A right triangle is shown in the graph.

Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (f, g) and a point on the circle at (x, y). Show all necessary math work.

Part B: If (f, g) = (3, –1) and h = 8, determine the domain and range of the circle.

Part C: Is the point (10, –4) inside the border of the circle if (f, g) = (3, –1) and h = 8? Explain using mathematical evidence.

The partitions involves dividing the line into subsegments

The coordinate of the point on the directed line segment is (0.5,-2)

The given parameters are:-

line segment = (-1, -1) to (5,-5)

Segment ratio = 1 : 3

The coordinates of the partition is calculated as:

\((x,y) = (\frac{mx_2 + nx_1}{m+ n},\frac{my_2 + ny_1}{m+ n})\)

Substitute known values

\((x,y) = (\frac{1 *5 + 3 * -1}{1+ 3},\frac{1 *-5 + 3 * -1}{1+ 3})\)

Evaluate the products

\((x,y) = (\frac{2}{4},\frac{-8}{4})\)

Evaluate the quotients

\((x,y) = (0.5,-2)\)

Hence, the coordinate of the partition is (x,y) = (0.5,-2)

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he will need to score 32 points per game he wil; beat the record by 3 points with 190,meaning the new median is greater than the older median so your answer is C.

Answer:

Step-by-step explanation:

Givens

x2 = 5

x1 = - 1

y2 = 8

y1 = 6

Equation

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

Solution

d = sqrt( (5 - - 1)^2 + (8 - 6)^2 )

d = sqrt( 36 + 4)

d = sqrt(40)

d = 2 * sqrt(10)

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Answer: What is the formula for finding the area of a triangle?

Not technically, but sometimes you may have to find the height using the Pythagorean Theorem, so if you have the hypotenuse and the base of a right triangle, the height, h = √(c^2 - b^2), so the area of the triangle could be found by A = 1/2 b √(c^2 - b^2), but it is the same principle as A = 1/2 b h.

Step-by-step explanation:

im in 6th grade to so thats easy

The price of the car that the man bought is $3000.

Let the initial amount be given as x.

In this case, the man bought an old car and had to spend as much as 15% of what he paid for it, on repairs.

This will be:

x + (15% × x) = 3450

x + 0.15x = 3450

1.15x = 3450

Divide

x = 3450 / 1.15

x = 3000

The car is $3000.

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The price the man bought the old car is 300, 000 units

A man bought an old car and had to spend as much as 15 percent of what he paid for it, on repairs. His total spend including repairs was 345000.

The price he bought the car can be calculated as follows:

let

x = amount he paid for the car

Hence,

amount for repair = 15% of x

amount for repair = 15 / 100 x

amount for repair = 0.15x

Hence,

0.15x + x  = 345000

1.15x = 345000

divide both sides by 1.15

x = 345000 / 1.15

x = 300000

Therefore he bought the car for 300, 000

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The equation of the line that passes through the points (-8,1) and (4, -1) is

y+0.16x=-0.28 by the concept of coordinate geometry.

One of the most intriguing mathematical ideas is said to be coordinate geometry. The relationship between geometry and algebra is explained by coordinate geometry (also known as the analytic geometry) using graphs that include curves and lines. It gives them access to geometric concepts in algebra and gives them tools for solving geometric issues. An ordered pair of integers is used to indicate the location of points on a plane in this area of geometry.

Step 1: find slope=m

Step 2: y-y1=m(x-x1) (eq 1)

Step 3: simplify

According to question p (-8,1) and q (4, -1) are the points

m= \(\frac{-1-1}{4+8}\)

m=-2/12

m=-1/6

m=-0.16

Now, put value of m, y1, x1 in equation 1

y-1=-0.16(x+8)

y+0.16x=-0.28

Therefore, the equation of the line that passes through the points (-8,1) and (4, -1) is y+0.16x=-0.28

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The requried volume of the pedestal is 135 cubic inches.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of a triangular prism is given by the formula V =base x h, where the base is the area of the base and h is the height of the prism.

In this case, the area of the base is given as 9 in², and the height of the prism is given as 15 inches.

Therefore, the volume of the pedestal is:

V = base x h

V = 9 in² x 15 inches

V = 135 cubic inches

So the volume of the pedestal is 135 cubic inches.

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Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

2 stickers

Step-by-step explanation:

We multiply his 7 friends by 8 (stickers given to each friend) to get 56 stickers given total.

We subtract 56 from 58 to get 2 stickers remaining for Justin.

Step-by-step explanation:

Justin is giving out 8 stickers to 7 of his friends

To find out how many stickers he passed out, you would need to do 7×8

7×8 = 56

Now you want to subtract 56 from 58 to figure out how many stickers he had left

58 - 56 = 2

Justin is left with 2 stickers

I am sorry if this didn't make sense

I hope this helps!!!!

Answer:

c. x/7

Step-by-step explanation:

seven is dividing something, and X is the placeholder in this equation.

So, since x is being divided by seven, that rules out B., because that's backwards.

A. and D. don't involve division, so they're both incorrect as well.

Thus we are left with C. x/7

1064 x

19

________

20216 legos

Sharon has 20216 legos

Answer:

14.5 pounds of apples.

Step-by-step explanation:

$3.77 ÷ $.26 = 14.5

Apples = 14.5 pounds

Hope this helps! :)

The solution is:

If my parents are going to pay the 5%, then, they will pay: $2979.

