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algol [13]
3 years ago
5

Triangle ABC was dilated and translated to form similar triangle A'B'C'.

Mathematics
2 answers:
Sergeu [11.5K]3 years ago
7 0

correct answer is 5/2

Hunter-Best [27]3 years ago
3 0
Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.

On this exercise is asked to find the scale factor by which the triangle ABC was 
dilated to produce the triangle A'B'C'. 
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.

As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.

Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)

Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)

As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.  

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Claire runs 10 km in 1 hour. How many kilometers does she run in half an hour? In 2 1/2hours?
Salsk061 [2.6K]

Answer: 5 km and 25 km

7 0
3 years ago
Pls help me I kinda don’t get it.
suter [353]
A). Pi m

Explanation:

Arc length formula:

Arc length = (Ø/360°) * 2*Pi*r
Ø = given angle (degrees)
r = radius

Plug given numbers in:

(45°/360°)* 2* Pi * 4
This will give you the answer of Pi
4 0
3 years ago
Find the value of x and y to the nearest tenth
Readme [11.4K]
The value of 'x' is 24.2 and the value of 'y' is 46.5.

To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
    cos30° = b/34 [adjacent over hypotenuse]
    b = 34cos30° [cross-multiply]
    b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
     l² + l² = hyp²
     29.4² + h² = 34²
     h² = 1156 - 864.36
     √h² = √291.64
     h = 17.1
<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.     
  Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
     x = 17.1 × √2
     x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u />     y = a + b
     y = 17.1 + 29.4
     y = 46.5

And there you have it! <em>Hope this helps.</em>
     <em>
</em>
5 0
3 years ago
Evaluate, leave ur answer in index form. 2³ × 2^-1​
vitfil [10]

Multiply = add powers

3 + - 1 = 2

- - means +

+ + means +

- + means -

Thus, answer is 2^2

Hope this helps!

3 0
1 year ago
6. Carla runs 3 miles in 30 minutes.
NARA [144]

Answer:

Carla ran 0.1 miles per minute.

Step-by-step explanation:

To solve this, we need to use the distance formula.

The formula is d=rt, where d is the distance traveled, r is the rate in which the distance is traveled, and t is the amount of time it took to go that distance. So lets plug it all in.

d=rt

3=(r)(30)

Now, we need to do the inverse of multiplying 30 to both sides, which would be the same as dividing by 30 on both sides.

3/30=(r)(30/30)

0.1=r

The rate is 0.1. Carla ran 0.1 miles per minute.

3 0
2 years ago
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