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Consider the expression [15+(−5)]+6 /2

. What is the result of the first simplification that would need to take place, according to the order of operations?(1 point)

11 answers

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 first look for any operations inside parentheses.

In the expression \([15 + (-5)] + 6 / 2\), the first simplification takes place inside the parentheses:

\[ 15 + (-5) = 10 \]

Thus, the first simplification is \(15 + (-5)\).

Consider the following expression: 4+(−6)⋅2/−(−3)2
. What is the simplified denominator?(1 point)

To simplify the expression \( -(-3)^2 \), we first calculate \((-3)^2\):

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

Now, applying the negative sign in front, we have:

\[ -9 \]

Thus, the simplified denominator of the expression \(4 + (-6) \cdot 2 / -(-3)^2 \) is \(-9\).

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? (1 point)
Responses

The entry fee for the car was $10.00.
The entry fee for the car was $10.00.

The entry fee for the car was $12.50.
The entry fee for the car was $12.50.

The entry fee for the car was $2.50.
The entry fee for the car was $2.50.

Each individual entry fee was $10.00.

The expression \(2.5x + 10\) can be broken down as follows:

  • \(2.5x\): This part represents the individual entry fees for Julio and Ashley. If \(x\) represents the number of individuals (in this case, 2 for Julio and Ashley), then \(2.5\) would be the cost per individual.

  • \(10\): This part represents the entry fee for the car.

From this analysis, the correct interpretation is:

The entry fee for the car was $10.00.

Given the equation 8x−3y=2x+9y, which of the following statements is correct?(1 point)
Responses

8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.

There are four variables.
There are four variables.

8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.

8 is the only factor of 8x.

To analyze the equation \( 8x - 3y = 2x + 9y \):

  1. Constants: In the context of this equation, constants are numbers without variables. Here, 8, -3, 2, and 9 are not constants; they are coefficients (multipliers) of the variables \(x\) and \(y\).

  2. Variables: The variables in this equation are \(x\) and \(y\). Thus, there are only two variables.

  3. Coefficients: The terms 8, -3, 2, and 9 are indeed coefficients of the variables \(x\) and \(y\) in the equation.

  4. Factors: The statement about 8 being the only factor of \(8x\) is incorrect. The coefficient 8 is indeed a factor, but other factors could also be involved when considering the term \(8x\).

Considering this analysis, the correct statement is:

8, -3, 2, and 9 are coefficients.

Question
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

0.4 and 3

0.4 and 3

3
3

−7
negative 7

0.4

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

  • Constants are the values that do not change and are not multiplied by a variable. Here, the constants are \(0.4\) and \(3\).
  • The term \(-7x\) contains a coefficient of \(-7\) which is multiplied by the variable \(x\).

Given this breakdown, the correct answer regarding the constants in the equation is:

0.4 and 3.

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
Start Fraction 3 left parenthesis x plus 4 right parenthesis over 2 End Fraction

x8
Start Fraction x over 8 End Fraction

2
2

3(x+4)

In the equation \( x/8 = \frac{3(x+4)}{2} \), the expression that represents a product is any expression where two or more values are multiplied together.

Now, let's analyze the provided options:

  1. 3(x + 4)2: This notation is ambiguous but seems to imply \(3(x + 4)\) multiplied by \(2\), which suggests a product.

  2. \(x/8\): This is a division, not a product.

  3. 2: This is a constant, not a product.

  4. 3(x + 4): This is a clear product, as it represents the multiplication of \(3\) and the expression \((x + 4)\).

The correct answer that represents a product is:

3(x + 4).