Translate words and mathematical expressions
What is the algebraic expression for the following word phrase: the product of 5 and the sum of 9 and y?
The algebraic expression for the given word phrase is 5 * (9 + y).
Thank you :D, can you explain why its 5 * (9 + y)
Certainly! In the given word phrase, "the product of 5 and the sum of 9 and y", we have two operations mentioned: product and sum.
The phrase "the product of 5 and the sum of 9 and y" implies that we need to multiply two values. The first value is 5, and the second value is the sum of 9 and y.
The sum of 9 and y can be represented as (9 + y). Therefore, the phrase "the product of 5 and the sum of 9 and y" can be translated to the algebraic expression 5 * (9 + y), where 5 is multiplied by the sum of 9 and y.
Know your properties
Which property is illustrated by the following statement? 6x (yz) = 6 (xyz)
The property illustrated by the statement 6x(yz) = 6(xyz) is the associative property of multiplication. This property states that when multiplying three or more numbers, the grouping of the factors does not affect the product. In other words, you can multiply the factors in any order or group them differently, and the product will remain the same. In this case, the factors are 6, x, y, and z, and they are grouped differently but still result in the same product.
Integer Operations & PEMDAS
What is the simplified form of the following expression? 5 [33 / (6^2 - 5^2) + 2]
To simplify the expression 5 [33 / (6^2 - 5^2) + 2], we can follow the order of operations, known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
First, let's solve the expressions within the parentheses:
6^2 equals 36
5^2 equals 25
So, the expression becomes: 5 [33 / (36 - 25) + 2]
Next, we simplify the subtraction inside the parentheses:
36 - 25 equals 11
Now, the expression becomes: 5 [33 / 11 + 2]
Next, we perform the division:
33 divided by 11 equals 3
The expression becomes: 5 [3 + 2]
Next, we do the addition inside the brackets:
3 + 2 equals 5
So, the expression simplifies to: 5 * 5
Finally, we perform the multiplication:
5 multiplied by 5 equals 25
Therefore, the simplified form of the expression 5 [33 / (6^2 - 5^2) + 2] is 25.
Evaluate Expressions
Evaluate: a/c + b^2 d, for a = 10, b = 3, c = 5, and d = 2.
To evaluate the expression a/c + b^2 d with a = 10, b = 3, c = 5, and d = 2, we substitute the given values into the expression and perform the calculations.
a/c + b^2 d = 10/5 + 3^2 * 2
Let's simplify each term step by step:
10 divided by 5 is 2.
So the expression becomes: 2 + 3^2 * 2
Next, we evaluate 3 squared:
3^2 equals 9.
The expression becomes: 2 + 9 * 2
Now, we multiply:
9 multiplied by 2 equals 18.
So the expression becomes: 2 + 18
Finally, we add the remaining terms:
2 + 18 equals 20.
Therefore, the value of the expression a/c + b^2 d with a = 10, b = 3, c = 5, and d = 2 is 20.