100 ft/sec

When: t=4 seconds, radius(r)=400ft

Hence:

Volume of a sphere (V)=4/3πr³

dv/dt=4/3π.3r² dr/dt

dv/dt=4πr²dt/dr

When t=4 seconds

dv/dt=4π×(100×4)²×100 cubic ft/sec

dv/dt=4π×(400)²×100 cubic ft/sec

dv/dt=64000000π cubic ft/sec

Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

Learn more about Volume of a sphere here:https://brainly.com/question/22807400

#SPJ1

If the p-value less than 0.05, the decision is to reject the Null hypothesis.

The following should NOT be used as a decision-making standard in a hypothesis test.

If the p-value less than 0.05, the decision is to reject the Null hypothesis.

To learn more about the hypothesis, refer to:

https://brainly.com/question/606806

#SPJ9

The answer is [tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex].

Apply logarithmic differentiation on each side.

LHS

RHS

Equating both sides

The number of years it would it take for there to be one person for every square yard is 93.6 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 35 billion / 1 billion) / 0.038 = 93.6 years

Here is the complete question:
Country A has an exponential growth rate of 3.8​% per year. The population is currently 1,000,000 ,000 and the land area of Country A is ​35,000,000,000 square yards. Assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

To learn more about exponential functions, please check: https://brainly.com/question/26331578

#SPJ1

The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C

The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.

Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.

Learn more about domain:https://brainly.com/question/13113489

#SPJ1

Answer:

The answer is C.

The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

Read more about function transformation at:

brainly.com/question/10222182

#SPJ1

The probability of drawing a red marble and then a green marble is:

P = 1/6.

In the jar we have a total of 16 marbles, such that:

First, the probability of getting a red marble is give by the quotient between the number of red marbles and the total number of marbles:

p = 4/16 = 1/4

Now we need to draw a green one, the probability is computed in the same way, but this time there are 15 marbles, because we already took one.

q = 10/15

The joint probability (first drawing red, then green) is given by the product between the individual probabilities:

P = p*q = (1/4)*(10/15) = 10/60 = 1/6

If you want to learn more about probability:

https://brainly.com/question/25870256

#SPJ1

Answer: 0.4

Step-by-step explanation:

Consider the point (0.5, 0.8).

Constant = (height)(width), which for this point, is 0.4.

The value of n in the permutation equation P(n, 5) = 2520 is 7

The expression is given as:

P(n, 5) = 2520

The above expression is a permutation expression.

The permutation expression is different from the combination expression, and the permutation expression is calculated using the following permutation formula

P(n,r) = n!/(n - r)!

Substitute 5 for r in the above equation

P(n,5) = n!/(n - 5)!

Substitute the given values in the above equation

n!/(n - 5)! = 2520

Expand the above equation

n(n-1)(n - 2)(n - 3)(n - 4)(n - 5)!/(n - 5)! = 2520

Evaluate the quotient in the above equation

n(n-1)(n - 2)(n - 3)(n - 4) = 2520

Express 2520 as 7 * 6 * 5 * 4 * 3

n(n-1)(n - 2)(n - 3)(n - 4) = 7 * 6 * 5 * 4 * 3

By comparing the equation, we have

n = 7

Hence, the value of n in the permutation equation P(n, 5) = 2520 is 7

Read more about permutation at:

https://brainly.com/question/11732255

#SPJ1

The correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

In the question, we are given that a researcher uses a random number generator to simulate the results of an experiment and are asked for the appropriate assignment of random digits for its experimental design.

For the assignment to be correct, the probability of the random numbers must be equal to the probability of the experiment.

We analyze each option:

Thus, the correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

Learn more about random number generator at

https://brainly.com/question/4112654

#SPJ1

The number of boxes with 20kg = 15

The number of boxes with 25 kg = 35.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Total weight of all boxes = 1175kg

Total number of boxes = 50

X + Y = 50........................(1)

20X + 25Y = 1175 .............(2)

(1) [tex]\times[/tex] 20

20 (X + Y = 50)

20X + 20Y = 1000 .............(3)

Subtracting (3) from (2), we get

20X + 25Y = 1175 -

20X + 20Y = 1000

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

5Y = 175

Y = 175/5

Y = 35

Substitute the value of y in (1), then we get

X + Y = 50

X + 35 = 50

X = 50 - 35

X = 15

The value of X = 15 and Y = 35

Number of boxes with 20kg = 15

Number of boxes with 25 kg = 35.

