Titus is asked to prove hexagon FEDCBA is congruent to hexagon
F'E'D'C'B'A' in the graph below. Titus thinks that if he transforms hexagon
FEDCBA by (x,y) - (x + 16. y - 10) he can show the two figures are
congruent. Is he correct? Explain why or why not. If Titus is incorrect, what
series of transformations will correctly prove FEDCBA F'E'D'C'B'A'S
у
6
В.
>E
4
2
с
D
-14 -12 -10 -8
x
-6
4
2
4
6
8
10 12
-20
-2
in
A'
4
E!
-6
В"
-8
lo
c
-10
Is Titus correct? YES NO
Explain why or why not (required)

Answer:

The equation of the circle is x² + y² + 12x - 14y - 165 = 0 , its center is (-6, 7) and its radius is 5√10 units.

Step-by-step explanation:

a. The center of the circle

Since the equation of the tangent of the circle is 3x - y = 15, we write it in standard form. So y = -3x - 15. Its gradient is -3. The perpendicular line tot he tangent is the radius and it passes through the center of the circle and the point (9, 12). For two perpendicular lines of gradient m₁ and m₂, m₁m₂ = -1. If m₁ = -3, then m₂ the gradient of our radius line is gotten from m₁m₂ = -1

m₂ = -1/m₁ = -1/-3 = 1/3

Since the radius also passes through the point (9, 12), its equation is gotten from

(y - y₁)/(x - x₁) = m₂ where (x₁, y₁) = (9, 12)

Substituting the value of the variables into the equation, we have

So, (y - 12)/(x - 9) = 1/3

cross-multiplying, we have

3(y - 12) = (x - 9)

expanding the brackets, we have

3y - 36 = x - 9

collecting like terms, we have

3y = x - 9 + 36

3y = x + 27

So, the equation of the radius line is

3y - x = 27.

Now, since the center of the circle lies on the line 2y + x = 8, the radius line and this line intersect at the center of the circle. So, we solve both equations simultaneously to find the center of the circle.

So, 3y - x = 27  (1)

     2y + x = 8    (2)

adding (1) and (2), we have

5y = 35

y = 35/5

y = 7

Substituting y = 7 into (2), we have

2y + x = 8

2(7) + x = 8

14 + x = 8

x = 8 - 14

x = -6

So, the center of the circle is at (-6, 7)

b. The radius of the circle

The radius of the circle is the length of the line from the tangent point to the center of the circle. So, r = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (-6, 7) and (x₂, y₂) = (9, 12).

Substituting these into r, we have

r = √[(9 - (-6))² + (12 - 7)²]

= √[(9 + 6)² + (12 - 7)²]

= √[15² + 5²]

= √[225 + 25]

= √250

= √25 × √10

= 5√10 units

c. The equation of the circle

Now, the equation of a circle with center (h,k) and radius, r is

(x - h)² + (y - k)² = r² where (h. k) = (-6,7)

Substituting the variables into the equation, we have

(x - (-6))² + (y - 7)² = (√250)²

(x + 6)² + (y - 7)² = 250

expanding the brackets, we have

x² + 12x + 36 + y² - 14y + 49 = 250

collecting like terms, we have

x² + y² + 12x - 14y + 36 + 49 - 250 = 0  

x² + y² + 12x - 14y - 165 = 0

So, the equation of the circle is x² + y² + 12x - 14y - 165 = 0 , its center is (-6, 7) and its radius is 5√10 units.

Answer:

20

Step-by-step explanation:

30% of 20 is 6

Answer:

14 is the answer

Step-by-step explanation:

I hope I helped

The value of x is 14.

The correct option is C.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The smaller triangle was dilated to form the larger triangle.

A smaller triangle has side lengths of 3 and 5.

A larger triangle has side lengths of 9 and x + 1.

That means,

the ratio,

3/5 = 9/(x + 1)

3x + 3 = 45

x = 14

Therefore, the value is 14.

To learn more about the ratio;

https://brainly.com/question/13419413

#SPJ6

Answer:  So the cost to rent each chair is $1.25 and the cost to rent each table is $8.50  

Step-by-step explanation:

Let C = cost to rent each chair

Let T = cost to rent each table

 4C + 8T = 73

2C + 3T = 28

 Multiply the 2nd equation by (-2) and then add the equations together  

  4C + 8T = 73

-4C - 6T = -56

 2T = 17

T = 17/2 = 8.5

 Plug this in to the 1st equation to solve for C

 4C + 8(17/2) = 73

4C + 68 = 73

4C = 5

C = 5/4 = 1.25

Answer:

Step-by-step explanation:

If you're late on your cell phone bill, you'll generally be fined as much as 5 percent of the amount due or $5, whichever is higher. Late charges may not kick in immediately. At AT&T, for example, the fee is applied six days after your due date. Often, your late fee will be subject to taxes.

