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3 years ago

Write the coordinates of the vertices after a dilation with a scale factor of 1/5, centered at the origin.

Mathematics

1 answer:

eimsori [14]3 years ago

3 0

Answer:

The coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:

U'(-1, -2)

V'(0, -2)

W'(-1, 2)

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

If the scale factor > 1, the image is enlarged

If the scale factor is between 0 and 1, it gets shrunk

If the scale factor = 1, the object and the image are congruent

Rule to calculate the dilation by a scale factor 1/5 centered at the origin

P(x, y) → P'(1/5x, 1/5y)

Here, P'(1/5, 1/5y) is the image of P(x, y).

Given the vertices of the triangle UVW

U (-5, -10)

V (0, -10)

W (-5, 10)

Rule to calculate the dilation by a scale factor 1/5 centered at the origin

P(x, y) → P'(1/5x, 1/5y)

U (-5, -10) → U'(1/5(-5), 1/5(-10)) → U'(-1, -2)

V (0, -10) → V'(1/5(0), 1/5(-10)) → V'(0, -2)

W (-5, 10) → W'(1/5(-5), 1/5(10)) → W'(-1, 2)

Therefore, the coordinates of the vertices after the dilation by a scale factor 1/5 centered at the origin will be:

U'(-1, -2)

V'(0, -2)

W'(-1, 2)

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The lengths of the sides of a triangle are x + 5 inches, 2x - 3 inches,

Natali5045456 [20]

Answer:

15 inches

Step-by-step explanation:

x+5+2x-3+7x+1=103

10x+3=103

10x=100

x=10

3 0

4 years ago

Write the equation of the line with a slope of 2 that passes through the points -2,-7 and 5,7

lubasha [3.4K]

Answer:

Therefore the equation of the line through ( -2 , -7 ) and ( 5 , 7 ) is

2x - y = 3

Step-by-step explanation:

Given:

Slope = 2 = m ( say )

Let,

point A( x₁ , y₁) ≡ ( -2 , -7 )

point B( x₂ , y₂) ≡ ( 5 , 7 )

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula,

$(y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\$

Equation of a line passing through a points A( x₁ , y₁) and i having slope m is given by the formula,

$(y - y_{1} )=m\times(x-x_{1}) \\$

Substituting the given values in a above equation we get

$(y-(-7))=2\times (x-(-2))\\ \\(y+7)=2(x+2)\\\\(y+7)=2x+4\\2x-y=3\\2x-y=3...............\textrm{which is the required equation of the line AB}$

Therefore the equation of the line through ( -2 , -7 ) and ( 5 , 7 ) is

2x - y = 3

8 0

3 years ago

What is the probability of rolling a sum of 5 on a standard pair of six-sided dice? express your answer as a fraction or a decim

viva [34]

The probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

According to the given question.

A standard pair of dice is rolled.

So, the sample sapce for rolling a pair of dice = {(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4),(5, 5),(5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

⇒ Total number of outcomes = 36

And, the outcomes for getting a sum of five on a sandard pair of six sided dice = {(2, 3), (3, 2), (4, 1), (1, 4)}

⇒ Total number of favorable outcomes = 4

As we know that " probability is the ratio of total number of favorable outcomes to the total number of outcomes".

Therefore,

The probability of rolling a sum of 5 on a standard pair of six-sided dice

= 4/36

= 1/9

Hence, the probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

Find out more information about probability here:

brainly.com/question/11234923

#SPJ4

8 0

2 years ago

Algebra pyramid please answer !! be the first to be marked as a brainliest .

azamat

Answer:

The first pyramid:

63x

39x 24x

23x 16x 8x

The second pyramid:

162x

82x 80x

4x 78x 2x

The third pyramid:

12a+2b

9a+b 3a+b

9a b 3a

The fourth pyramid:

-19a

-5a -14a

3a -8a -6a

Step-by-step explanation:

All that an alegbra pyramid is is adding the two terms below it.

So you can see how I added the terms that lied below each number, such as in number 1: I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.

Hope this helped!

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3 years ago

Yw = yw what is the reason

kotegsom [21]

Answer:

The Communicative Property of Multiplication

Step-by-step explanation:

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