CPT 3 Quiz Review A

When any number is multiplied by zero, the result is always zero. In this equation, when zero is multiplied by any number (in this case, x), the result will always be zero. Therefore, the answer to the equation 0 * x is 0.

The number that is known as the multiplicative identity is 1. In multiplication, any number multiplied by 1 will always result in the same number. Therefore, 1 acts as the identity element for multiplication, as it leaves other numbers unchanged when multiplied by them. The words "one" and "One" are also correct representations of the number 1.

The equation ab(c) = (ab)c demonstrates the Associative Property of Multiplication. This property states that the grouping of factors in a multiplication expression does not affect the result. In this case, the factors a, b, and c can be multiplied in any order and the product will remain the same.

The given equation, a + b = b + a, demonstrates the commutative property of addition. This property states that the order in which numbers are added does not affect the result. In other words, when adding two numbers, switching their positions will not change the sum. This property is applicable to the addition of any real numbers.

The given equation 9(x + 3) = 9(x) + (9)(3) demonstrates the distributive property. This property states that when multiplying a number by a sum, you can distribute the multiplication to each term inside the parentheses. In this case, the 9 is being multiplied by the sum of x and 3, and the equation shows that you can distribute the 9 to both x and 3 separately.

The given expression is a sum of two terms: 3x + 1 and 8x + 9. To simplify this expression, we combine like terms by adding the coefficients of x and the constants separately. The coefficient of x in the first term is 3 and in the second term is 8, so the sum of the coefficients is 3 + 8 = 11. Similarly, the constant term in the first term is 1 and in the second term is 9, so the sum of the constants is 1 + 9 = 10. Therefore, the simplified expression is 11x + 10.

The given expression is a combination of like terms. By combining the terms with the same variable, we can simplify the expression. In this case, combining the x terms (-7x and 2x) gives us -5x, and combining the y terms (5y and 8y) gives us 13y. Therefore, the simplified expression is -5x + 13y.

The given expression is 4(x + 8) - 9. To simplify it, we first distribute the 4 to both terms inside the parentheses, resulting in 4x + 32. Then, we subtract 9 from this expression, giving us the final simplified form of 4x + 23.

The given expression is a combination of two terms: -3(x + y) and 5(x - y). To simplify this expression, we can distribute the -3 and 5 to the terms inside the parentheses. This gives us -3x - 3y + 5x - 5y. We can then combine like terms by adding the x terms and the y terms separately. This gives us -3x + 5x - 3y - 5y, which simplifies to 2x - 8y. Therefore, the correct answer is 2x - 8y.