Answer:

7.21308 is the late fee so in total it is going to be 98.08308

Step-by-step explanation:

Your welcome

Answer:

A

Step-by-step explanation:

1/6^2 =

1/36

Answer:

B

Step-by-step explanation:

When you divide 2 numbers with the same base, you subtract the exponents. We know fractions are basically division, so we would do 3-5. You get -2 as your exponent and we know negative exponents can be written two ways: [tex]6^{-2} and \frac{1}{x6^{2} }[/tex]. Both of those are there, so they are not the correct answer. B can be determined as the one not because the exponent is positive.    

Answer:

awnser one is 7 and question 2 is -10

Step-by-step explanation:

−12−2−−55=?  question one

In the first fraction, the negative numerator and negative denominator cancel each other.

Since the the second fraction is negative and you are subtracting, remove the negative sign and switch the operation to addition.

The equivalent equation is

122+55=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(12/2, 5/5) = 10

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(122×55)+(55×22)=?

Complete the multiplication and the equation becomes

6010+1010=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

60+1010=7010

Since 70 divided by 10 equals 7 then,

7010=7

Therefore:

−12−2−−55=7    

Question 2

−81+6−3=?

In the second fraction, move the negative sign from the denominator to the numerator and the value remains the same.

The equivalent equation is

−81+−63=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(-8/1, -6/3) = 3

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(−81×33)+(−63×11)=?

Complete the multiplication and the equation becomes

−243+−63=?

The two fractions now have like denominators so you can add the numerators.

Then:

−24+−63=−303

Since -30 divided by 3 equals -10 then,

−303=−10

Therefore:

−81+6−3=−10

Solution by Formulas

Apply the fractions formula for addition, to

−81+6−3

and solve

(−8×−3)+(6×1)1×−3

=24+6−3

=30−3

=−10

Answer:

9

Step-by-step explanation:

It's just telling you that the value of x is 3, so in the equation,

you replace x with 3,

2(3) + 3,

2 x 3 = 6,

6+ 3 = 9

Answer:

9

Step-by-step explanation:

They give you the equation:

2x+3

And they give you the (x):

x=3

So you simply replace (x) with 3

2x+3

2(3)+3

now solve

2•3= 6

6+3 = 9

9 is your answer.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Answer:

sqrt(29)

Step-by-step explanation:

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

x1 = 6

x2 = 8

y1 = -8

y2 = -3

distance = sqrt(  ( 8 - 6)^2 + (-3 - -8)^2  )

distance = sqrt( 2^2 + 5^2)

distance = sqrt(29)

Answer:

29

Step-by-step explanation:

29

Answer:

[tex]y=-\frac{2}{3}x+2[/tex]

Step-by-step explanation:

y = -2/3 x + 2

Answer:y=-2/3x+2

Step-by-step explanation:

Trust me

Answer:

No

Step-by-step explanation:

A triangle with a side of five is only a perfect right triangle when it's in a 5,12,13 ratio.

Furthermore, to check, 5^2 is 25 and 3^2 is 9. 25+9 is 34, which doesn't not have a square root of 6.

Answer:

domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis

Answer: 14

Step-by-step explanation:

Check it

Answer:

k = 14

Step-by-step explanation:

The Remainder theorem states that if f(x) is divided by (x + h) then the remainder is f(- h)

If (x + h) is a factor of f(x) then the remainder is zero, that is f(- h) = 0

Given (x + 2) is a factor of f(x) then f(- 2) = 0, that is

(- 2)³ + 8(- 2)² - 2k + 4 = 0

- 8 + 8(4) - 2k + 4 = 0

- 8 + 32 - 2k + 4 = 0

- 2k + 28 = 0 ( subtract 28 from both sides )

- 2k = - 28 ( divide both sides by - 2 )

k = 14

Answer:

21

Step-by-step explanation:

Answer:

J. 80°

Step-by-step explanation:

Answer:

who tell me how to start?

Answer:

Expanded form - write 5 ( p+6 ) - 5 ( p - 2)  

as an equation  y = 5 (p+6) -5(p-6)

simplifyed form - 40

Step-by-step explanation

Answer:

#5 the slope is 1/2

#6 the slope is -5/4

Step-by-step explanation:

Answer:

x=155

Step-by-step explanation:

since its a straight line, it has to equal 180 in total.

SQR is 25, so to find PQS you subtract 180-25

Which equals 155

Answer:

SAS

Step-by-step explanation:

The information represents a Side, Angle, Side triangle

Answer:

SAS !

Step-by-step explanation:

it means Side, Angle & Side triangle and it does show that :)

Answer:

The two lines intersect at (6, -4) which is the solution to this system of equations.

x = 6

y = -4

[tex]\left \{ {{-3x-9y = 18} \atop {4x+3y=12}} \right.[/tex] can be rewritten as [tex]\left \{ {{y=-\frac{1}{3}x-2 } \atop {y=-\frac{4}{3}x+4 }} \right.[/tex] to make graphing easier.

Answer:

im trying to figure out the same thing

Step-by-step explanation: