Question

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?
Answer
Thank you :D, can you explain why its 5 * (9 + y)
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Know your properties
Which property is illustrated by the following statement? 6x (yz) = 6 (xyz)
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Integer Operations & PEMDAS
What is the simplified form of the following expression? 5 [33 / (6^2 - 5^2) + 2]
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Evaluate Expressions
Evaluate: a/c + b^2 d, for a = 10, b = 3, c = 5, and d = 2.
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Is the product rational or irrational?: 2.84 * 7.1 (The one has a line on top of it.)
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simplify the following expression: 1/5 (15 + 10x)
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Simplify the following expression: 1 over 5 (15 + 10x)
Answered by GPT 3.5
The algebraic expression for the given word phrase is 5 * (9 + y).
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
The product 2.84 * 7.1 is a rational number.

A rational number can be expressed as a fraction where the numerator and denominator are both integers. Although the numbers 2.84 and 7.1 are decimal numbers, they can be written as fractions in their simplest form.

2.84 can be written as 284/100, which simplifies to 71/25.
7.1 can be written as 71/10.

When we multiply these fractions, we get:

(71/25) * (71/10) = 5041/250

The resulting fraction 5041/250 is a ratio of two integers, and therefore it is a rational number.
Answered by GPT 3.5
To simplify the expression 1/5 (15 + 10x), we can distribute the 1/5 to each term within the parentheses:

1/5 (15 + 10x) = 1/5 * 15 + 1/5 * 10x

This simplifies to:

3 + 2x

Therefore, the simplified form of the expression 1/5 (15 + 10x) is 3 + 2x.
Answered by GPT 3.5
To simplify the expression 1 over 5 (15 + 10x), we can still distribute the 1/5 to each term inside the parentheses:

1/5 (15 + 10x) = 15/5 + 10x/5

Simplifying the fractions, we have:

3 + 2x/5

Therefore, the simplified form of the expression 1 over 5 (15 + 10x) is 3 + 2x/5.