Identify each of the following as rational or irrational.

Step-by-step explanation:

A rational number can be written as a fraction of two integers.

√23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction.

104.42 is rational because it can be expressed as 10442/100 . We can express it as this because

104.42 * 1 = 104.42 * 100/100 = 10442/100, and multiplying something by 1 keeps it the same

√64 is rational because it is equal to 8, and 8/1 is equal to 8

49.396 with the 6 repeating is rational because we can express 49.39 as

49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with

49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.

For example, 0.6 with the 6 repeating can be represented as 6/9. This is because 0.6 * 10 = 6, and we divide that by 9. Similarly, 0.006 with the 6 repeating can be represented by 0.06/9

We add the two fractions together to get

4939/100 + 0.06/9

multiply both fractions by the other's denominator to even them out and make the numerator of the second fraction an integer

(4939*9)/(100*9) + (0.06*100)/(9*100)

= 44451/900 + 6/900

= 44460/900

Assuming that the last number has only the digits given, that is rational because, similarly to 104.42, it can be multiplied by a power of 10 to result in (integer)/(integer), making it rational. If the dots represent infinite digits, then it is not rational because there are infinite digits that are not repeating, and there is no way to know the last digit, so it is impossible to write a fraction from it

I can help with A. The area of a triangle is base times height divided by 2. The area of a rectangle is length times width.

The area of the first one's rectangle is 4.5 times 5.5, which is 24.75.

The area of each triangle is 6.75 for the two side ones and 6.875 for the top and bottom ones.

Added together, the area of the first envelope is 52 in squared.

The area of the second one's middle rectangle is 24.75. The area of the top one is 11. The area of the bottom one is 19.25.

The shapes on either side of the middle rectangle are trapezoids. To find the area of a trapezoid, you add the lengths of both bases and multiply that by its height. Then, you divide that by 2.

The lengths of both bases in this case are 4 and 4.5, which makes 8.5. Then, you multiply this by 0.75 and get 6.375. This divided by 2 is 3.8175.

All of the areas added together equal 62.365.

The first one has a bigger area. Hope this helps!

Heather :)

Sorry if this is wrong