Mathematics College

The points (−7,−4) and (3,8) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.

Answers

Answer 1

The length of the radius of the circle is √61.

Here there are two endpoints of the circle (-7,-4) and (3,8)

To find the length between the two points we have a formula:

length = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }[/tex]

So here we have

([tex]x_{1} , y_{1}[/tex]) = (-7, -4)

([tex]x_{2} , y_{2}[/tex]) = ( 3,8)

Putting the value we have,

[tex]\sqrt{(3 -(-7)^{2} + ( 8-(-4)^{2} }[/tex]

=[tex]\sqrt{10^{2} + 12^{2} }[/tex]

=[tex]\sqrt{100+ 144}[/tex]

=√244

=2√61

The diameter is 2√61

radius = diameter/2

= 2√61/2

= √61

Therefore the length of the radius of a circle is √61.

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Related Questions

Among the following which is the best
example for unlike terms?
O8x, 9t
O 9x-2x
О 3р. 5р
All of the choices

Answers

Answer 8x, 9t

The variable X and T are different and cannot be combined.

Hope this helps :)

Which table represents a linear function?

Answers

The most appropriate choice for function will be given by-

The first option is correct

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

For the first table,

Slope of function from x = 1 to x = 2

= [tex]\frac{1 - \frac{1}{2}}{2 - 1}[/tex]

=[tex]\frac{1}{2}[/tex]

Slope of function from x = 2 to x = 3

= [tex]\frac{\frac{3}{2}-1}{3 - 2}[/tex]

= [tex]\frac{1}{2}[/tex]

Slope of function from x = 3 to x = 4

= [tex]\frac{2-\frac{3}{2}}{4 - 3}[/tex]

= [tex]\frac{1}{2}[/tex]

Here the slope is same. So the function is linear

For the second table,

Slope of function from x = 1 to x = 2

= [tex]\frac{\frac{1}{2} - 1}{2 - 1}[/tex]

=[tex]-\frac{1}{2}[/tex]

Slope of function from x = 2 to x = 3

= [tex]\frac{\frac{1}{3}-\frac{1}{2}}{3 - 2}[/tex]

= [tex]-\frac{1}{6}[/tex]

Here the slope is not same. So the function is not linear

For the third table,

Slope of function from x = 1 to x = 2

= [tex]\frac{9 - 7}{2 - 1}[/tex]

= 2

Slope of function from x = 2 to x = 3

= [tex]\frac{13 - 9}{3 - 2}[/tex]

= 4

Here the slope is not same. So the function is not linear

For the Fourth table,

Slope of function from x = 1 to x = 2

= [tex]\frac{6 - 0}{2 - 1}[/tex]

=[tex]6[/tex]

Slope of function from x = 2 to x = 3

= [tex]\frac{16 - 6}{3 - 2}[/tex]

= 10

Here the slope is not same. So the function is not linear

So the first option is correct

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Can’t find the correct answer pls help

Answers

(14,-18) to get to 0 to 7 is 7 points and 3 to -8 is -10 points so you add that to ST (7,-8) and that’s gives u (14,-18)

write the quadratic equation whose roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable

Answers

The quadratic equation is y = 4. (x + 2)(x - 1).

Given,

The roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable.

To Write the Quadratic Equation by using above given:
Now, According to the question:

Roots are -2 and 1

Leading Coefficient is = 4

Using Variable is = x

Formulate the equation of polynomial function is

y = 4. (x + 2)(x - 1)

Hence, The quadratic equation is y = 4. (x + 2)(x - 1).

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convert 450 m/s to m/h

Answers

1,620,000 m/h

1) To convert 450 m/s we can set out the following:

[tex]\frac{450}{1s}\text{ }\times3600s=1,620,000[/tex]

Since 1 hour is equivalent to 3600s then we can simply multiply by 3600 once the unit meter remains the same. m/s to m/h

2) Hence, the answer is 1,620,000 m/h

Bea is asked to graph this system of equations: 8x - 6y= 3 -3y + 4x = 4 How many times will the lines intersect?

Answers

Given the system of equations:

8x - 6y = 3

-3y + 4x = 4

To find how many times the lines will intersect. let's solve the system of equation using substitution method.

8x - 6y = 3 ........................................1

-3y + 4x = 4 ......................................2

From equation 1, make x the subject:

8x - 6y = 3

8x = 3 + 6y

[tex]\begin{gathered} x=\frac{3}{8}+\frac{6}{8}y \\ \\ x=\frac{3}{8}+\frac{3}{4}y \end{gathered}[/tex][tex]\text{Substitute (}\frac{3}{8}+\frac{3}{4}y)\text{ for x in equation 2}[/tex]

We have:

[tex]\begin{gathered} -3y+4(\frac{3}{8}+\frac{3}{4}y)=4 \\ \\ -3y+\frac{3}{2}+3y=4 \\ \\ \end{gathered}[/tex]

Multiply through by 2 to eliminate the fraction:

[tex]\begin{gathered} -3y(2)+\frac{3}{2}(2)+3y(2)=4(2) \\ \\ -6y+3+6y=8 \end{gathered}[/tex]

[tex]\begin{gathered} -6y+6y=8-3 \\ \\ 0=5 \end{gathered}[/tex]

Since we have 0 = 5, it means the system of equations has no solution.

Therefore, the lines will not intersect, because this system has no solution.

ANSWER:

A. The lines will not intersect, because this system has no solution.

Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
o Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
o Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)

What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) /

Answers

If the average weight calculated by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.

Given that average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows.

We are required to find the margin of error of Val's data.

Margin of error is the difference between the actual data and the calculated data.

Margin of error=1.96*σ/[tex]\sqrt{n}[/tex]

In our case σ=50 and n is 100.

Margin of error=1.96*50/[tex]\sqrt{100}[/tex]

=1.96*50/10

=1.96*5

=9.80

Hence if the average weight calculated by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.

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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.48 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 3% and the bottom 3%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.

Answers

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued covariates whose distributions are unknown.

Some of their significance comes from the main limit theorem. This claim states that, in some cases, the average of many samples (observations) of a stochastic process with limited mean and variance constitutes itself as a random variable, whose distribution tends to become more normal as the number of samples increases. Because of this, the distributions of physical quantities, like misspecification, which are thought to be the consequence of hundreds of distinct processes, are frequently close to normal.

First we will find the bottom 3% such that P(X ≤ x) = 0.03

⇒ [tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.03[/tex]

⇒[tex]P(Z\leq \frac{x-5.48}{0.07} )=0.03[/tex]

Now we will use the normal table to calculate the corresponding z-score.

[tex]\frac{x-5.48}{0.07} =-1.88\\\\\implies x = 5.348[/tex]

Now we will find the same for the top part of the distribution.

[tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.97\\\\\implies P(Z\leq \frac{x-5.48}{0.07} )=0.97[/tex]

Now we will use the normal table to calculate the corresponding z-score.

[tex]\frac{x-5.48}{0.07} =1.88\\\\\implies x = 5.612[/tex]

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

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Find the orthogonal trajectories of the family of curves. y^2=6KX^3

Answers

Y4 =9KX is your answer

The orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

What is the orthogonal trajectory?

An orthogonal trajectory of a family of curves is any curve that forms right angles with each member of the family. The curve does not always have to cross each member of the family.

It is given that,

y² = 6Kx³

Differentiate both sides we get,

[tex]\rm 2y = 6k(3x^2) \frac{dy}{dx} \\\\ \frac{dy}{dx} =\frac{2y}{18Kx^2}[/tex]

Substitute the value of K as

[tex]\rm K = \frac{y^2}{6x^3}[/tex]

[tex]\frac{2y}{18(\frac{y^2}{6x^3})x^2} = \frac{dy}{dx} \\\\ \frac{dy}{dx} = \frac{2x}{3y}[/tex]

Consider the negative reciprocal to find the perpendicular slope.

