1. To which subset(s) does the number √42 belong?

Rational numbers
Irrational numbers
Whole numbers, integers, rational numbers
While numbers, natural numbers, integers

2. Evaluate the following expression for the values given.

P/s + r^2q ( p = 60, q = 6, r = 5, s = 4)

165
180
69
590

3. What is the simplified form of the expression?

-(8d - 3w)

8d + 3w
8d - 3w
-8d + 3
-8d - 3w

4. A video store membership costs $30 to join and $12 each month. Use an algebraic expression to find the cost of the video store membership for 5 months.

30
60
90
105

5. Simplify the following expression.

4(16 + 12x)

64x + 48
64 + 48x
64 + 12x
64 - 36x

My answers:
1. Irrational
2. 165
3. 8d + 3w
4. 90
5. 64 + 48x

#1: correct

#2: correct
#3: -8d+3w

For #1, I meant to write in the choices Whole Numbers not While numbers. Sorry

1 and 2 >> I don't know.

3. I don't think any of the answer choices are correct.

4. and 5. Correct.

Please do not put my name in the School Subject box. I'll answer the questions I can.

1. To determine which subset the number √42 belongs to, we need to assess whether it is a rational or irrational number.

To do this, we first find the square root of 42. The square root (√) of a number is the value that, when multiplied by itself, gives the original number. In this case, we need to find the square root of 42.

Using a calculator or an appropriate mathematical technique, we can find that √42 ≈ 6.4807407.

Now, to determine the subset, we need to understand the properties of rational and irrational numbers:

- Rational numbers are numbers that can be expressed as a quotient or fraction of two integers (where the denominator is not zero). They either terminate or repeat after the decimal point. Examples include 1/2, 3/4, 0.9, and 2.
- Irrational numbers are numbers that cannot be expressed as fractions. They are non-terminating and non-repeating decimals. Examples include π (pi), √2, and √3.

Since we found that √42 is a non-repeating and non-terminating decimal, it cannot be expressed as a fraction, indicating that it is an irrational number. Therefore, the answer to the first question is "Irrational numbers."

2. To evaluate the expression P/s + r^2q for the given values p = 60, q = 6, r = 5, s = 4, we substitute the values into the expression:

P/s + r^2q = 60/4 + 5^2 * 6.

Now, we perform the calculations step by step:

60/4 = 15.
5^2 = 5 * 5 = 25.
25 * 6 = 150.

Now, substitute these values into the expression:

15 + 150 = 165.

Therefore, the answer to the second question is 165.

3. To simplify the expression -(8d - 3w), we distribute the negative sign (-) to every term inside the parentheses:

-(8d) - (-3w) = -8d + 3w.

Therefore, the simplified form of the expression -(8d - 3w) is -8d + 3w.

4. To find the cost of the video store membership for 5 months, we start with the initial cost of joining the video store, which is $30. Then, we add the monthly cost for each additional month. In this case, the monthly cost is $12.

So, the cost of the video store membership for 5 months is calculated as follows:

$30 (joining cost) + ($12 * 5) (5 months at $12 each).

$30 + $60 = $90.

Therefore, the cost of the video store membership for 5 months is $90.

5. To simplify the expression 4(16 + 12x), we apply the distributive property, which states that the product of a number and a sum is equal to the sum of the products of the number with each term inside the parentheses.

Using this property, we multiply 4 by both terms inside the parentheses:

4 * 16 + 4 * 12x = 64 + 48x.

Therefore, the simplified form of the expression 4(16 + 12x) is 64 + 48x.

So, your answers are:

1. √42 belongs to the subset of Irrational numbers.
2. The expression evaluates to 165 for the given values.
3. The simplified form of the expression -(8d - 3w) is -8d + 3w.
4. The cost of the video store membership for 5 months is $90.
5. The simplified form of 4(16 + 12x) is 64 + 48x.