What is the value of a?
5
5 1/3
6 2/3
7

This is a neat little question. I don't think I've seen it before.
Step one 

Find c
3^2 + 4^2 = c^2
9 + 16 = c^2
c^2 = 25
c = 5

Step 2

Set up your first equation for b^2
a^2 + 4^2 = b^2 from triangle XWY

Step 3

Set up your second equation for b^2
25 +b^2 = (a + 3)^2 from triangle XWZ

Step 4

Put the results of Step 2 into step 3 and solve
25 + a^2 + 16 = (a + 3)^2 Collect the like terms on the left.
41 + a^2 = (a + 3)^2 Expand the brackets on the right
41 + a^2 = a^2 + 6a + 9 Transfer the 9 to the left.
32 + a^2 = a^2 + 6a Subtract a^2 from both sides.
6a = 32 Divide by 6
a = 32 / 6
a = 5 2/6
a = 5 1/3

This took me a long time to type and explain. I hope you consider giving me brainliest answer.

1.

2.

3.

4.

5.

6.

Step-by-step explanation:

I'll explain for you to understand and do it yourself the next time you have to.

Let's do it with

A) Multiply by 10 to eliminate the repeating decimal (3)

What we did is move one of the 3's to the left and since we have infinite 3's, they'll just keep appearing.

B) Now we substract that by the original number:

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Here you can see both numbers have infinite 3's after the decimal point, so we can eliminate them and leave 3 - 0 which is 3.

C) Now we're gonna write an equation for what we did.

because we multiplied by 10 the fraction, and substracted the same fraction from it giving a result of 3.

Solving:

We divide both sides by 9 to isolate ''fraction''

Reduce the fraction to the lowest possible value

This is the result.

NOW THAT WE KNOW THE STEPS

Let's try the second one.

A)

B)

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C)

IN THE THIRD PROBLEM, IT'S THE SAME STEPS TO FOLLOW EXCEPT THAT WE DO NOT REMOVE 1, BECAUSE 1 IS A SIGNIFICANT NUMBER.

A)

B)

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C)

FOURTH PROBLEM IS THE SAME AS THIRD

A)

B)

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C)

THE FIFTH PROBLEM IS THE SAME.

A)

B)

We can add another 6 in the first number to equal the number of decimals. Remember that we can do this because we have infinite 6's.

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C)

To convert 4.2 to a whole number we multiply by 10 to move the decimal point once. Since we are changing the expression, we must also multiply by 10 the denominator so that we equilabrate the operation.

Reduce the fraction

LAST PROBLEM.

A)

B)

To match the number of decimals, we can add more 3's because it's the repeating number.

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C)

you can also rewrite this as a mixed number.