[tex]\frac{-3y}{2x} =\frac{dy}{dx} \\\\ - \int {\frac{1}{2x} \ dx = \int \frac{1}{3y} dy \\\\[/tex]

[tex]-\frac{x^2}{4}+C = \frac{y^2}{6}[/tex]

Simplify,

[tex]\rm 6(-\frac{x^2}{4}+C)= y^2 \\\\ y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

Thus, the orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

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For each system to the best description of a solution if applicable give the solution

Answers

System A

[tex]\begin{gathered} x-4y=4 \\ -x+4y+4=0 \end{gathered}[/tex]

solve the first equation for x

[tex]x=4+4y[/tex]

replace in the second equation

[tex]\begin{gathered} -(4+4y)+4y+4=0 \\ -4-4y+4y+4=0 \\ 0=0 \end{gathered}[/tex]

The system has infinitely many solutions, They must satisfy the following equation

[tex]\begin{gathered} x-4y=4 \\ -4y=4-x \\ y=\frac{4}{-4}-\frac{x}{-4} \\ y=\frac{x}{4}-1 \end{gathered}[/tex]

System B

[tex]\begin{gathered} x-2y=6 \\ -x+2y=6 \end{gathered}[/tex]

solve for x for the first equation

[tex]x=6+2y[/tex]

replace in the second equation

[tex]\begin{gathered} -(6+2y)+2y=6 \\ -6-2y+2y=6 \\ -6=6 \end{gathered}[/tex]

The system has no solution.

How do I solve the missing verticals angles for L2 and L3?

Answers

The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:

Then, if we apply this theorem to the figure shown we can say that

[tex]\begin{gathered} L1=L3 \\ L2=L4 \end{gathered}[/tex]

This means that:

[tex]\begin{gathered} L2=110.6 \\ L3=69.4 \end{gathered}[/tex]

a. Write a formula for the perimeter P of the square.Type your answer into the box below.b. Write a formula for the area A of the square,Type your formula into the box below.

Answers

a. The formula for the perimeter of a square is P=4L, where L is the length of it's sides.

b. The formula for the area of a square is A=LxL=L^2, where L is the length of it's sides.

Please help me solve this problem it’s my last question on my hw

Answers

To solve this problem, we will use the following expression:

[tex]\frac{favorable\text{ outcomes}}{total\text{ outcomes}}.[/tex]

In this case:

[tex]\begin{gathered} Total\text{ outcomes}=21+6+6=33, \\ favorable\text{ outcomes}=6. \end{gathered}[/tex]

Substituting the above values in the expression, we get:

[tex]\frac{6}{33}.[/tex]

Finally, simplifying the above result, we get that the probability that his shirt number is from 67 to99 given that he weighs at most 210 pounds is:

[tex]\frac{2}{11}.[/tex]

Answer:

[tex]\frac{2}{11}.[/tex]

price. Find the sale price. There are 252 students on the student council at West High School. If there are 700 students enrolled, what percent are on the student council?

Answers

We have in total 700 students

252 students are on the students council

700 is 100%

252 is x

x represents the percentage of the student's council, in order to calculate x we need to do the next operation

[tex]x=\frac{252\cdot1}{700}=0.36[/tex]

252 is the 36%

the percent of students that are on the student council is 36%

A linear function is shown on the graph
6
What is the domain of the function?
O(x10≤x≤4)
O(x10 Oy 12sy≤6)
0012 Question 1 (Answered)

Answers

The coloured dots in the graph means that it is in a closed interval .

x is between 0 in the y axis and 4 this intervals are included because the colour dots at the end of the straight line mean so

MATHEMATICALLY we say

[tex]0 \leqslant x \leqslant 4[/tex]

THAT IS THE DOMAIN OF THE GRAPH

THAT IS THE DOMAIN OF THE GRAPHOPTION A IS THE ANSWER.

