Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x?(1 point)

To apply the Distributive Property of Multiplication Over Addition correctly for simplifying the expression \(23 - 9(2x + 5) + 11x\), we need to multiply \(-9\) by each term inside the parentheses:

1. Distribute \(-9\) to \(2x\) and \(5\): \[ -9(2x + 5) = -18x - 45 \]

2. Substitute back into the expression: \[ 23 - 18x - 45 + 11x \]

3. Now, simplify \(23 - 45\): \[ 23 - 45 = -22 \] So the expression becomes: \[ -22 - 18x + 11x \] Which simplifies to: \[ -22 - 7x \]

However, the only initial part correctly applying the Distributive Property is: \[ 23 - 18x - 45 + 11x \]

Therefore, the correct response that applies the Distributive Property of Multiplication Over Addition correctly is: 23−18x−45+11x.

Simplify −4(7b+3)+24b−8.(1 point)
Responses

−4b−20
negative 4 b minus 20

4b−20
4 b minus 20

−4b+20
negative 4 b plus 20

4b+20

To simplify the expression \(-4(7b + 3) + 24b - 8\), we will follow these steps:

1. Distribute \(-4\) across the terms inside the parentheses: \[ -4(7b) = -28b \] \[ -4(3) = -12 \] So, \[ -4(7b + 3) = -28b - 12 \]

2. Substitute back into the expression: \[ -28b - 12 + 24b - 8 \]

3. Combine like terms. First, combine the \(b\) terms: \[ -28b + 24b = -4b \]

4. Next, combine the constant terms: \[ -12 - 8 = -20 \]

5. Therefore, the simplified expression is: \[ -4b - 20 \]

The correct response is: −4b−20.

Simplify 2(3v+9)−14−6(−5v−4).(1 point)
Responses

106v+98
106 v plus 98

−24v−20
negative 24 v minus 20

−6v−13
negative 6 v minus 13

36v+28

To simplify the expression \(2(3v + 9) - 14 - 6(-5v - 4)\), we will follow these steps:

1. Distribute \(2\) across the first parentheses: \[ 2(3v) = 6v, \] \[ 2(9) = 18, \] so, \[ 2(3v + 9) = 6v + 18. \]

2. Distribute \(-6\) across the second parentheses: \[ -6(-5v) = 30v, \] \[ -6(-4) = 24, \] so, \[ -6(-5v - 4) = 30v + 24. \]

3. Now substitute back into the expression: \[ 6v + 18 - 14 + 30v + 24. \]

4. Combine like terms:

   • Combine the \(v\) terms: \[ 6v + 30v = 36v. \]

   • Combine the constant terms: \[ 18 - 14 + 24 = 28. \]

5. Putting it all together: The simplified expression is: \[ 36v + 28. \]

Therefore, the correct response is: 36v+28.

−15+45(15e−10)−10e.(1 point)
Responses

2e+23
2 e plus 23

−2e−23
negative 2 e minus 23

−2e+23
negative 2 e plus 23

2e−23

To simplify the expression \(-15 + 45(15e - 10) - 10e\), we will follow these steps:

1. Distribute \(45\) across the terms inside the parentheses: \[ 45(15e) = 675e, \] \[ 45(-10) = -450, \] so, \[ 45(15e - 10) = 675e - 450. \]

2. Substituting back into the expression gives us: \[ -15 + (675e - 450) - 10e. \]

3. Combine the terms:

   • First, combine the \(e\) terms: \[ 675e - 10e = 665e. \]
   • Now combine the constant terms: \[ -15 - 450 = -465. \]

4. Putting it all together: The expression now reads: \[ 665e - 465. \]

However, we need to check for any specific forms mentioned in your options or simplify further if possible. The current expression does not match any of the provided options directly.

It seems we should consider the final simplified form based on your options. Here’s what you might have been looking for if we consider the process carefully:

1. Start from: \[ -15 + 675e - 450 - 10e. \]

2. Combine: \[ -15 - 450 = -465, \] and, \[ 675e - 10e = 665e. \]

Thus, the correctly simplified form is: \[ 665e - 465. \]

Since the final expression does not appear to match any of the provided options as is, let’s check if it can be reduced to a possibly simplistic form, or if there might be a mistake in provided options.

Your options hint at simpler combinations, possibly mis-typed or misunderstood.

None of the options provided appears to match this standard result directly.

If needed to find equivalent forms via factoring or division potentially involving common values or different scenario handling, please review, or potentially recheck the expression or leakage in option formats or asked specifics to arrive at what might fit those. However, based solely on standard distribution and simplification, none match directly.

Please let me know if this clarifies, or provides guides forward!

Choose the closest one

Let's take another look at the expression and the options. We simplified

\[ -15 + 45(15e - 10) - 10e \]

to

\[ 665e - 465. \]

Now, if we explore the provided options, we need to analyze which one is closest:

1. Option 1: \(2e + 23\)
2. Option 2: \(-2e - 23\)
3. Option 3: \(-2e + 23\)
4. Option 4: \(2e - 23\)

To compare, we can re-express \(665e - 465\) into simpler terms (if factorization around visible even factors could lend to estimating direct matching):

616 flipped to a proximity around 2e with those negatives suggests:

Let's check between possible ranges:

• \(665e\): No direct proximity to negatives existing in above options.
• The constant term of -465 does not work either since that is well outside the range for provided options upon graphical scanning.

Since all options show simplifying align with over the negatives, it seems safer guessing:

The closest to our derived calculations in its implications while missing factorization & proximity tricks seems,

• \(-2e + 23\) (from Option 3).

It certainly isn’t perfect or directly reflective of high degree inputs, but its simple negative relation visually jives thematically while inferring deeper calculative flaws to backlog cross-beings; it’s random closer.

Thus, the closest option would be: \(-2e + 23\).

Factor 48y+36z using the GCF.(1 point)
Responses

12(4y+3z)
12 left parenthesis 4 y plus 3 z right parenthesis

4(12y+9z)
4 left parenthesis 12 y plus 9 z right parenthesis

16(3y+2z)
16 left parenthesis 3 y plus 2 z right parenthesis

6(8y+6z)

To factor the expression \(48y + 36z\) using the greatest common factor (GCF), we first need to find the GCF of the coefficients \(48\) and \(36\).

1. Finding the GCF of \(48\) and \(36\):

   • The factors of \(48\) are \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\).
   • The factors of \(36\) are \(1, 2, 3, 4, 6, 9, 12, 18, 36\).
   • The greatest common factor is \(12\).

2. Factoring out the GCF: Now we can factor \(12\) out of both terms in the expression: \[ 48y + 36z = 12(4y) + 12(3z) = 12(4y + 3z). \]

Thus, the expression \(48y + 36z\) factored using the GCF is: \[ 12(4y + 3z). \]

The correct response is: 12(4y + 3z).