I will need to save $62.06 each month to accomplish my goal.

Here,

I'm going to a 4-year college that will cost $14895/year.

It means that I will need to pay: 14895*4 = $59.580

If my parents are going to pay the 5%, then, they will pay: $2979.

Now, if I want to save my total contribution for all four years, and I have four years to accomplish  the goal, then:

Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.

Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.

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complete question:

You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.

How much do you need to pay for each year of attending?

If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?

The correct options are:

Esmerelda converted the mixed number to the wrong improper fraction.

Esmerelda added the numerators.

Esmerelda did not divide –24 by 6 correctly.

The errors made by Esmerelda are as follows:

1. Esmerelda converted the mixed number to the wrong improper fraction.

2. Esmerelda added the numerators.

3. Esmerelda did not divide –24 by 6 correctly.

Let's go through each error:

1. Esmerelda converted the mixed number to the wrong improper fraction:

Esmerelda incorrectly converted "Negative 5 and one-fourth" to "Negative StartFraction 21 over 4 EndFraction." The correct conversion would be "Negative StartFraction 5 over 4 EndFraction" since the mixed number -5 1/4 can be expressed as -5 + 1/4 = -5  (1/4) = -5 (4/4) + (1/4) = -5 (4 + 1)/4 = -5 (5/4) = -5 (5 over 4).

2. Esmerelda added the numerators:

Esmerelda incorrectly added the numerators of the fractions, resulting in "Negative StartFraction 21 over 4 EndFraction" instead of the correct numerator of -5 * 4 = -20.

3. Esmerelda did not divide –24 by 6 correctly:

Esmerelda made an error in dividing -24 by 6, resulting in "StartFraction 24 over 6 EndFraction" instead of the correct value of -24 divided by 6, which is -4.

Therefore, the correct options are:

- Esmerelda converted the mixed number to the wrong improper fraction.

- Esmerelda added the numerators.

- Esmerelda did not divide –24 by 6 correctly.

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Answer:

y\(\geq 20-x\)

\(y\geq 40-5x\)

Step-by-step explanation:

8 nickels = 40 cents

y < 8

x < 35

Let's test

1 nickel and 35 pennies. That doesn't work

4 nickel and 20 pennies. That works. Perhaps we be more precise?

5 nickels and 15 pennies. Right on the point. 20 coins.

Hope this helps :)

Have a nice day!

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

Answer is B

Step-by-step explanation:

EDGE2022

The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Note that two matrices are said to be equal if they have the same order, and their corresponding elements are also the same.

Given that,

Compare the corresponding terms to get,

Thus, the first option is the correct choice.

The amount of the sale of the home is $2090181.82

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

Commission = 5.5% on the sale of a home

Also, we have

Commission  = 114960

using the above as a guide, we have the following:

5.5% on the sale of a home = 114960

So, we have

5.5% * sale of a home = 114960

Divide both sides by 5.5%

sale of a home = 114960/(5.5%)

Evaluate

sale of a home = 2090181.82

Hence, the sale of the home is $2090181.82

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Answer:

8.25

Step-by-step explanation:

Question 2 will assist the answer to question 1.

You can calculate the horizontal and vertical lengths of two coordinates by subtracting the smallest x coordinate by the largest, doing the same for the y coordinates too:

(-3, 5) (5, 7)

5 - (-3) = 8, the width of x

7 - 5 = 2, the height of y

To calculate the distance between two coordinate sets, use the following formula:

x,y = \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Where x1 and y1 are the coordinates of the first set and x2 and y2 are the second set.

Now plug the values in:

\(\sqrt{(5 - -3)^2 + (7 - 5)^2}\)

\(\sqrt{(8)^2 + (2)^2}\)

\(\sqrt{64 + 4}\)

\(\sqrt{68}\) = 8.25

Hope this helps!

Answer:

y= -3/5 x

Step-by-step explanation:

I hope this helps!!!

Answer:

Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.

Step-by-step explanation:

The trigonometric formula refers the two sides length of the triangle and it also consists of included angle to find out the area

A = \(\frac{1}{2}\) ab sin C

QPR contains two sides and the included angle

XYZ has one side and the two angles

DEF has only three sides

And, the ABC contains two sides but does not have the included angle

Based on the explanation above, the correct option is B

Answer: the second option aka B

Step-by-step explanation: The other person explained it and I'm just here to tell you they gave the correct and answer for edge 2020.

A bottle of orange juice contains 64 fluid ounces. The percent of bottle of orange juice is water is 75% and there are 48 cups of orange juice are there in bottles.

Percentage:

In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Using this formula

Percentage = Ounces of water/Ounce bottle of orange juice

Where:

Ounces of water = 48 ounces

Ounce bottle of orange juice = 64 ounce

Let plug in the formula

Percentage = 48/64

Percentage = 0.75×100

Percentage = 75%

Therefore,

the percent of bottle of orange juice is water is 75%.

Complete Question:

A bottle of orange juice contains 64 fluid ounces. how many cups of orange juice are in three bottles. What percent of bottle of orange juice is water

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Answer:

the percent of bottle of orange juice is water is 75%.

Step-by-step explanation:

Answer:

C. -24 no real roots

Step-by-step explanation