If 9x - 3 = 4, what does 9x - 2 = ?

Answers

it is given that

9x - 3 = 4

then we can write this

9x - (2+1) = 4

9x - 2 -1 =4

9x - 2 = 4 +1

9x - 2 = 5

so the answer is 5

Find the range and mean of each data set. Use your results to compare the two data sets.Set A:Set B:2 10 8 19 2314 16 15 17 16

Answers

Range of a Data Set :

The range of a set of data is the difference between the highest and lowest values in the set

MEAN :

The mean is the mathematical average of a set of two or more numbers

Set A: 2, 10, 8, 19, 23

Arrange the data of set A in ascending order;

Set A : 2, 8, 10, 19, 23

For range; the highest term is 23, lowers term is 2

Range = highest - lowest

Range = 23 - 2

Range = 21

for Mean; the sum of all entries divided by the total number of entries in data set.

In data A, total number of entries are : 5

[tex]\begin{gathered} \text{ Mean = }\frac{2+8+10+19+23}{5} \\ \text{Mean}=\frac{62}{5} \\ \text{Mean}=12.4 \end{gathered}[/tex]

Thus, mean of set A is 12.4

Now, for set B;

Set B : 14 16 15 17 16

Arrange the elements of set B in the ascending order;

Set B : 14, 15, 16, 16, 17

For range; the highest term is 17, lowers term is 14

Range = highest - lowest

Range = 17-14

Range = 3

Thus, range of set B is 3

for mean of set B;

The sum of all entries divided by the total number of entries in data set.

In data B, total number of entries are : 5

[tex]\begin{gathered} \text{ Mean = }\frac{14+16+15+17+16}{5} \\ \text{Mean}=\frac{78}{5} \\ \text{Mean}=15.6 \end{gathered}[/tex]

Thus, the mean for set B is 15.6

Answer : The mean of set A is 12.4 and range is 21

The mean of set B is 15.6 and range is 3

What is the solution to this system of equations?X+ 2y = 4| 2x-2y = 5(3.-5)(3.)no solutioninfinitely many solutions

Answers

The given system of equation :

x +2y =4

2x -2y =5

On adding both equation we get

x+2y+2x-2y=4+5

3x=9

x=3

So, for y, substitute x=3

x+2y=4

3+2y=4

2y=4-3

2y=1

y=1/2

The solutions is (3,1/2)

The system of linear equation have infintely many solution if they are coincidient, i.e. slope are equal

The given expression :

x+2y =4

2y=4-x

y=(4-x)/2

y = 2-x/2

So slope is (-1/2)

The second equation : 2x-2y=5

2y=2x-5

y=(2x-5)/2

y=x-

Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge $41 per hour and painters charge $16 per hour.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

Answers

A) The inequality for the situation is 41x + 16y < 6900

B) The painter can work less than 97 hours without exceeding the budget of Hanson.

Given,

The total money spend by Hanson = < $6900

The charge for carpenters = $41 per hour

The charge for painters = $16 per hour

A) We have to find an inequality for this situation.

Lets take,

Carpenters working hours = x

Painters working hours = y

So, the inequality will be like:

41x + 16y < 6900

B) Now, we have to find the number of hours the painter can work without exceeding his budget if he hires carpenter.

Carpenters working hours = 50

Then, the charge will be = 50 × 41 = 2050

Then,

6900 - 2050 = 4850

The balance amount will be less than 4850.

So, the working hours of painter:

y < 4850 / 50

y < 97

That is, the painter can work less than 97 hours without exceeding the budget of Hanson.

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The question is incomplete. Completed question is given below:

Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge$41 per hour and painters charge $16 per hour.

Part A: Write an inequality to represent the situation.

