Solve the following equations using any method. Show your work. Eind the exact solution. Write
the solutions in simplest form.
5. x² + 4x = 3

The area of the composite figure is 136 sq. units.

Given that a composite figure we need to find it area,

The figure is composed of a triangle and a rectangle,

So to find its area we will simply calculate the areas of both the polygons and add them,

So, the area of a triangle = 1/2 x base x height

The area of a rectangle = length x width

So,

The required area = 1/2 x (16-8)(13-7) + 7 x 16

= 1/2 x 8 x 6 + 112

= 24 + 112

= 136

Hence, the area of the composite figure is 136 sq. units.

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Tally's probability of being on the red team is 1/4, or 0.25 when represented as a decimal.

Each team has four students because there are four equal-sized teams.

So Tally's chances of being on the red team are 4 (the number of students on the red team) divided by 16 (the total number of students):

4/16 = 1/4

As a result, Tally's likelihood of being on the red team is 1/4, or 0.25 when represented as a decimal.

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The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively.

Length is a concept used to describe the magnitude of a particular object or distance between two points. It is typically measured in units such as feet, inches, meters, miles, and kilometers. Length is often used to describe the size of an object and the distance between two points. Length can also be used to measure the time required to travel between two points. Length is a fundamental concept in mathematics, physics, and engineering.

The first dotted line shown at the top of the chart is 23.39.

b. With Overall Mean selected, what is the length of the second dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)

The second dotted line shown at the top of the chart is 23.28.

c. With Overall Mean selected, what is the length of the third dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)

The third dotted line shown at the top of the chart is 24.17.

Conclusion: The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively. This data can be used to analyze the age of respondents in Market Research.

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The value of the expression when j=-2 and k=-1 is 8.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

Let's substitute j=-2 and k=-1 in the given expression and simplify it:

(jk⁻²/j⁻¹k⁻³)³

= ((-2)(-1)⁻²)/((-2)⁻¹(-1)⁻³))³ // Substitute j=-2 and k=-1

= ((-2)/(1/(-1)²))/((-1/(-1)³)))³

= ((-2)/1)/(-1/1))³

= (-2)/(-1))³

= 8

Therefore, the value of the expression when j=-2 and k=-1 is 8.

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Answer:

Step-by-step explanation:

(n-2) x 180 = 1260

n-2 = 1260/180

n-2 = 7

n = 9

Therefore, the regular polygon has 9 sides.

Answer:

[tex]\frac{1}{3}[/tex] product per minute

Step-by-step explanation:

We Know

A factory worker can make 15 products in 45 minutes.

What is the worker's unit rate of completion?

We Take

15 / 45 = [tex]\frac{1}{3}[/tex] product per minute

So, the workers unit rate of completion is  [tex]\frac{1}{3}[/tex] product per minute

The corresponding p-value is 0.147 rounded to three decimal places.

Now, For find the p-value, we need to use a t-distribution with (n - 1) degrees of freedom,

where n is the sample size.

Since n = 50,

Hence, we have;

n - 1 = 50 - 1 = 49 degrees of freedom.

Hence, Using a t-table or calculator with 49 degrees of freedom, we find that the p-value for a t-statistic of -1.07 is approximately 0.147.

Therefore, the corresponding p-value is 0.147 rounded to three decimal places.

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Answer:

6

Step-by-step explanation:

60/10=6

Hope this helps :)

The equation's usable range is 6.6 km d 13.2 km.

Expression is the relation of the numbers and the variables written by the use of mathematical signs.

Kellen exercises for a minimum of an hour and a maximum of two hours. As a result, the equation's useful domain is 1 t 2. Since that time can take on any positive or negative value, the theoretical scope of the equation d = 6.6t is all real numbers.

Substitute the values of the practical domain into the equation.

t = 1, d = 6.6(1) = 6.6 km.

t = 2, d = 6.6(2) = 13.2 km.

Therefore, the equation's usable range is 6.6 km d 13.2 km.

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Answer:

Answer: 9,924.966.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sorry it is hard to explain the process by typing!

[tex]{\Large \begin{array}{llll} \cfrac{x^{-\frac{1}{2}}}{x^{\frac{2}{3}}x^{\frac{3}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}}x^{\frac{3}{2}}x^{\frac{1}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}+\frac{3}{2}+\frac{1}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}+2}}\implies \cfrac{1}{x^{\frac{8}{3}}} \end{array}}[/tex]

a) Point estimate = 10/19 = 0.526

b) The sample should be randomly selected from the population.

The sample size should be large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of students who have a job in the population.

The sampling distribution of the sample proportion should be approximately normal.

c) confidence interval = (0.259, 0.793)

d) confidence interval = (0.176, 0.876)

e) n = 365 students

Given data ,

a)

The point estimate for the proportion of GSU students who have a job is simply the proportion of students in the class who have a job, which is:

point estimate = 10/19 = 0.526 (rounded to three decimal places)

b)

To create a confidence interval for the proportion of GSU students who have a job, the following conditions must be met:

The sample should be randomly selected from the population.

