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Which of the following statements about the equation 2x−5=8+x

is correct?

Statement #1: There are two constants in the equation.

Statement #2: x does not have a coefficient.

Statement #3: There are two terms in the equation.

(1 point)
witch Statement #
is correct.

7 answers

Let's analyze each statement about the equation \(2x - 5 = 8 + x\):

  1. Statement #1: There are two constants in the equation.

    • The constants in the equation are \(-5\) and \(8\). So, this statement is correct.

  2. Statement #2: x does not have a coefficient.

    • In the term \(2x\), the coefficient of \(x\) is \(2\). In the term \(x\), it is understood to have a coefficient of \(1\). Therefore, this statement is incorrect.

  3. Statement #3: There are two terms in the equation.

    • The equation has more than two terms: \(2x\), \(-5\), \(8\), and \(x\). So, this statement is incorrect.

Based on the analysis, the correct statement is Statement #1.

Next one

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?(1 point)

To simplify the expression \([15 + (-5)] + 62\), we need to follow the order of operations, which dictates that we should perform operations inside parentheses first.

  1. Step 1: Evaluate the expression inside the parentheses: \(15 + (-5)\).
    • This simplifies to \(15 - 5 = 10\).

Now the expression becomes: \[10 + 62\]

Thus, the first simplification that needs to take place is calculating \(15 + (-5)\), which equals \(10\).

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

Let's analyze the expression \( 4 + (-6) \cdot 2 - (-3)^2 \).

To find the simplified denominator, we need to take a close look at all the operations, especially the one involving the powers and subtraction.

  1. Calculate \( (-3)^2 \):
    • The square of \(-3\) is \(9\).

Now substitute this back into the original expression:

\[ 4 + (-6) \cdot 2 - 9 \]

  1. Next, calculate \( (-6) \cdot 2 \):
    • This equals \(-12\).

Substituting that back in gives us:

\[ 4 - 12 - 9 \]

  1. Now we can simplify:

\[ 4 - 12 = -8 \] \[ -8 - 9 = -17 \]

If we are looking for a "denominator," and since there isn't a division present in the expression given, we may have misunderstood the reference to a "denominator."

However, if you are asking about the final result of the complete expression after simplifications, that result is \(-17\). If you meant something else by "simplified denominator," please clarify!

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

Let's analyze the expression \( 4 + (-6) \cdot 2 / -(-3)^2 \). We are specifically looking for the simplified denominator of the fraction.

  1. Calculate \( -(-3)^2 \):
    • First, calculate \((-3)^2\): \[ (-3)^2 = 9 \]
    • Now take the negative: \[ -9 \]

So, the denominator of the expression \( \frac{4 + (-6) \cdot 2}{-(-3)^2} \) simplifies to \(-9\).

Therefore, the simplified denominator is \(-9\).