(2+8) + 10 ^2 +60 divided 10
2 answers:
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Using the concept of proportional, it is found that the value of x for the given similar triangles is 2.
<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.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Since two triangles ΔACD and ΔABE are similar triangles, then their corresponding sides will be proportional.
Therefore, AC/ AB = AD / AE
By substituting the measures of the sides here;
AC/ AB = AD / AE
(x + 10) / 10 = (15 +3) / 15
15(x + 10) = 180
x + 10 = 12
x = 12 - 10
x = 2
Therefore, the value of x for the given similar triangles is 2.
More can be learned about proportions at;
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Answer:
sum(2^(n+1), for n=1 to 6)
Step-by-step explanation:
To answer this question, you need to know two things:
- what is an expression for the n-th term
- how many terms are there
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The series shown is a geometric series with first term 4 and common ratio 8/4 = 2. The generic form of the n-th term is ...
an = a1×r^(n-1) . . . . first term a1, common ratio r
You can use this form directly in your summation expression, or you can simplify it a bit.
an = 4×2^(n-1) = (2^2)(2^(n-1)) = 2^(n-1+2)
an = 2^(n+1)
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The value 128 is 2^7, so n+1 = 7, or n=6 for that term
Your summation expression could be ...
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<em>Additional comment</em>
The n-th term can also be written as 2×2^n.