The sample size should be large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of students who have a job in the population.

The sampling distribution of the sample proportion should be approximately normal.

c)

Assuming the conditions for a confidence interval are met, a 95% confidence interval for the proportion of GSU students who have a job can be calculated as follows:

margin of error = z√(p(1-p)/n)

where z is the z-score corresponding to a 95% confidence level (z = 1.96), p is the point estimate of the population proportion (0.526), and n is the sample size (19).

margin of error = 1.96 √(0.5260.474/19) = 0.267 (rounded to three decimal places)

confidence interval = point estimate ± margin of error = 0.526 ± 0.267

confidence interval = (0.259, 0.793)

Therefore, we can say with 95% confidence that the true proportion of GSU students who have a job is between 0.259 and 0.793.

d)

A 99% confidence interval for the proportion of GSU students who have a job can be calculated using the same formula as above, but with a z-score of 2.576 (corresponding to a 99% confidence level):

margin of error = 2.576sqrt(0.5260.474/19) = 0.350 (rounded to three decimal places)

confidence interval = 0.526 ± 0.350

confidence interval = (0.176, 0.876)

Therefore, we can say with 99% confidence that the true proportion of GSU students who have a job is between 0.176 and 0.876.

e)

To determine the sample size needed to be within 3 percentage points of the true proportion with the point estimate of 0.526, we can use the formula:

n = (z² * p * (1-p)) / E²

where z is the z-score corresponding to the desired confidence level (z = 1.96 for a 95% confidence level), p is the point estimate of the population proportion (0.526), and E is the desired margin of error (0.03).

n = (1.96^2 * 0.526 * 0.474) / 0.03^2

n = 364.16

Hence , we would need a sample size of at least 365 students to be within 3 percentage points of the true proportion using the point estimate from the class data.

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1. The 99% confidence interval is from 877.094 to 942.906.

2. The 99% confidence interval is from 883.267 to 936.733.

3. The 99% confidence interval is from 838.437 to 981.563.

What is interval?

In statistics, an interval refers to a range of values in which a population parameter, such as the mean or proportion, is estimated to lie with a certain level of confidence.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(20/√21) = 877.094

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(20/√21) = 942.906

Therefore, the 99% confidence interval is from 877.094 to 942.906.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(40/√21) = 883.267

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(40/√21) = 936.733

Therefore, the 99% confidence interval is from 883.267 to 936.733.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(80/√21) = 838.437

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(80/√21) = 981.563

Therefore, the 99% confidence interval is from 838.437 to 981.563.

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Answer:

|Z| = √((-6)^2 + 12^2) = √(36 + 144) = √180

= (√36)(√5) = 6√5

Answer: Barry would save approximately $15,208.08 by paying off the loan 8 years early.

Step-by-step explanation:

To calculate how much Barry would save by paying off the loan 8 years early, we first need to calculate the total amount of interest he would pay over the remaining 8 years.

We can use the formula for calculating the remaining balance on a loan:

Balance = (P * ((1 + r/n)^(nt)) - (A * (((1 + r/n)^(nt)) - 1)/(r/n)))

where:

P = principal amount (initial loan amount)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = time (in years)

A = monthly payment

Substituting the given values in the formula, we can calculate the remaining balance:

Balance = ($55,000 * ((1 + 0.068/12)^(1220)) - ($419.84 * (((1 + 0.068/12)^(1220)) - 1)/(0.068/12)))

Balance = $31,019.97

Now, we need to calculate the total interest paid over the remaining 8 years. We can do this by subtracting the remaining balance from the total amount of interest that would be paid over the entire 20-year loan term:

Total interest paid over 20 years = (A * 12 * 20) - P

Total interest paid over 20 years = ($419.84 * 12 * 20) - $55,000 = $50,969.63

Total interest paid over the remaining 8 years = (A * 12 * 8) - Balance

Total interest paid over the remaining 8 years = ($419.84 * 12 * 8) - $31,019.97 = $35,761.58

Therefore, Barry would save approximately $15,208.08 by paying off the loan 8 years early.

Since these inequalities contradict each other, there is no value of b that satisfies both.

We have,

Starting with the first inequality:

2b - 8 > 5

Adding 8 to both sides:

2b > 13

Dividing by 2:

b > 6.5

Moving on to the second inequality:

3b + 13 < 9

Subtracting 13 from both sides:

3b < -4

Dividing by 3:

b < -4/3

So, we need to find a value of b that satisfies both b > 6.5 and b < -4/3. Since these inequalities contradict each other, there is no value of b that satisfies both.

Therefore,

Since these inequalities contradict each other, there is no value of b that satisfies both.

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The swap rate for a two-year deferred, three-yearinterest rate swap with settlement at the end of the year is 3.7%

Implied forward rate = (1+Present year rate)^Present year /(1+Previous year rate)^Previous year -1

The swap rate for a two-year deferred, three-yearinterest rate swap with settlement at the end of the year=

= [(1 +0.034)2 / (1+0.031)1 ] -1

= [1.069156 / 1.031] -1

= 1.037 - 1

= 0.037

= 3.7%

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The total number of students is 2960.

35% of students went to Disneyland and 1924 of students went to Knotts.

Therefore, the total number of student can be calculated as follows:

The total number of student is the total number of student that went to Disneyland and Knotts.

let

x = total number of student

Therefore,

35% of x = Student that went to Disneyland

Hence,

65% of x = 1924

65 / 100 x = 1924

cross multiply

65x = 192400

divide both sides of the equation

x = 192400 / 65

x =   2960

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Answer:

The equation of the circle is (x + 7)^2 + (y - 13)^2 = 25.

Step-by-step explanation:

The equation of a circle with a center (a,b) and radius r is given by:

(x - a)^2 + (y - b)^2 = r^2

So, for the center (-7, 13) and a radius of 5 units, the equation of the circle is:   (x - (-7))^2 + (y - 13)^2 = 5^2

Simplifying this equation, we get:

(x + 7)^2 + (y - 13)^2 = 25

Therefore, the equation of the circle with center (-7,13) and radius 5 units is (x + 7)^2 + (y - 13)^2 = 25.

We get a negative number, which means that Rocco does not have enough money to make the purchase. In fact, he is short by $158.

An equation is a mathematical statement that shows that two expressions are equal. Equations are used to represent relationships between variables and to solve problems in various fields such as mathematics, physics, engineering, and economics. In an equation, there are typically two sides separated by an equals sign (=). The expressions on each side of the equals sign may include variables, constants, mathematical operations, and functions. The goal of solving an equation is to find the value(s) of the variable(s) that make both sides of the equation equal.

Here,

If Rocco has only $192 in his savings account and the set of golf irons costs $350, then he does not have enough money to buy the golf irons.

To see why, we can subtract the price of the golf irons from Rocco's savings:

$192 (Rocco's savings) - $350 (price of golf irons) = -$158

Therefore, Rocco does not have enough money to buy the set of golf irons with the remaining amount in his savings account.

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Associative property holds for all types of numbers  and associative properties holds true addition as well as multiplication but not true for subtraction as well as division.

A number system is defined as a system of writing to express numbers.

The associative property holds for all types of numbers including real numbers, complex numbers, integers, fractions, and even irrational numbers.

There is no type of number for which the associative property does not hold.

associative properties holds true addition as well as multiplication but not true for subtraction as well as division.

Hence, associative property holds for all types of numbers  and associative properties holds true addition as well as multiplication but not true for subtraction as well as division.

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Question #14:

Find the work done by the force field, [tex]\vec F(x,y,z)= < x-y^2, \ y-z^2, \ z-x^2 >[/tex],

on a particle that moves along the line segment from (0,0,1) to (3,1,0).

The parametrized form of a line is given as,

[tex]x=x_0+v_xt[/tex]

[tex]y=y_0+v_yt[/tex]

[tex]z=z_0+v_zt[/tex]

Where [tex](x_0,y_0,z_0)[/tex] is a point the line passes through and [tex]\vec v= < v_x,v_y,v_z >[/tex] is the direction of the line.

[tex]\Longrightarrow \vec v= < 3-0,1-0,0-1 > \Longrightarrow \boxed{ \vec v= < 3,1,-1 > }[/tex]

[tex]\Longrightarrow \boxed{(x_0,y_0,z_0)=(0,0,1)}[/tex]

[tex]z=-t+1, 0\leq t\leq 1[/tex]

This would imply that, [tex]dx=3dt,dy=dt,dz=-dt[/tex]

[tex]Work, W=\int\limits^a_b {\vec F(x,y,z) \cdot} < dx,dy,dz > \,dt[/tex]

[tex]\Longrightarrow \vec F(x,y,z)= < 3t-t^2, \ t-(-t+1)^2, \ -t+1-(3t)^2 >[/tex]

[tex]\Longrightarrow \boxed{\vec F(x,y,z)= < 3t-t^2, \ -t^2+3t-1, \ -9t^2-t+1 > }[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [ < 3t-t^2, \ -t^2+3t-1, \ -9t^2-t+1 > \cdot} < 3,1,-1 > ] \,dt[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [( 3t-t^2)(3)+(-t^2+3t-1)(1)+(-9t^2-t+1)(-1) ] \,dt[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [ 9t-3t^2-t^2+3t-1+9t^2+t-1 ] \,dt[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [5t^2+13t-2 ] \,dt[/tex]

