Describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.(4 poi

Answer 1

All integers are also whole numbers, but not all whole numbers are integers.

Integers are the set of counting numbers, their negatives, and zero. Whole numbers are the set of counting numbers and zero.

For example, the number 3 is an integer because it is a counting number. It is also a whole number because it is a counting number and zero.

However, the number -2 is an integer because it is the negative of a counting number. It is not a whole number because it does not include zero.

Therefore, every integer is also a whole number since it includes zero, but not every whole number is an integer since it may not include negative numbers.

Answer 2

The diagonal of a square equals 2–√
times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 70 feet on a side?(1 point)
ft.

Answer 3

The length of the diagonal of a square is given by the formula diagonal = side length * (2-√2).

Given that the square root of 2 is approximately 1.4, we can substitute this value into the formula:

diagonal = 70 * (2-1.4) = 70 * 0.6 = 42

Therefore, the approximate length from one corner to an opposite corner of the square park is 42 feet.

Answer 4

Convert 0.09¯¯¯¯¯ to a rational number in simplest form.(1 point)

Answer 5

To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number in simplest form, we need to set up an equation.

Let x = 0.09¯¯¯¯¯

We can multiply both sides of the equation by 100 to remove the repeating decimal:

100x = 9.999¯¯¯¯¯

Now, we subtract the original equation from the new equation:

100x - x = 9.999¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.909¯¯¯¯¯

We subtract the original equation from the new equation:

99x = 9.909¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.819¯¯¯¯¯

Now we can write the repeating decimal in fraction form:

$99 x$ = $9.819819819819...$

To convert the repeating decimal to a fraction, we assign a variable to the repeating part.

Let y = 0.819819819819...

Now, we can subtract y from the left side of the equation to obtain:

99y = 9.819819819819... - 0.819819819819...

Simplifying the equation:

99y = 9

Now, we divide both sides of the equation by 99:

y = 9/99

Since y represents the repeating part of the original decimal, we need to add it to the non-repeating part, 0.09.

0.09 + y = 0.09 + 9/99

Combining like terms:

0.09 + 9/99 = 0.09 + 1/11 = 0.09 + 0.090909090909...

Now, we have a repeating fraction. To simplify it, we can again assign a variable to the repeating part:

Let z = 0.090909090909...

Subtracting z from the original equation:

z = 0.090909090909... - 0.09

Simplifying the equation:

z = 1/11

Now, we can add the non-repeating part, 0.09, to the repeating fraction:

0.09 + z = 0.09 + 1/11

Combining like terms:

0.09 + 1/11 = (9/100) + (1/11)

Adding the fractions:

(9/100) + (1/11) = 19/100

Therefore, the rational number equivalent to the repeating decimal 0.09¯¯¯¯¯ in simplest form is 19/100.