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Ierofanga [76]
3 years ago
15

The smaller triangle was dilated to form the larger triangle. What is the value of x? A smaller triangle has side lengths of 5,

13, 12. A larger triangle has side lengths of x, blank, 18. 6.9 7.5 10 11
Mathematics
2 answers:
White raven [17]3 years ago
5 0

Answer:

7.5

Step-by-step explanation

CUZ IMMA BIG BRAIN

riadik2000 [5.3K]3 years ago
4 0

Answer:

x = 7.5

Step-by-step explanation:

Dilation is a transformation in which the size of a given figure is either increased or decreased by a scale factor.

Given that the length of sides of the smaller triangle are; 5, 13, 12.

Given also that the length of the dilated triangle are; x, blank, 18.

Comparing the length of the last sides of the two triangles, we have;

(scale factor x 12) + 12

                        = (\frac{1}{2} x 12) + 12

                        = 6 + 12

                        = 18

Thus the scale factor for the dilation is \frac{1}{2}. So that:

x = (\frac{1}{2} x 5) + 5

   = 2.5 + 5

   = 7.5

x = 7.5

And also,

blank = (\frac{1}{2} x 13) + 13

          = 6.5 + 13

blank  = 19.5

Therefore, the length of the sides of dilated triangle are: 7.5, 19.5, 18

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Step-by-step explanation:

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Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66
Ipatiy [6.2K]

Answer:

Summation notation is:

\sum_{n=1}^{16}[5(x-1)-9]

If you prefer it a little more simplified:

\sum_{n=1}^{16}(5x-14)

Step-by-step explanation:

First my favorite part, finding a pattern between the consecutive terms.

This is an arithmetic series because the terms are going up by 5 each time.

So arithmetic sequence, think linear equations:

x     |      y

1            -9

2           -4

3             1

4             6

..................

n             66

We are going to have to find that n but will will eventually...

The equation for a line in point slope form is y-y_1=m(x_x_1) where (x_1,y_1) is a point on the line and m is the slope.

We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).

I'm going to use the first point (1,-9).

So the equation in point slope form is y-(-9)=5(x-1)

Subtract 9 on both sides:

y=5(x-1)-9

Now we need to know how many terms we are adding so what is x if y=66.

66=5(x-1)-9

Add 9 on both sides:

75=5(x-1)

Divide both sides by 5:

15=x-1

Add 1 on both sides:

16=x

We have 16 terms in this sequence where the 16th term is 66.

Summation notation is:

\sum_{n=1}^{16}[5(x-1)-9]

You could simplify the 5(x-1)-9.

Distribute:  5x-5-9

Add like terms:  5x-14

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Step-by-step explBanation:

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Answer:

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Step-by-step explanation:

For each year, there are only two possible outcomes. Either a levee fails during the year, or no levees fail. In each year, the probabilities of levees failing are independent from each other. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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And p is the probability of X happening.

In this problem we have that:

A levee was designed to protect against floods with an annual exceedance probability of 0.02. This means that p = 0.02

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66.76% probability that the levee will NEVER fail in the next 20 years.

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