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 (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points) Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points) Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)

Answer:

y = 9/10x - 7/5

Step-by-step explanation:

Slope = 9/10

Point (6,4)

y-intercept = 4 - (9/10)(6) = 4 - 54/10

= - 7/5

[tex]2x^2 -5x-8 =0\\\\\implies x = \dfrac{ -(-5) \pm \sqrt{(-5)^2 - 4\cdot 2 \cdot (-8)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{5 \pm \sqrt{89}}{4}\\\\\\\text{Hence}~ x = \dfrac{5 + \sqrt{89}}{4},~~ x = \dfrac{5 - \sqrt{89}}{4}[/tex]

Answer:

[tex]\sf \boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]

[tex]\sf \boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]

[tex]\sf 2x^2-5x-8=0[/tex]

☁ We'll solve this equation using The Quadratic Formula:

[tex]\boxed{\sf \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]

A= 2, b= -5, c= -8

[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}}{2\times \:2}[/tex]

[tex]\mapsto \sf \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}[/tex]

[tex]**\sf \left(-5\right)^2=5^2[/tex]

[tex]\mapsto \sf \sqrt{5^2+4\times \:2\times \:8}[/tex]

[tex]\mapsto \sf \sqrt{5^2+64}[/tex]

[tex]\mapsto \sf \sqrt{89}[/tex]

______________

[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{89}}{2\times \:2}[/tex]

☁ Now, we'll Separate solutions, first, we'll solve the equation when ± is plus:

[tex]\mapsto \sf \cfrac{-\left(-5\right)+\sqrt{89}}{2\times \:2}[/tex]

☁ Multiply 2*2 =4

[tex]\boxed{\sf \cfrac{5+\sqrt{89}}{4}}[/tex]

_________________

☁ Now solve the equation when ± is minus:

[tex]\mapsto \sf \cfrac{-\left(-5\right)-\sqrt{89}}{2\times \:2}[/tex]

☁  Multiply 2*2 =4

[tex]\boxed{\sf \cfrac{5-\sqrt{89}}{4}}[/tex]

[tex]\sf Solution \:1:\boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]

[tex]\sf Solution \:2:\boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]

☁❅☁❅☁☁❅☁❅☁☁❅☁❅☁❅☁

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Answer:

a₁₀ = 105

Step-by-step explanation:

There is a common difference between consecutive terms , that is

33 - 24 = 42 - 33 = 51 - 42 = 9

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 24 and d = 9 , then

a₁₀ = 24 + (9 × 9) = 24 + 81 = 105

The 10th number of the arithmetic sequence will be 105.

Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The arithmetic sequence is given below.

24, 33, 42, 51, ....

The first term is 24 and the common difference will be

d = 33 - 24

d = 9

Then the 10th term of the arithmetic sequence will be

a₁₀ = 24 + (10 - 1) × 9

a₁₀ = 24 + 9 × 9

a₁₀ = 24 + 81

a₁₀ = 105

The 10th number of the arithmetic sequence will be 105.

More about the arithmetic sequence link is given below.

https://brainly.com/question/12373434

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Answer:

31200=300.5%

Step-by-step explanation:

31200=3+1200

=31+1200

=(31×200200)+1200

=600200+1200=601200

We know that

601200

is the same as

601÷200

Then using

gives us

=3.005

Convert the decimal to a percent:

3.005×100

and rounding to a Max of 2 Decimal Places

=300.5%

Answer:

1. 6²=36

2. 289[tex]\frac{1}{2}[/tex] = 17

3. [tex]14^{-2}[/tex] = [tex]\frac{1}{196}[/tex]

4. 10³=1000

5. [tex]5^{4}[/tex]=625

Step-by-step explanation:

Answer:

1. 6² = 36

2. 289^1/2 = 17

3. 14^-2 = 1/196

4. 10³ = 1000

5. 5⁴ = 625

Step-by-step explanation:

I just used the rule that logₓy = n means that xⁿ = y and a logarithm without a base, has a base of 10 (called a "common logarithm").

Answer:

11/20x + 4

Step-by-step explanation:

Well you can jsut solve it normally following the order of operations.

So first you can distribute -(1/4x-1) which turns into 1/4x+1

4/5x+3+1/4x+1 combine like terms and you’d hey 11/20x +4

Answer:

116°

Step-by-step explanation:

(Angle sum property of a triangle = 180°)

angle A + angle C + angle ABC = 180°

66° + 50° + angle BAC = 180°

116° + angle ABC = 180°

angle ABC = 180° - 116°

angle ABC = 64°

angle ABD + angle ABC = 180°

angle ABD + 64° = 180°

angle ABD = 180° - 64°

angle ABD = 116°

So, the measure of the unknown angle is 116°

Answer:

17.999999999999999

Step-by-step explanation:

Answer:

