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Answer:

[tex]y = x[/tex]

Step-by-step explanation:

Given

[tex]A =(6,3.7)[/tex]

[tex]B = (5.4,2)[/tex]

[tex]C = (1,3)[/tex]

[tex]A' = (3.7, 6)[/tex]

[tex]B' = (2, 5.4)[/tex]

[tex]C' = (3, 1)[/tex]

Required

The equation for the line of reflection

Taking points A and A' as a point of reference:

[tex]A =(6,3.7)[/tex] and [tex]A' = (3.7, 6)[/tex]

First, calculate the midpoint (M)

[tex]M = (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]

[tex]M = (\frac{3.7+6}{2},\frac{6+3.7}{2})[/tex]

[tex]M = (\frac{9.7}{2},\frac{9.7}{2})[/tex]

[tex]M = (4.85, 4.85)[/tex]

Calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{6 - 3.7}{3.7 - 6}[/tex]

[tex]m = \frac{2.3}{-2.3}[/tex]

[tex]m = -1[/tex]

The midpoint of a reflection is always perpendicular to the points being reflected.

So, the slope of [tex]M = (4.85, 4.85)[/tex] is:

[tex]m_2 = -\frac{1}{m}[/tex]

[tex]m_2 = -\frac{1}{-1}[/tex]

[tex]m_2 = 1[/tex]

The equation is then calculated as:

[tex]y = m_2(x - x_1) + y_1[/tex]

Where:

[tex](x_1,y_1) = (4.85,4.85)[/tex]

[tex]y = 1(x - 4.85) + 4.85[/tex]

[tex]y = x - 4.85 + 4.85[/tex]

[tex]y = x[/tex]

Hence, the equation of line of reflection is:

[tex]y = x[/tex]

Answer:

c

Step-by-step explanation:

Answer:

a. 45 + 20x

   30 + 26x

b. 2.5 hours

c. 95

Step-by-step explanation:

45 + 20x = 30 + 26x

subtract 30 from both sides of the equation

15 + 20x = 26x

subtract 20x from both sides of the equation

15 = 6x

divide 6x on both sides of the equation

2.5 = x

Answer:

y=x

Step-by-step explanation:

When y=x, then the line goes up 1 and right 1.

Answer: 52.8 kilometers

Step-by-step explanation:

This week she plans to run 2²/₅ times as much as last week.

If she ran 22 kilometers last week, then multiple 22 by 2²/₅ to find out the number of kilometers to run this week.

First convert the improper fraction to a proper one:

2²/₅ = 12/5

= 12/5 * 22

= 264/5

= 52.8 kilometers

Answer:

3x(3x-5)

Step-by-step explanation:

I can do this in my head but I hope it is right but if not I'm sorry

Answer:

- 3x ( x² - 4x + 5 )

Step-by-step explanation:

- 3x ( x² - 4x + 5 )

The distance travelled by the runner running at a rate of 12 mph for 15 min is 3 miles.

Speed is the ratio of distance travelled to time taken. Speed is given by:

Speed = distance/time

Given that the runner is running at a rate of 12 mph for 15 min, hence:

speed = 12 mph, time = 15 min * 1/60 min per hour = 0.25 hours.

Hence:

Speed = distance/time

12 mph = distance/0.25 hours

distance = 3 miles

The distance travelled by the runner running at a rate of 12 mph for 15 min is 3 miles.

Find out more at: https://brainly.com/question/22610586

Answer:

$141

Step-by-step explanation:

1200-(1200*30/100 )

and i did that six time each tume with the new numbers i got

Answer:

382.041666667

Step-by-step explanation:

Answer:

382.0416

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

f(x)=-x-5

f(-4)=-(-4)-5

f(-4)=4-5

f(-4)=- 1

Answer:

6 hours.

Step-by-step explanation:

The formula sort of has to be invented.

Al

rate = 1 shed / 2 hours

Tom

rate = 1 shed / x hours.

Together.

rate = 1 shed / 1.5 hours.

Equation

1 shed / 2 hours + 1 shed / x hours = 1 shed / 1.5 hours.

1/2 + 1/x = 1/1.5          Put the fractions over a common denominator.

(x + 2) / 2x = 1 / 1.5   Cross Multiply

1.5(x + 2) = 2x           Remove the Brackets.

1.5x + 3 = 2x             Subtract 1.5x from both sides

3 = 2x - 1.5x

3 = 0.5x                    Multiply both sides by 2

6 = x

It would take Al 6 hours to do the shed on his own.

Answer:109.1 feet

Step-by-step explanation:

What function uses the ADJACENT and the HYPOTENUSE?

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\cos N = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{73}{x}

cosN=

hypotenuse

adjacent

​

=

x

73

​

\cos 48=\frac{73}{x}

cos48=

x

73

​

x\cos 48=73

xcos48=73

Cross multiply.

\frac{x\cos 48}{\cos 48}=\frac{73}{\cos 48}

cos48

xcos48

​

=

cos48

73

​

Divide each side by cos 48.

x=\frac{73}{\cos 48}=109.0968\approx 109.1\text{ feet}

x=

cos48

73

​

=109.0968≈109.1 feet

Type into calculator and roundto the nearest tenth of a foot.

Answer:

7. Each sweatshirt is $60

8. Table is    3,60 and   5, 100  and   8,160  and   9,180  and     12,240

9. You would graph table by plotting the x,y coordinates of each point on a graph and connecting the dots to show linear relationship

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

please follow rate thank

Answer:

44.7

Step-by-step explanation:

Find the mean of the data set shown below. Round to the nearest tenth, if necessary.

This Week's High Temperatures (°F)

29, 38, 45, 31, 50, 58, 62

The formula for the Mean of a given set of data is

= Sum of terms/ Number of terms

Number of terms = 7

Hence,

Mean = 29+ 38+ 45+ 31+ 50+ 58+ 62/7

Mean = 44.714285714286

Approximately to the nearest tenth= 44.7

Answer:

4n+2

Step-by-step explanation:

Answer:

803.84

Step-by-step explanation:

Radius is half of the diameter.

32/2=16

3.14*16^2=803.84

Answer:

803.84 in^2.

Step-by-step explanation:

Radius = 1/2 * 32 = 16

Area = 3.14 * 16^2

= 803.84.

Answer:

2 and 16

Step-by-step explanation:

Answer:

35 years old

Step-by-step explanation:

Let Janice's age = j.

Let Ross's age = r.

j = 5r

j = r + 28

Set the equations equal to each other.

5r = r + 28

4r = 28

r = 7

j = 5r

j = 5(7)

j = 35

Answer: 35 years old

Answer:

(19+7)÷2-5

Step-by-step explanation:

you need to add 19 and 7 together first to get 8 then go in order of operations

Answer:

4 eggs per cup

Step-by-step explanation:

Answer:

u think its A if not sorry

Step-by-step explanation:

Answer:

1, 2 and 5

Step-by-step explanation:

Answer:(0, -28) and (4,0)

Step-by-step explanation:

[tex]7(0)-y =28\\-y=28\\y=-28\\(0, -28)[/tex]

[tex]7x-0= 28\\x=4\\(4,0)[/tex]

Answer:

B and C

Step-by-step explanation:

A, when x = 0, y = 5

B, when x = 4, y = 3

C, when x = 12, y = -1

D, when x = 1, y = 9/2

Answer:

1.) The product of 12 and 3/4 is less than 12. This is because you are multiplying 12 by a number less than 1.

2.) The product of 5 and 1/2  is less than 5, this is because you are multiplying 5 by a number less than one.

Step-by-step explanation:

If multiplied by a number less than one then it will be smaller than original

If multiplied by one will be the same as original

If multiplied by a number greater than one it will be greater than original

your answer would be 33.

step 1

2(+14)−1(2−5)

2+28−1(2−5)

step 2 distribute

2+28−1(2−5)

2+28−2+5

step 3 then add the numbers

2+28−2+5

2+33−2

combine

2+33−2

ANSWER IS

33