Using the power rule to integrate: [tex]\frac{d}{dx}[x^n]=nx^{n-1}[/tex]

[tex]\Longrightarrow W=\frac{5}{3}t^3+\frac{13}{2}t^2-2t \left. \right|_{0}^1[/tex]

[tex]\Longrightarrow W=[\frac{5}{3}(1)^3+\frac{13}{2}(1)^2-2(1)]-[0][/tex]

[tex]\Longrightarrow W=\frac{5}{3}+\frac{13}{2}-2[/tex]

[tex]\Longrightarrow \boxed{ W=\frac{37}{6}} \therefore Sol.[/tex]

Question #15:

Given:

[tex]w_m=170 \ lb[/tex]

[tex]w_c=25 \ lb[/tex]

[tex]w_m+w_c=195 \ lbs[/tex]

[tex]r_s=25 \ ft[/tex]

[tex]h_s=90 \ ft[/tex]

[tex]1 \ rev. =2\pi \Rightarrow 3 \ rev. =\bold{6\pi}[/tex]

Find:

[tex]W= \ ?? \ ft-lbs[/tex]

Equation:

[tex]W=\int\ {\vec F \cdot } \, d\vec r \Longrightarrow W=\int\ {[\vec F(\vec r(t)) \cdot r'(t)}]dt[/tex]

[tex]\vec F(x,y,z)= < 0,0,195 > \ and \ r(t)= < 25cos(t),25sin(t),\frac{90}{6\pi}t >[/tex]

[tex]r'(t)= < -25sin(t),25cos(t),\frac{15}{\pi} >[/tex]

[tex]\Longrightarrow W=\int\ {[\vec F(\vec r(t)) \cdot r'(t)}]dt[/tex]

[tex]\Longrightarrow W=\int\ {[ < 0,0,195 > \cdot < -25sin(t),25cos(t),\frac{15}{\pi} > ]dt[/tex]

[tex]\Longrightarrow W=\int\ {[ (195)(\frac{15}{\pi}) ]dt[/tex]

[tex]\Longrightarrow W=\int\ {\frac{2925}{\pi} dt[/tex]

Limits: [tex]0\leq t\leq 6\pi[/tex]

[tex]\Longrightarrow W=\int\limits^{6\pi}_0 {\frac{2925}{\pi} } \, dt[/tex]

[tex]\Longrightarrow W= {\frac{2925}{\pi}t \left. \right|_{0}^{6\pi}[/tex]

[tex]\Longrightarrow W= [{\frac{2925}{\pi}(6\pi)]-[0][/tex]

[tex]\Longrightarrow \boxed{W= 17,550 \ ft-lbs} \therefore Sol.[/tex]

Let me know if these were correct! As I strive to give the most accurate answers! Thank you.

Answer:

A.  parallelogram

Step-by-step explanation:

It's not a rectangle because all 4 angles are not 90

It's not a rhombus because all 4 sides are not equal.

It's not a square because all 4 sides are not equal and all 4 angles are not 90.

It's a parallelogram because it's a quadrilateral with 2 pairs of opposite sides that are parallel.

a. For the supermarket manager, the mode is one that  is the right tool as the appropriate form of the measure of central tendency as it would tell them which type of lettuce that was bought most often.

b. For the students, the mean is one that will be the right measure of central tendency as it would give them the idea of the average of all their test scores.

c. For the real estate agent, the median is one that is be the right measure of central tendency as it would tell them the selling price that is in the middle of all the given comparable houses.

Lastly, The student that is known to be is reporting the mean as the average. , this is one that tends to misrepresents their course performance due to the fact that the mean is affected by outliers for example as the 75%, 70%, and 55% scores. The median is one that can give a better representation of their performance.

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See text below



1. Here are three examples where the mean, median, and mode can be used to describe a situation. Which measure of central tendency would you use for each one? Why? (Don't forget the why.)

a. A supermarket manager wants to know how many types of lettuce customers purchase most often.

b. Students want to know the average of all their test scores in a certain grading period.

c. A real estate agent wants to set the selling price of a three-bedroom house so that there are as many comparable houses above as below the price. 2. A student's parents promise to pay for next semester's tuition if an A average is earned in chemistry. With examination grades of 97%, 97%, 75%, 70%, and 55%, the student reports that an A average has been earned. Which measure of central tendency is the student reporting as the average? How is this student misrepresenting the course performance with statistics?

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4) D

A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

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Answer:

The y-value of the function is 4 in the table when the x-value is 0 after framing the linear equation.

Step-by-step explanation:

- Hope this helps

Answer:

3

Step-by-step explanation:

By using distance formula

√(x2-x1)^2+(y2-y1)^2

√(5-5)^2+(4-1^2

√0+(3)^2

√9

=3