MATHEMATICS HIGH SCHOOL

Polygon ABCDE is dilated by a scale factor of 3 with the center of dilation at the origin to create polygon A'B'C'D'E'. If the endpoints of BC are B(3, 5) and C(5, 10), what is the slope of B'C'?

Answers

Answer 1

Answer:

Answer;

slope = 5/2

Solution and Explanation;

-Polygon which is dilated by a scale factor of 3.

The endpoints of BC are B (3,5) and C (5,10) .

The image of B and C under the dilation will be;

B' = 3 (3,5) = (9,15)

C' = 3(5,10) = (15, 30)

The slope is given by change in y divided by change in x

slope = (30-15)/(15-9)

= 15/6

= 5/2

Answer 2

Answer: The question or problem ask to calculate the slope of the said dilated polygon which it was dilated by a scale factor of 3. In my own calculation the slope of the BC is 5/2 or -5/-2 and the dilated polygon has a the same slope of the original polygon. I hope this would help

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Evaluate 15÷3·(-2) + |-10|

Answers

The answer is 0. If you plug it into a calculator it takes only 5 seconds.

What is the perimeter of a triangle with vertices located at (-1, 4), (2, 7), and (1, 5), rounded to the nearest hundredth? A. 7.63 units B. 7.89 units C. 8.71 units D. 9.24 units

Answers

we are given with the points (-1,4), (2,7) and (1,5) as the sides of the triangle. The area of the triangle can be determined by determining first the length of the sides. Via distance formula, the sides are 3 sqrt 2, sqrt 5 and sqrt 5. The perimeter thus is equal to 8.71 units

The perimeter of a triangle with vertices located at (-1, 4), (2, 7), and (1, 5) is 8.71 units

How to determine the perimeter?

The coordinates are given as:

(-1, 4), (2, 7), and (1, 5)

Calculate the distance between these points using:

$d = √((x_2 -x_1)^2 + (y_2 - y_1)^2)$

So, we have:

$AB = √((-1 -2)^2 + (4 - 7)^2) = 4.24$

$BC = √((2-1)^2 + (7 - 5)^2) = 2.24$

$AC = √((-1-1)^2 + (4 - 5)^2) = 2.24$

The perimeter P is then calculated using:

P = 4.24 + 2.24 + 2.24

Evaluate the sum

P = 8.71

Hence, the perimeter of the triangle is 8.71 units

Answers

Answer:

$1.05

Step-by-step explanation:

if you do 4.20 divided by 4 you get 1.05 and to see if its right you multiply 1.05 by 4 and you get 4.20.

A car is moving at a rate of 28 miles per hour and the diameter of its wheels is about 2 1/3 feet. Find the angular speed of the wheel in radians per minute.

Answers

The diameter of the wheel is 2 1/3 ft. So d = 2 + 1/3
Circumference
C = pi*d
C = 3.14*(2 + 1/3)
C = 7.326667

The circumference is roughly 7.32666 feet.
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Convert 7.32666 feet to miles

(7.32666 feet)*(1 mile/5280 feet) = 7.32666/5280 = 0.001387625 miles

7.32666 feet = 0.001387625 miles (approximate)

-------------------------------------------------------

(28 miles/1 hour)*(1 revolution/0.001387625 miles) = 28/0.001387625 = 20,178.3623097019 revolutions per hour

Now convert from "revolutions per hour" to "revolutions per minute"

(20,178.3623097019 rev/1 hour)*(1 hour/60 minutes) = 20,178.3623097019/60 = 336.306038495031

The final answer for part A) is 336.306038495031 revolutions per minute (this is approximate).

336.306038495031 rev/1 minute)*(2pi radians/1 rev) = 336.306038495031*2pi = 336.306038495031*2*3.14 = 2,112.0019217488

So the angular speed is roughly 2,112.0019217488 radians per minute

How many quarts, rounded to the nearest tenth,are in 72 liters

Answers

Answer:76.1

Step-by-step explanation: multiply the volume value by 1.057

Whats the measure of <2

Answers

Answer:

25 feet is equal to <2

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