25 and 1/12

1/3+1/3+2/3+1/2+1/2+3/4 = 4 and 1/12

6+5+4+3+2+1 = 21

7. The zeros of the quadratic function described by the graph below is

1

A. 2,1

B. -2,1

C. 2,-1

D. -2,-1

Answer:

5x+5=10

5x=10-5

5x=5

x=5/5

x=1

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Let's solve for x ~

therefore, value of x = 1 ~

[tex] \: \: \: \: \: \: [/tex]

[tex] = 3a ^{4} \times (7 {a}^{5} - 2)[/tex]

Step-by-step explanation:

[tex]21 {a}^{9} - 6 {a}^{4} [/tex]

[tex] = 3 {a}^{4} \times (7 {a}^{5} - 2)[/tex]

[tex] \: \: \: \: \: \: [/tex]

Answer:

⸻⸻⸻⸻⸻

Solving

2X + 3Y = 5.5

⸻⸻⸻⸻⸻

Simplifying

2X + 3Y = 5.5

⸻⸻⸻⸻⸻

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

⸻⸻⸻⸻⸻

Add -3y to each side of the equation.

2x + 3y + -3y = 5.5 + -3y

⸻⸻⸻⸻⸻

Combine terms: 3y + -3y = 0.

2x + 0 = 5.5 + -3y

2x = 5.5 + -3y

⸻⸻⸻⸻⸻

Divide each side by 2.

x = 2.75 + -1.5y

⸻⸻⸻⸻⸻

Simplifying.

x = 2.75 + -1.5y

⸻⸻⸻⸻⸻

Answer:

0.08

Step-by-step explanation:

the orange circle is all people who like iced coffee, since we want the probability of liking only iced coffee, we need to look at the part of the orange circle not overlapping with the blue circle. this is 0.08

Answer:

1. 1

2. 14

3.9

4. 15

5.17

step-by-step explanation:

take X and times it by 4 then add 9

Answer:

.

Step-by-step explanation:

Answer: 2 है यदि छत का क्षेत्रफल 600 वर्ग मीटर तथा चार दीवारों का क्षेत्रफल 1500 वर्ग मीटर हो तो

Step-by-step explanation:

Answer: X=11

Step-by-step explanation:

Add 7 to both sides of the equation     4x-7=2x+15

4x-7+7=2x+15+7

Simplify

Add the numbers :4x -7 + 7 = 2 x + 15 + 7

Add the numbers:4 x = 2x + 15+7

down

4x=2x+22

Subtract

2 2 x 2 x from both sides of the equation

4 x = 2x +22   4x - 2x = 2x +22- 2x

Simplify

2x = 2x +22-2x

Divide both sides of the equation by the same term

2x = 22 2x/ = 22/2 x =22/2x =22/2  x=11

Answer:

the probability is 1 and 2

Answer:

a. = 36km

b. Perimeter = 108km

c. Area = 486km^2

Step-by-step explanation:

Pythagoras theorem

a^2 + b^2 = c^2

27^2 + b^2 = 45^2

b^2 = 45^2 - 27^2

b^2 = 1296

b = [tex]\sqrt{1296}[/tex]

b = 36km

Perimeter

a + b + c

27 + 36 + 45 = 108

Perimeter = 108km

Area = [tex]\frac{ab}{2}[/tex]

Area = [tex]\frac{27 * 36}{2}[/tex]

Area = [tex]\frac{972}{2}[/tex]

Area = 486km^2

Answer:

1,3

Step-by-step explanation:

1 belongs in the green box because on a graph, you start from the x axis which is the horizontal line. The dot is on top of the 1, so the green box would be 1. On the vertical line, the dot is next to the 3, so 3 would go in the grey box.

Answer:

y = x

Step-by-step explanation:

So 1st we need to find the slope of the original line which is y = -x

(use slope formula)

2nd Now we just need to reverse the slope, and that gets us to y = x

Answer: 6

its obvious  

Answer:

Step-by-step explanation:

Slope: 3/1 (positive: line go uphill)

y-intercept: -5

Place your pencil on the vertical line (y) on -5. Go up 3 units and 1 to the right, repeat and trace the line (actually you only need two points to trace a line)

Answer:

A- 4

B- 5

C- 8

D- 4

E- 2

F- 7

I'm 99% sure these are right!! I hope this helps :(

Answer:

12.36

Step-by-step explanation:

Answer:

1 hour = $12.36

Step-by-step explanation:

10 hours = $123.60

=> 10/10 hours = 123.60/10

=> 1 hour = $12.36

Hoped this helped.

Answer:

12 for sure

Step-by-step explanation:

I just know

Answer:

cross-section

Step-by-step explanation:

prism is a type of three-dimensional (3D) shape with flat sides.

It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.

Answer:

Step-by-step explanation:

Answer:

15,000,000 grams

Step-by-step explanation:

300 * 50 = 15,000kg

kg to grams is *1000

15,000 * 1000 = 15,000,000

Answer:

15,000,000.

Step-by-step explanation: