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−15+4/5(15e−10)−10e

.(1 point)
Responses

2e+23
2 e plus 23

−2e+23
negative 2 e plus 23

−2e−23
negative 2 e minus 23

2e−23
2 e minus 23

5 answers

To simplify the expression \(-15 + \frac{4}{5}(15e^{-10}) - 10e\), we can do the following steps:

  1. Calculate \(\frac{4}{5}(15e^{-10})\): \[ \frac{4}{5}(15e^{-10}) = \frac{4 \times 15}{5} e^{-10} = 12e^{-10} \]

  2. Now substitute back into the expression: \[ -15 + 12e^{-10} - 10e \]

Since we cannot combine these terms further because they are not like terms (the first term is a constant and the others involve \(e\)), we can write it as: \[ -15 + 12e^{-10} - 10e \]

However, none of the given responses seem like a direct match for this result.

Let's consider if any of the provided answers match under certain circumstances for specific values of \(e\) or if there is any other interpretation to be made, but based on simple arithmetic, the closest nature of our expression does not exactly match any response.

If you need further help or clarification, feel free to ask!

Which answer option is closest to the right answer?

To evaluate the expression \(-15 + 12e^{-10} - 10e\) and find which response option is closest, we need to break down the possible choices:

  1. Given Options:

    • \(2e^{+23}\)
    • \(-2e^{+23}\)
    • \(-2e^{-23}\)
    • \(2e^{-23}\)

  2. Understanding Terms:

    • The expression \(12e^{-10}\) is a small positive number since \(e^{-10}\) is a small positive value (a little greater than zero).
    • The term \(-10e\) is a larger negative number since \(e\) (approximately 2.718) multiplied by -10 becomes a significant negative value.
    • The constant \(-15\) is a negative number that heavily weighs into the sum.

  3. Estimating the Overall Expression:

    • Since \(-10e \approx -27.18\) (using \(e \approx 2.718\)), and \(-15\) adds to this negative contribution: \[ -10e - 15 \approx -27.18 - 15 = -42.18 \]
    • This is roughly in the neighborhood of -42, which is significantly low and far from the positive responses.

The exponential terms \(12e^{-10}\) is positive but negligible when compared to \(-10e - 15\). Therefore, we conclude:

The overall value of the expression is negative and closer to zero than it is to any large positive number (the responses with \(e^{+23}\)).

Hence, the most suitable choice out of the given options in terms of being negative and consistent with our findings would be:

\(-2e^{-23}\)

Note: This option reflects a small negative value, although it may not mathematically add up perfectly from the derived expression; it's the only term indicating a negative value aligned with our deduction. The other options imply a much larger magnitude that does not represent the result we calculated.

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:

    • 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 common factors are: \(1, 2, 3, 4, 6, 12\)
    • The GCF is \(12\).

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

Thus, the expression \(48y + 36z\) factored using the GCF is:

\[ 12(4y + 3z) \]

Correct Response: \[ 12(4y + 3z) \]

This is the first option in the list you provided.