Solve for X Tysm for the help!

Mathematics

1 answer:

Anna007 [38]2 years ago

4 0

Answer:

x = 25

Step-by-step explanation:

If the triangles are similar, we know that their corresponding sides are in an equal ratio, so we can set them equal to each other. It's

To set it up, we'll use two fractions. Note that the top numbers, x and 25, are both from the same triangle, and the bottom numbers, 6 and 10, are both from the other triangle. You won't have success if you do this the wrong way.

$\frac{x}{6}$ = $\frac{25}{10}$

Cross-multiply:

10x = 25*6

10x = 250

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How many distinguishable 11 letter "words" can be formed using the letters in MISSISSIPPI?

SCORPION-xisa [38]

This is given by the multinomial coefficient:

$\dbinom{11}{1,4,4,2}=\dfrac{11!}{1!4!4!2!}=34650$

If you're not familiar with the multinomial coefficient, you may be able to see it more clearly if you count the number of possible combinations taking each distinct letter $n$ times, where $n$ is the number of times it shows up in the original word.

$\underbrace{\dbinom{11}1}_{\text{M}}\underbrace{\dbinom{10}4}_{\text{I}}\underbrace{\dbinom64}_{\text{S}}\underbrace{\dbinom22}_{\text{P}}=\dfrac{11!}{1!10!}\dfrac{10!}{4!6!}\dfrac{6!}{4!2!}\dfrac{2!}{2!0!}=\dfrac{11!}{1!4!4!2!}$