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


Part B: If (a, b) = (5, –2) and c = 10, determine the domain and range of the circle.


Part C: Is the point (10, 2) inside the border of the circle if (a, b) = (5, –2) and c = 10? Explain using mathematical evidence.

The linear function that is graphed on the grid is g(x) = (15/2)x + 45   , the correct option is (d) .

In the question ,

a linear function graph is shown ,

we have to find that linear function .

So , From the given graph we can see that

the graph passes from the points (2 , 60) and (6 , 90)

in order to find the equation , we first need to find the slope .

slope = (90 - 60)/(6 - 2)

= 30/4

= 15/2

So , the equation of the line passing through the points (2 , 60) and slope 15/2 is

(y - 60) = 15/2(x - 2)

y - 60 = (15/2)x - 15

Adding 60 to both the sides ,

we get

y - 60 + 60 = (15/2)x - 15 + 60

y = (15/2)x - 15 + 60

y =  (15/2)x + 45

function is (15/2)x + 45

Therefore , The linear function that is graphed on the grid is g(x) = (15/2)x + 45  .

The given question is incomplete , the complete question is

Which linear function is graphed on the grid shown below ?

(a) g(x) = (2/15)x - 6

(b) g(x) = (2/15)x + 45

(c) g(x) = (15/2)x - 6

(d) g(x) = (15/2)x + 45

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Answer:

                             y = (-1/4)x + 9/4

Step-by-step explanation:

i got u

Answer:

One solution: x =21.6

Step-by-step explanation:

Equation

12x + 6 = 14(2x – 24)                    Remove the brackets

Solution

12x + 6 = 28x - 336                      Add 336 to both sides.

12x + 6+336 = 28x - 336             Combine

12x + 342 = 28x -336+336        

12x + 342 = 28x                            Subtract 12x from both sides.

12x-12x + 342 = 28x - 12x             Combine

342 = 16x                                      Divide by 16

342/16 = 16x/16

21.6=x  

The equation of the line in the graph is y = 4x - 9..

The equation of a line in slope intercept form can be represented as follows:

The line forms a linear equation.

Therefore,

y = mx + b

where

Therefore, using (0, -9)(3, 3) let's find the slope

m = 3 + 9 / 3 - 0

m = 12 / 3

m = 4

Therefore, let's find the y-intercept using (0, -9).

-9 = 4(0) + b

b = -9

Therefore, the equation is y = 4x - 9.

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Step-by-step explanation:

3 consecutive even integer numbers :

x

x + 2

x + 4

their sum is the perimeter : 60 ft.

x + x + 2 + x + 4 = 60

3x + 6 = 60

3x = 54

x = 18

the shortest of the 3 sides is 18 ft.

and then we have the other 2 sides with 20 and 22 ft.

Step-by-step explanation:

the angle TSW is the total angle and is 73°.

from that total angle, we have one part : angle 1 = 36°.

as angle TSW = angle 1 + angle 2

we have

73 = 36 + angle 2

angle 2 = 73 - 36 = 37°

Answer:

10th term

Step-by-step explanation:

given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n

5n + 2 = 52 ( subtract 2 from both sides )

5n = 50 ( divide both sides by 5 )

n = 10

that is the 10th term has a value of 52

Answer:i think its 13.70 or 14.00

Step-by-step explanation:

Answer:

$3.27

Step-by-step explanation:

$13.80 x 1.03 (which will add the 3% to the total, skipping a step) = $14.21

Then take $14.21 x .0.23 which will give you just the tip amount of $3.2683 or rounded to the nearest cent, $3.27

Answer:

it is a subset where you are going to make sets from that one set

Answer: 35

Step-by-step explanation:

If 85 students signed up for mathematics but 50 of those students also signed up for both then you need to subtract 85 from 50 to get 35.

The interval where the product will be at least break even equals to 18 units.

In accounting, the break-even point refers to the production level at which total revenues equal total expenses.

