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Lorico [155]
3 years ago
11

A similarity transformation maps `Delta`ABC to `Delta`JKL. The measure of `/_A` of preimage `Delta`ABC is 105°. The scale factor

of the dilation in the similarity transformation is 1.5. If `/_A` in the preimage corresponds to `/_J` in the image, what is m`/_J`?
Mathematics
1 answer:
RoseWind [281]3 years ago
5 0

Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.

Therefore, even if \Delta ABC is dilated to \Delta JKL by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle \Delta ABC will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.

Please note that this is true for all two dimensional geometric shapes.

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The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle.
Viktor [21]
Let
x,y, and z the long sides of the triangle 

we know that

x+y+z=170 ft------> equation 1
x/y=25/14----> y=14x/25------> equation 2
y/z=14/12-----> equation 3
x/z=25/12----> z=12x/25------> equation 4

substitute equation 2 and equation 4 in equation 1
x+[14x/25]+[12x/25]=170------> multiply by 25 both sides
25x+14x+12x=4250
51x=4250
x=4250/51
x=250/3
y=14x/25------> y=(250/3)*(14/25)----> y=140/3
z=12y/14-----> (140/3)*12/14----> z=40

Using Heron's formula,
Area of the triangle = √s (s-a) (s-b) (s-c)
where s is the semiperimeter
s=170/2-----> s=85 ft
Area=√85*[85-250/3]*[85-140/3]*[85-40]
Area=9.22*[1.67]*[38.33]*[45]------> Area=26558.21 ft²

the answer is
26558.21 ft²
6 0
3 years ago
What is the slope of the line shown below?
Dima020 [189]

Answer:

A. -2/7

Step-by-step explanation:

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What is the missing digit? LOTS OF POINTS​!
RideAnS [48]

Answer:

The missing digits are 3 and 1.

Step-by-step explanation:

6+3÷3-1=2

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3 0
3 years ago
Read 2 more answers
WILL GIVE BRAINLIEST FOR RIGHT ANSWER
Snowcat [4.5K]

Answer:

1.5

Step-by-step explanation:

2 ft. / the number of sides for width (2) = 1 then 3 ft. / number of sides for length (2) = 1.5

1.5 x 1 = 1.5

4 0
2 years ago
Sam watched television the past five nights for 42 minutes, 23 minutes, 56 minutes, 19 minutes, and 67 minutes. What was the med
guajiro [1.7K]

Answer:

42 minutes is the median amount of time

Step-by-step explanation:

The Median is the middle value of data set.

If there is "odd" number of numbers, and there are n numbers, the median is:

(n/2) + 1 th  number

If there is "even" number of numbers, and there are n numbers, the median is:

Average of n/2th and (n/2) + 1 th number

Here, we have 5 numbers, so the median would be:

(5/2) + 1 th number

That is

3rd number

But, we need to arrange the numbers from least to greatest. Lets write it:

19, 23, 42, 56, 67

The third number is 42, this is the median

3 0
2 years ago
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