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2 years ago

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics

1 answer:

timofeeve [1]2 years ago

4 0

Answer: Choice B

Open circle at 3. Shading to the right

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Work Shown:

3(8 - 4x) < 6(x - 5)

24 - 12x < 6x - 30

24 + 30 < 6x + 12x

54 < 18x

18x > 54

x > 54/18

x > 3

We use an open circle at 3 to indicate we don't include this endpoint as part of the solution. The solution set is everything larger than 3, so we shade to the right of this open circle.

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2 years ago

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2 years ago

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Answer:

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

Step-by-step explanation:

It is given that the snack shop makes 3 mixes of nuts in the following proportions.

Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.

Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.

Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.

they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.

We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.

Mix I Mix II Mix III

peanuts 6 5 3

cashews 2 3 4

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$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

The product of both matrices is

$AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

$AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}$

$AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}$

Therefore matrix AB gives the total number of lbs of each nut required to fill the order.

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3 years ago

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Answer:

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