Question

Add 5 (0.5 k - 1) + 2 ( 0.4 - k + )

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

It seems like there might be a typo in the second term of the expression. The plus sign at the end of the second term "( 0.4 - k + )" seems out of place. Assuming the plus sign is a typo and should not be there, let's simplify the expression without it:

Add 5(0.5k - 1) + 2(0.4 - k).

First, distribute the coefficients (5 and 2) across the terms in the parentheses:

5 * 0.5k - 5 * 1 + 2 * 0.4 - 2 * k

Now multiply:

(5 * 0.5)k - (5 * 1) + (2 * 0.4) - (2 * k)
2.5k - 5 + 0.8 - 2k

Combine like terms:

(2.5k - 2k) - 5 + 0.8
0.5k - 5 + 0.8

Now combine the constants:

0.5k - (5 - 0.8)
0.5k - 4.2

So, the simplified expression is:

0.5k - 4.2

Answer 2

Subtract 1/2(z+4)-3(1/4z+1) Use fraction in final form

Answer 3

[AI-generated answer — Bot GPT-4 Turbo]

Subtract \( \frac{1}{2}(z+4) \) - \( 3 \left( \frac{1}{4}z + 1 \right) \):

First, distribute the fractions across the terms in the parentheses:

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

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

Now multiply:

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

Combine like terms:

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

To combine the z terms, convert the first fraction to have a denominator of 4 to match the second fraction:

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

Now combine the fractions:

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

This is the final expression, with the z term represented as a fraction:

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

Answer 4

English please

Answer 5

[AI-generated answer — Bot GPT-4 Turbo]

Certainly! Let's perform the subtraction step by step in plain English.

We have the expression:

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

First, we need to distribute, which means applying the fraction in front of the parentheses to each term inside:

\( \frac{1}{2} \) times z gives us \( \frac{1}{2}z \).

\( \frac{1}{2} \) times 4 gives us \( \frac{1}{2} \times 4 \), which simplifies to 2.

Now we'll do the same thing for the second set of parentheses:

3 times \( \frac{1}{4}z \) gives us \( 3 \times \frac{1}{4}z \). The 3 multiplies with \( \frac{1}{4} \), giving us \( \frac{3}{4}z \).

3 times 1 is simply 3.

Now we have all the parts we need to put together:

\( \frac{1}{2}z + 2 \) and \( -\frac{3}{4}z - 3 \).

Next, we combine like terms, which means grouping the terms with z together and the constant terms together:

\( \frac{1}{2}z - \frac{3}{4}z \) and \( 2 - 3 \).

To subtract the z terms, we need a common denominator, which is 4 in this case:

\( \frac{2}{4}z - \frac{3}{4}z \) gives us \( -\frac{1}{4}z \).

2 minus 3 simply gives us -1.

Now we combine the results:

\( -\frac{1}{4}z - 1 \).

So, our final answer in plain English is:

"Negative one quarter z minus one."

Answer 6

[AI-generated answer — Explain Bot]

To simplify the given expression, follow these steps:

Step 1: Distribute the numbers in each group of parentheses to the terms inside.

5(0.5k - 1) + 2(0.4 - k)

= 5 * 0.5k + 5 * (-1) + 2 * 0.4 - 2 * k

= 2.5k - 5 + 0.8 - 2k

Step 2: Combine like terms.

Combine the terms with 'k' (coefficients of k) and the terms without 'k' (constant terms).

2.5k - 2k - 5 + 0.8

= (2.5k - 2k) + (-5 + 0.8)

= 0.5k - 4.2

So, the simplified expression is 0.5k - 4.2.