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add:%205(0.5k%E2%88%921)+2(0.4%E2%88%92k)

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To add the two expressions you provided, we need to carefully handle the exponential terms and organize the expression. The terms appear to be:

  1. \( 5(0.5k^{-1}) \)
  2. \( 2(0.4e^{-k}) \)

Let's simplify each term step by step:

  1. The first term: \[ 5(0.5k^{-1}) = \frac{5 \times 0.5}{k} = \frac{2.5}{k} \]

  2. The second term: \[ 2(0.4e^{-k}) = 0.8e^{-k} \]

Now, we can write the original expression as: \[ \frac{2.5}{k} + 0.8e^{-k} \]

This is the result of your expression. If you would like to perform further operations or simplifications, or if this was not what you intended, please clarify!

The answer has to be in a decimal form

To express the combined result of the terms in decimal form, we have:

\[ \frac{2.5}{k} + 0.8e^{-k} \]

This expression cannot be simplified further into a single decimal number, as it includes a variable \( k \). However, we can express the terms in decimal format as they currently stand, which are:

  1. For \( \frac{2.5}{k} \):

    • This value will depend on the specific numeric value of \( k \).

  2. For \( 0.8e^{-k} \):

    • This also depends on the specific numeric value of \( k \) since \( e^{-k} \) is an exponential function.

If you have a specific value for \( k \) that you want to substitute into the expression, please provide that, and I can compute the decimal value for you.

If you are looking for a more general grasp of how this behaves with different values of \( k \), here’s an example of what the calculation would look like with a hypothetical value of \( k = 1 \):

  1. Calculate \( \frac{2.5}{1} + 0.8e^{-1} \):
    • \( \frac{2.5}{1} = 2.5 \)
    • \( e^{-1} \approx 0.367879 \)
    • \( 0.8e^{-1} \approx 0.8 \times 0.367879 \approx 0.2943032 \)

Combining these: \[ 2.5 + 0.2943032 \approx 2.7943032 \]

If you have a specific value for \( k \), I can calculate that value directly.

I think this is way more complicated than it has to be it only says to add: 5 (0.5 - k) + 2 (0.4 - k) and then put the answer in a decimal form

I apologize for the misunderstanding! Let's simplify the expression you've given step by step.

You want to add:

\[ 5(0.5 - k) + 2(0.4 - k) \]

Let's distribute the coefficients in each term:

  1. For the first term: \[ 5(0.5 - k) = 5 \times 0.5 - 5 \times k = 2.5 - 5k \]

  2. For the second term: \[ 2(0.4 - k) = 2 \times 0.4 - 2 \times k = 0.8 - 2k \]

Now we can combine these results:

\[ (2.5 - 5k) + (0.8 - 2k) \]

Combine the constant terms and the \( k \) terms:

  • Constant terms: \[ 2.5 + 0.8 = 3.3 \]

  • \( k \) terms: \[ -5k - 2k = -7k \]

Putting it all together, the expression simplifies to:

\[ 3.3 - 7k \]

This is the final expression in decimal form. If you have a specific value for \( k \), you could substitute it in to get a numerical result. Otherwise, this is the simplified form. Thank you for your patience!

Sorry the expression is actually: 5 (0.5 - 1) + 2 (0.4 - k)

No problem! Let's simplify the corrected expression:

\[ 5(0.5 - 1) + 2(0.4 - k) \]

Step 1: Simplify \( 5(0.5 - 1) \)

\[ 0.5 - 1 = -0.5 \]

Now multiply by 5:

\[ 5(-0.5) = -2.5 \]

Step 2: Simplify \( 2(0.4 - k) \)

Distributing 2:

\[ 2(0.4) - 2(k) = 0.8 - 2k \]

Step 3: Combine the results

Now combine the two parts together:

\[ -2.5 + (0.8 - 2k) \]

Simplifying this gives you:

\[ -2.5 + 0.8 - 2k = -1.7 - 2k \]

Final Result

Therefore, the simplified expression is:

\[ -1.7 - 2k \]

This is expressed in decimal form. If you need further assistance or want to evaluate it for a specific value of \( k \), please let me know!

Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form

To subtract the given expression \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \), let's simplify it step by step.

Step 1: Distribute the terms

  1. Distributing \( \frac{1}{2}(z + 4) \):

\[ \frac{1}{2}z + \frac{1}{2} \cdot 4 = \frac{1}{2}z + 2 \]

  1. Distributing \( 3\left(\frac{1}{4}z + 1\right) \):

\[ 3\left(\frac{1}{4}z\right) + 3(1) = \frac{3}{4}z + 3 \]

Step 2: Write the full expression

Now, substituting these distributed results back into the original expression gives us:

\[ \left( \frac{1}{2}z + 2 \right) - \left( \frac{3}{4}z + 3 \right) \]

Step 3: Combine like terms

Now we can rewrite this as:

\[ \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \]

Combining the \( z \) terms and the constant terms:

  1. Combine the \( z \) terms:

    To combine \( \frac{1}{2}z \) and \( -\frac{3}{4}z \), we need a common denominator.

    The denominator for \( \frac{1}{2} \) is 2 and for \( \frac{3}{4} \) is 4. The least common multiple of 2 and 4 is 4.

    • Rewrite \( \frac{1}{2}z \) as \( \frac{2}{4}z \):

    \[ \frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z \]

  2. Combine the constant terms:

    \[ 2 - 3 = -1 \]

Final Result

Putting it all together, we have:

\[ -\frac{1}{4}z - 1 \]

Thus, the final answer is:

\[ -\frac{1}{4}z - 1 \]

subtract: (3b - 2c) - (6c+2b) - (b+c)

To subtract the expression \( (3b - 2c) - (6c + 2b) - (b + c) \), we will proceed step by step.

Step 1: Distribute the negative sign

First, we need to distribute the negative signs across each of the terms inside the parentheses:

\[ (3b - 2c) - (6c + 2b) - (b + c) = (3b - 2c) - 6c - 2b - b - c \]

Step 2: Combine like terms

Next, we will combine the \( b \) terms and the \( c \) terms separately:

  1. Combine the \( b \) terms:

    • The \( b \) terms are \( 3b \), \( -2b \), and \( -b \): \[ 3b - 2b - b = 3b - 2b - 1b = (3 - 2 - 1)b = 0b = 0 \]

  2. Combine the \( c \) terms:

    • The \( c \) terms are \( -2c \), \( -6c \), and \( -c \): \[ -2c - 6c - c = (-2 - 6 - 1)c = -9c \]

Step 3: Write the final result

Now combine the results:

\[ 0b - 9c = -9c \]

Final Result

Thus, the final result of the expression is:

\[ -9c \]