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d1i1m1o1n [39]
3 years ago
10

Question: Consider the similarity transformation of ΔABC to produce ΔEDF.

Mathematics
1 answer:
german3 years ago
3 0

Answer:

see the explanation

Step-by-step explanation:

we have triangle  ΔABC

step 1

Rotate 90 degrees clockwise ΔABC about point C to obtain ΔA'B'C'

Remember that

A rotation is a rigid transformation

An object and its rotation are the same shape and size, but the figures may be turned in different directions

so

ΔABC and ΔA'B'C' are congruent

ΔABC≅ ΔA'B'C

step 2

Dilate the triangle ΔA'B'C' to obtain triangle ΔEDF

Remember that

A dilation is a non rigid transformation

A dilation produces similar figures

If two figures are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent

Find the scale factor of the dilation

The scale factor is equal to the ratio of corresponding sides

In this problem

Let

z ----> the scale factor

so

z=\frac{ED}{AB}=\frac{DF}{BC}=\frac{EF}{AC}

Multiply the length sides of triangle ΔA'B'C' by the scale factor z to obtain the length sides of triangle ΔEDF

Note: in this problem the scale factor z is less than 1

That means ----> the dilation is a reduction

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Your dogs water bowl is 3/4 full. After taking a drink, the water bowl is 1/3 full. What fraction of the bowl did your dog drink
makvit [3.9K]

Answer:

The dog drank 5/12 of the bowl

Step-by-step explanation:

Common denominator

3/4 = 9/12

1/3 = 4/12

9/12 - 4/12 = 5/12

8 0
2 years ago
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horsena [70]

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4 0
2 years ago
P/-8 + 9 &gt; 13 <br> pls explain i don't get it
KonstantinChe [14]

Answer:

p < -32

Step-by-step explanation:

<em>Given:</em> p/-8 + 9 > 13

<em>Rewrite:</em> \frac{p}{-8} + 9 > 13

<em>Subtract 9 from both sides:</em> \frac{p}{-8}  > 4

<em>Move the negative (it is a fraction): </em>\frac{-p}{8} > 4

<em>Multiply both sides by 8:</em> -p > 32

<em>Times by -1 (-p -> -1p): </em>p > -32

<em>Flip the sign (multiplied by a negative): </em>p < -32

Hope this helps, have a nice day :D

3 0
2 years ago
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A circular swimming pool has diameter 60 feet and is centered in a fenced-in square region measuring 80 feet by 80 feet. a concr
borishaifa [10]
If I read the question correctly, the information about the 80x80 fencing and the grass region are all irrelevant information. 

In order to find the area of the side walk we are going to use the formula A=pi(r^2) where r = the radius. The diameter of the pool is 60 feet and the the sidewalk is 5 feet bigger all around meaning we had 5 feet to both sides of this 60 feet giving you an overall diameter of 70 feet (or 60 + 5*2). To find the radius take half of the diameter. 70/2 = 35. 

Now we plug in 35 to the equation. A = Pi(35^2) = 1225pi. Leave your answer like this as we are not finished and will need to round at the end for an accurate answer. This is NOT the end, that number is the area of the sidewalk AND the pool.

The sidewalk is not a full circle, just a border so we now have to find the area of the actual pool and subtract it from this 1225pi for the sidewalk's area. Same formula, Area = pi(r^2). The diameter of the pool is 60 meaning the radius is 30 (or 60/2). Plug into the equation, pi(30^2) = 900pi.

Now do 1225pi - 900pi to get 325pi. Break out your calculator and hit the approximation button. 325pi is approximately 1021.018 if rounded to 3 decimal places.

The area of the 5-foot wide sidewalk encircling the pool is approximately 1021.018 square feet. 


5 0
3 years ago
Jocelyn and Madelyn go to the movie theater and purchase refreshments for their friends.
Alik [6]

let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:

2p + 3d = 18.25

4p + 2d = 27.50

From this, we can use substitution or elimination to solve:

For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.

For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.

I'll be using elimination in this case:

-2(2p + 3d = 18.25) --> -4p - 6d = -36.50

-4p - 6d = -36.50

4p  + 2d = 27.50

-4d = -9.00

d = 2.25

4p + 2 * 2.25 = 27.50

4p + 4.50 = 27.50

4p = 23.00

p = 5.75

Now let's check our answer:

2 * 5.75 + 3 * 2.25 = 18.25

11.50 + 6.75 = 18.25

18.25 = 18.25

So drinks cost $2.25 and popcorn $5.75

7 0
2 years ago
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