Algebra Unit 1 Assessment

The given pattern describes the commutative property of multiplication, which states that the order of the factors does not affect the product. In other words, when multiplying two numbers, it doesn't matter which number comes first, the result will be the same. So, 5 x 4 is equal to 4 x 5.

The expression 5 x 2 + 4 can be evaluated by following the order of operations, which states that multiplication should be done before addition. Multiplying 5 and 2 gives us 10, and then adding 4 gives us a final result of 14.

To simplify the expression 25 ÷ (4 + 1) + 3, we need to follow the order of operations, which states that we should first evaluate any expressions inside parentheses. The expression inside the parentheses is 4 + 1, which equals 5. Therefore, the expression becomes 25 ÷ 5 + 3. Next, we perform the division, which is 25 ÷ 5 = 5. Finally, we add 3 to 5, resulting in 8. Therefore, the correct answer is 8.

The given answer correctly shows the order of the numbers from least to greatest. It states that -4 is less than 1, and 1 is less than 3. This is the correct order of the numbers based on the given information.

To evaluate 2y - 3x when x = 3 and y = 4, we substitute the given values into the expression. So, 2(4) - 3(3) becomes 8 - 9, which equals -1. Therefore, the correct answer is -1.

The expression 4p - 2q is evaluated by substituting p = 2 and q = 3 into the expression. Thus, 4(2) - 2(3) = 8 - 6 = 2. Therefore, the correct answer is 2.

The numbers are being arranged in descending order, from greatest to least. In this case, 0 is the greatest number since it is greater than both -3 and -9. -3 is greater than -9, so it comes next. Finally, -9 is the smallest number, so it comes last. Therefore, the correct arrangement is 0 > -3 > -9.

The daily length of the delivery route is 52 miles. This is calculated by dividing the total distance traveled in 5 days (260 miles) by the number of days (5). This gives us an average of 52 miles per day.

The given expression is a product of two binomials, (4a + 3b + 9c - 5d) and (5x - 8y). To find the number of terms in the product, we need to multiply the number of terms in each binomial. The first binomial has 4 terms (4a, 3b, 9c, -5d) and the second binomial has 2 terms (5x, -8y). Multiplying these two numbers gives us 6, which means there are 6 terms in the given expression.

The pattern in the given equations is that whenever one of the variables is 0, the result is always 0. This is because any number multiplied by 0 is always 0. Therefore, in the equation 0 x n = 0, no matter what value n takes, the result will always be 0.

The given expression involves addition, subtraction, and exponentiation. To solve it, we start by calculating the value inside the parentheses, which is 5 - 2 = 3. Then, we square this value, obtaining 3² = 9. Next, we add 7 to 9, resulting in 7 + 9 = 16. Finally, we subtract 2 from 16, giving us 16 - 2 = 14. Therefore, the correct answer is 14.

In the given equation, (x - 10)/2 = 4, we need to solve for x. To isolate x, we can multiply both sides of the equation by 2 to get rid of the denominator. This gives us x - 10 = 8. Adding 10 to both sides, we have x = 18. Therefore, the correct answer is x = 18.

The given expression follows the order of operations, which states that multiplication should be performed before addition. Therefore, the multiplication of 6 and 2 should be done first, resulting in 12. Then, the addition of 3 and 12 should be done, resulting in a final answer of 15.

The expression (4a + 3b + 9c - 5d) (5x - 8y) represents the multiplication of two binomials. When multiplying two binomials, the result is a quadratic expression. In this case, the expression has two terms, which means there are two factors. Therefore, the correct answer is 2.

The two numbers that have the absolute value of 16 are 16 and -16. Absolute value is a mathematical function that returns the positive value of a number, regardless of its sign. In this case, both 16 and -16 have a positive absolute value of 16, making them the correct answer.

The number (-1/3) is a rational number because it can be expressed as a fraction, where the numerator (-1) and the denominator (3) are both integers. Rational numbers include all integers and fractions, which can be written as a ratio of two integers.

Since 1/5 of the students are out-of-state transfers, this means that 4/5 of the students are Maryland residents. To find the number of Maryland residents, we can multiply 4/5 by the total number of students enrolled. Therefore, 4/5 * 23,000 = 18,400.

The number 0 belongs to the set of whole numbers because it is a non-negative integer. It also belongs to the set of integers because it can be expressed as a fraction with a denominator of 1. Additionally, 0 is a rational number because it can be expressed as the ratio of two integers.