Part B: If he hires a carpenter for 50 hours, what is the maximum number of hours the painter can work without exceeding his budget?

help me with the 17 pls just give me the answer

Answers

Solution

Evaluate each function below for the given equation

17.

[tex]f(x)=11x-9[/tex]

f(2) is when the value of x = 2

[tex]\begin{gathered} f(x)=11x-9 \\ f(2)=11(2)-9 \\ f(2)=22-9 \\ f(2)=13 \end{gathered}[/tex]

18.

[tex]g(x)=-4(g+2)\text{ for g\lparen5\rparen}[/tex]

g(5) is when the value of x = 5

[tex]\begin{gathered} g(x)=-4(g+2) \\ g(x)=-4g-8 \\ g+4g=-8 \\ 5g=-8 \\ g=-\frac{8}{5} \end{gathered}[/tex]

19.

[tex]f(x)=3+2(-x)[/tex]

f(-1) is when the value of x = -1

[tex]\begin{gathered} f(x)=3+2(-x)\text{ for x = -1} \\ f(-1)=3+2(-(-1)) \\ f(-1)=3+2 \\ =5 \end{gathered}[/tex]

grant is rolling a six sided number die eight times. How many possible outcomes are there?

Answers

The die has 6 faces

[tex]\begin{gathered} \text{ In n number of throws, the number outcomes is given by 6}^n \\ ^{} \end{gathered}[/tex][tex]\begin{gathered} \text{ In 8 throws, the possible outcomes will be 6}^8 \\ =1679616 \end{gathered}[/tex]

A washer and a dryer cost $935 combined. The washer costs $85 more than the dryer. What is the cost of the dryer?

Answers

Answer: $325

Step-by-step explanation:

7.4.PS-15 Question Help Juanita has 3 rectangular cards that are 7 inches by 8 inches. How can she arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter? How will the area of the polygon compare to the combined area of the 3 cards? The perimeter of the polygon is 58 in. (Type a whole number.) How will the area of the polygon compare to the combined area of the 3 cards? O A. The areas will be equal. OB. The area of the polygon will be greater than the combined area of the cards. OC. The area of the polygon will be less than the combined area of the cards. OD. This is impossible to determine with the given information. Click to select your answer and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 8 of 10 Back Next →

Answers

Since there is no overlapping the area of the polygon must be equal to the combined area of the cards.

Evaluate each function in the table at f (3).
Enter the correct answers in the boxes in the table.
Σ
Functions
Function
f(x) = 3x + 5
f(x)=x²-1.5
3
f(x) = 2x
ƒ(3)

Answers

The answer to the given functions are:

1) f (3) = 3 × 3 + 5 = 14

2) f( 3 ) = (3)² - 1.5 = 7.5

3) f (3) = 3×2 = 6

What are functions ?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

A function is a type of rule that produces one output for a single input.. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Given : Functions are f(x) = 3x + 5 ------- 1

f(x)=x²-1.5 --------- 2 and f(x) = 2x -----------3

Thus when we put x = 3 we will get the following values that is ;

1 becomes f (3) = 3 × 3 + 5 = 14

and 2 becomes f( 3 ) = (3)² - 1.5 = 7.5

And 3 becomes f (3) = 3×2 = 6

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Pls help asap

Find the product of 5.3 x 10^12 and 5.12 x 10^9. Write the final answer in scientific notation.

2.7136 x 10^21

2.7136 x 10^22

27.136 x 10^21

27.136 x 10^22

Answers

Answer:

B. 2.7136 x 10^22

Step-by-step explanation:

Hope this helps :))

TRIG ANALYSIS- THE LAW OF SINES- THE AMBIGUOUS CASERecall that your triangle should be set up so that angside b, and angle C is opposite side c.PLEASE HELP. WILL MARK BRAINLIEST

Answers

The sine law is described by the equation

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

1) Given angle C, length of side b, and length of side c, we are looking for the value of angle B. The angle B can be computed using

[tex]\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}[/tex]