Consider the following expression: 4+(−6)⋅2/−(−3)2. What is the simplified denominator?

Answer 1

Let's focus on the denominator of the expression given:

\[ -(−3)^2. \]

First, calculate \((-3)^2\):

\[ (-3)^2 = 9. \]

Now, apply the negative sign in front:

\[ -(−3)^2 = -9. \]

So, the simplified denominator is

\[ -9. \]

Answer 2

Consider the expression [15+(−5)]+62 . What is the result of the first simplification that would need to take place, according to the order of operations?

Answer 3

According to the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), we need to simplify any expressions inside parentheses first.

In the expression \([15 + (-5)] + 62\), the first operation to simplify is the calculation inside the brackets:

\[ 15 + (-5) \]

Calculating this gives:

\[ 15 - 5 = 10. \]

So, the result of the first simplification is:

\[ 10. \]

Answer 4

julio and Ashley went to the drive-in theater. They paid an entry fee for the car and individual entry fees for themselves. Their total cost can be modeled by the expression 2.5x+10 . Which of the following answer choices accurately interprets a part of the algebraic expression?
Responses:The entry fee for the car was $12.50.
Each individual entry fee was $10.00.
The entry fee for the car was $10.00.
The entry fee for the car was $2.50.

Answer 5

In the expression \(2.5x + 10\):

• \(2.5x\) represents the individual entry fees for Julio and Ashley.
• The \(10\) represents the entry fee for the car.

To interpret this in terms of the options provided:

1. The entry fee for the car was $12.50. (Incorrect)
2. Each individual entry fee was $10.00. (Incorrect)
3. The entry fee for the car was $10.00. (Correct)
4. The entry fee for the car was $2.50. (Incorrect)

Therefore, the correct interpretation is:

The entry fee for the car was $10.00.

Answer 6

Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point)
Responses: 8, −3, 2, and 9 are constants.
There are four variables.
8 is the only factor of 8x.
8, −3, 2, and 9 are coefficients.

Answer 7

Let's analyze the equation \( 8x - 3y = 2x + 9y \).

In this equation:

• \(8\) is the coefficient of \(x\).
• \(-3\) is the coefficient of \(y\).
• \(2\) is the coefficient of \(x\) on the right side of the equation.
• \(9\) is the coefficient of \(y\) on the right side of the equation.

From this, we can evaluate the provided statements:

1. 8, −3, 2, and 9 are constants. (Incorrect) - These are coefficients, not constants.
2. There are four variables. (Incorrect) - The variables are \(x\) and \(y\); there are only two variables.
3. 8 is the only factor of 8x. (Incorrect) - While 8 is a coefficient, it is not the only factor that could apply to \(8x\).
4. 8, −3, 2, and 9 are coefficients. (Correct) - This is true as they are the numerical factors of the variables present in the equation.

Thus, the correct statement is:

8, −3, 2, and 9 are coefficients.

Answer 8

an equation can be broken down into expressions, terms, variables, constants, and coefficients. In the equation 0.4−7x=3 , what is/are the constant(s) in the equation?(1 point)
Responses:3, 0.4,0.4 and 3,−7

Answer 9

In the equation \(0.4 - 7x = 3\), we can identify the components as follows:

• Constants are fixed values that do not change. In this equation, both \(0.4\) and \(3\) are constants.
• Terms consist of constants, coefficients, and variables. In this case, the term \(-7x\) has a coefficient of \(-7\) and the variable \(x\).

Now, let's evaluate the provided options regarding the constants:

1. 3 - This is a constant. (Correct)
2. 0.4 - This is also a constant. (Correct)
3. 0.4 and 3 - Both are constants. (Correct)
4. −7 - This is a coefficient, not a constant. (Incorrect)

Thus, the correct answer is:

0.4 and 3.

Answer 10

Use the grouping symbols to interpret the following equation: x8=3(x+4)/2 . Which expression in the equation represents a product?(1 point)
Responses:3(x+4)/2, x/8, 3(x+4), 2

Answer 11

Let's analyze the equation \( x/8 = \frac{3(x + 4)}{2} \) to identify the expressions that represent a product.

A product refers to the result of multiplying two or more factors. In the equation:

1. \( \frac{3(x + 4)}{2} \): This expression involves multiplication, as it can be written as \( \frac{3 \cdot (x + 4)}{2} \). However, since it is divided by 2, it is technically not just a product.
2. \( \frac{x}{8} \): This expression is a single term that involves division and does not show any multiplication.
3. \( 3(x + 4) \): This expression clearly shows multiplication (3 times the quantity \(x + 4\)). This is a product.
4. \( 2 \): This is just a constant, not a product.

Thus, the expression in the equation that represents a product is:

3(x + 4).