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
\[
-9.
\]
\[
-(−3)^2.
\]
First, calculate \((-3)^2\):
\[
(-3)^2 = 9.
\]
Now, apply the negative sign in front:
\[
-(−3)^2 = -9.
\]
So, the simplified denominator is
\[
-9.
\]
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:
\[
10.
\]
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.
- \(2.5x\) 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.**
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.
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.**
Responses:3, 0.4,0.4 and 3,−7
- **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.**
Responses:3(x+4)/2, x/8, 3(x+4), 2
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).**