Given data

Cost is given as C = 45x + 450

Revenue is given as: R = 70x

In this case, the point of breakeven will be:

Cost = Revenue

45x + 450 = 70x

We will collect like terms:

70x - 45x = 450

25x = 450

We will divide both side by 25:

25x/25 = 450/25

x = 18

Therefore, the interval where the product will be at least break even equals to 18 units.

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Answer:

-25x-45y, because if we have got + and -, so we will write minus.

Answer: 3x²(5x+y)

Step-by-step explanation:

15x³ + 3x²y​

Apply exponent rule: 15x²x+3x²y

Rewrite 15 as 5*3: 5*3x²x+3x²y

Factor out common terms 3x²: 3x²(5x+y)

Hope this helps!!! :)

Answer:

Step-by-step explanation:

this is very complicated and i suggest you to go to einstin

Answer:

[tex]m=-8/3[/tex], the options are wrong

Step-by-step explanation:

[tex]3m-4-\frac{3}{2}m+8=0 \\ \\ 6m-8-3m+16=0 \\ \\ 3m+8=0 \\ \\ m=-\frac{8}{3}[/tex]

The question is incorrect.

Answer: (D) [tex]y=3x-5[/tex]

Step-by-step explanation:

Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].

Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].

If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.

We were told that the constant force acts upon an object, and  the acceleration of the object varies inversely with its mass, which can be interpreted as :

A = k/M

where M is the mass of the object.

A = acceleration

the k= proportionality constant

then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2

then substitute into the equation as:

25 =k*3

k= 25/3

then we were told that when mass is 5 kg, then acceleration will be ?

A= (25/3 )/5 = 1.667m/s^2.

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Answer: Radius is estimated to = 5.2

               Circumference is estimated to = 32.66

Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.

Martin now has: 6 + m

Answer:

B. After the booking fee the party will cost $20 per person

The 50 pounds of trail mix includes 28.57 pounds of cashews and 21.43 pounds of chocolate candies.

let

x + y = 50

2.75x + y = 50 × 2

Solve the equation simultaneously

x + y = 50

2.75x + y = 100

2.75x - x = 100 - 50

1.75x = 50

x = 50/1.75

x = 28.57 pounds

Substitute into

x + y = 50

28.57 + y = 50

y = 50 + 28.57

y = 21.43 pounds

So therefore, the pounds of cashew and chocolate candies needed are 28.75 and 21.43 respectively.

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The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The difference between two consecutive entries is constant, as we can see = 1.75

⇒ 7 - 5.25 = 1.75

⇒ 8.75-7 = 1.75

⇒ Slope(m) = 1.75

The slope represents the variable's rate of change.

y - 3 = m(x - 5.25)

y - 5.25 = 1.75(x-3)

y = 1.76x

Thus, the constant of variation is 1.75

This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.

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The question seems to be incomplete the correct question has been attached

well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]

[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]

Check the picture below.

When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.

When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.

The answers:

9514 1404 393

Answer:

 2×10¹

Step-by-step explanation:

For division, mantissas divide, and exponents subtract.

Answer:

2*10^1

Step-by-step explanation:

Process

When you divide powers, they can be subtracted -- numerator - denominator in powers

The numbers divide the way you normally would if the question is 6/3 = 2

Numerator power = 3

denominator power = 2

Solution

6*10^3/ 3*10^2 = (6/3) * 10^(3 -2) = 2 * 10^1 = 20

20 = 2 * 10^1

I think the answer is C. Because the energy from the sun does break Down rocks and release salt

on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.

What is division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.

To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.

We need to find 100/200,

on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).

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The missing values for gallons of gasoline remaining is 11,6,1.

Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).

We want to find the missing values for gallons of gasoline remaining.

The given equation is g=16-(1/20)d

When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get

g=16-(1/20)100

g=16-5

g=11

When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get

g=16-(1/20)200

g=16-10

g=6

When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get

g=16-(1/20)300

g=16-15

g=1

Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.

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