Answer:
.
Step-by-step explanation:
Dilate a point 
by a scale factor of 
with 
as the center, and the resultant point would be at 
.
In this question:
Point to dilate: 
.
Scale factor: 
.
Center of dilation: 
.
The resultant point would be:
, which simplifies to .
Rectangle. it’s a 2d 4 sided shape with 2 sets of parallel sides
There are four terms in that expression.
Using proportions, it is found that out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that out of 150 couples initially surveyed, 26 + 25 + 12 + 22 + 13 = 98 couples had at least one spouse preferring action movies, hence the proportion is:
p = 98/150 = 0.6533.
Out of the next 75 couples, the amount is:
A = 0.6533 x 75 = 49
Hence, out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.
More can be learned about proportions at brainly.com/question/24372153
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The value of 
is 
<h3>
Sine ratio </h3>
The sine ratio is given as:
<h3>
Trigonometry</h3>
In trigonometry, we have the following ratio
Substitute in the above equation
Collect like terms
Evaluate
Take square roots
Rationalize
From the question, 
is in the second quadrant, and cosine is negative.
So, we have:
In trigonometry, we have:
So, we have:
Hence, the value of is
Read more about trigonometry ratios at:
brainly.com/question/10417664