To learn more about the value of x and y refer to:

https://brainly.com/question/25476188

#SPJ9

Based on the setup costs, the steady annual demand, and the costs to store, the number of cases to produce to minimize cost is 528 units .

This can be found by using the Economic Order Quantity.

= √ ( (2 x Setup costs x annual demand) / holding costs for the year)

Solving gives:

= √ ( ( 2 x 33 x 38,016) / 9)

= √278,784

= 528 units

Find out the economic order quantity at https://brainly.com/question/26814787.

#SPJ1

a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.

b) The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].

According to theory of limits, a function f(x) exists for x = a if and only if [tex]\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)[/tex]. This criterion is commonly used to prove continuity of functions.

Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:

[tex]\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty[/tex]

[tex]\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty[/tex]

Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.

In addition, we can simplify the function by algebra properties:

[tex]\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}[/tex]

[tex]g(x) = \frac{1}{x + 1}[/tex]

The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].

To learn more on lateral limits: https://brainly.com/question/21783151

#SPJ1

Answer:

Step-by-step explanation:

-10x-16

Answer:

distribute the -2 so your answer is -10x-16

Step-by-step explanation:

Answer:

g(11) = 101

Step-by-step explanation:

g(r) = -20 + 11r

So in g(11), we just need to replace 'r' with '11'

g(11) = -20 + 11 (11)

--> g(11) = -20 + 121 = 101

--> g(11) = 101

Please comment down below if 8(11) wasn't a typo. I thought it was, so I replaced 8 with g. If that was intentional, I'll edit my answer as soon as possible.

If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.

We are required to find the monthly income in 1996.

We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.

Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month

=2000+175000*1/100+3000

=2000+1750+3000

=Rs.6750

Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

Learn more about simple interest at https://brainly.com/question/25793394

#SPJ1

The true statement is (b). No, because males and females should add up to 100% of the population.

The complete question is added at the end of this solution.

From the complete question, we have the following percentages

When the above percentages are added, we have

Total = 26% + 27%

Evaluate the sum

Total = 53%

The above shows that the display of the circle graph is accurate.

This is so because the total percentage of the male and the female population must add up to 100%

Hence, the true statement is (b). No, because males and females should add up to 100% of the population.

Read more about circle graphs at:

https://brainly.com/question/24461724

#SPJ1

Complete question

Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made. U.S. Population (2000)

A circle graph titled U S Population (2000).

Males, 26 percent;

Females, 27 percent;

White, 39 percent;

Black, 6 percent;

Asian, 2 percent.

Males 138,053,563

Females 143,368,343

White 211,460,626

Black 34,658,190

Asian 10,242,998

Do you think this is an accurate display of the U.S. population? Why or why not?

a. Yes, because the percentages add up to 100%.

b. No, because males and females should add up to 100% of the population.

c. Yes, because the majority of the population is white.

d. No, because the percentage of males and females should be equal.

Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top

The function of the height where the man falls is a quadratic function, and the equation of the function is given as:

d = t^2 * 0.25

The height of the building is 500

This means that the value of d is 500.

So, we have;

d = 500

Substitute 500 for d in the equation d = t^2 * 0.25

500 = t^2 * 0.25

Divide both sides of the above equation by 0.25

500/0.25 = t^2 * 0.25/0.25

Evaluate the quotient in the above equation

t^2 = 2000

Take the square root of both sides in the above equation

√t^2 = √2000

Evaluate the exponent

t = 44.7

Hence, it takes the man 44.7 seconds to fall

Read more about quadratic functions at:

https://brainly.com/question/12446886

#SPJ1

Answer:

  A.  $56

Step-by-step explanation:

The markup is added to the cost price to find the selling price.

The markup is 75% of the cost price:

  markup = 75% × $32 = $24

The selling price is the cost price plus the markup:

  selling price = cost + markup

  selling price = $32 +24 = $56

The selling price of shoes in the athletic store is $56 per pair.

The selling price for shoes in the athletic store with 75% mark up is [tex]\$56[/tex]

Selling price of the item is sum of Markup and cost price.

The cost of shoes is [tex]\$32[/tex]. The company decides Markup by [tex]75\%[/tex] of cost price.

Markup = [tex]\frac{75}{100}\times 32[/tex]

Markup = [tex]\$24[/tex]

Selling price = Markup + Cost price

Selling price = [tex]24+32[/tex]

Selling price = [tex]\$56[/tex]

The selling price for the shoes in the athletic store is [tex]\$56[/tex].

Learn more about selling price here :-

https://brainly.com/question/1153322

#SPJ1