Graphing Linear Inequalities and Systems of Linear Inequalities in Real-World Situations - Item 50373Question 2 of 7
A coffee shop orders at most $ 3 , 500 worth of coffee and tea. The shop needs to make a profit of at least $ 1 , 900 on the order. The possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea:

6 c + 13 t ≤ 3 , 500
3 . 50 c + 4 t ≥ 1 , 900

Which graph's shaded region represents the possible combinations of coffee and tea for this order?
Material Cost per
Pound Profit per
Pound
Coffee $6.00 $3.50
Tea $13.00 $4.00

CLEAR CHECK

A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space above both lines is shaded.

A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space between the 2 lines after they cross near the 500 mark is shaded.

A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space between the 2 lines between the Y-axis and where they cross near the 500 mark is shaded.

A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space below both lines is shaded.
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To draw the 6th term, represent it visually within the context of the pattern or sequence from which it is derived.

To draw the 6th term, we need to understand the context or pattern from which the term is derived.

Drawing the term usually involves representing the elements or characteristics of the pattern in a visual form.

Without specific information about the pattern, we can provide a general approach to drawing the 6th term.

Identify the Pattern:

Determine the sequence or pattern from which the 6th term is derived.

It could be a numerical sequence, a geometric pattern, or any other pattern.

For example, if the pattern is a number sequence of multiples of 3, the first few terms would be 3, 6, 9, 12, 15, and so on.

Visualize the Pattern: Based on the identified pattern, visualize how the elements change or progress from term to term.

This could involve drawing a diagram, a graph, or any visual representation that captures the pattern.

Consider using a coordinate grid, a number line, or any other suitable visual aid.

Locate the 6th Term:

Use the information from the pattern and the visualization to determine the specific position or value of the 6th term.

In our example of multiples of 3, the 6th term would be 18.

Draw the 6th Term: Finally, represent the 6th term in your chosen visual form.

This could mean marking the position on a number line, plotting a point on a graph, or incorporating the value into a diagram.

Note that the specific method of drawing the 6th term will depend on the nature of the pattern and the context in which it is given.

Providing more details about the pattern would allow for a more accurate and specific visual representation of the 6th term.

For similar question on sequence.

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The correct statement about rectangles is:

1. All rectangles are parallelograms.

2. Parallelograms have exactly 1 pair of parallel sides.

3. So, all rectangles have exactly 1 pair of parallel sides.

A rectangle is a type of parallelogram that has additional properties. By definition, a rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are parallel. Since all four sides of a rectangle are right angles, it follows that a rectangle has exactly 1 pair of parallel sides.

Option 1 states that only some rectangles are parallelograms, which is incorrect. All rectangles are parallelograms because they have opposite sides that are parallel.

Option 2 states that parallelograms have 2 pairs of parallel sides, which is also incorrect. Parallelograms have exactly 2 pairs of parallel sides, not 4. A rectangle is a special type of parallelogram that has additional properties such as all angles being right angles.

Option 3 states that only some rectangles have 2 pairs of parallel sides, which is incorrect. All rectangles have exactly 1 pair of parallel sides, not 2. Having 2 pairs of parallel sides would make a shape a parallelogram, not a rectangle.

Therefore, the correct statement is that all rectangles are parallelograms and have exactly 1 pair of parallel sides. 1,2,3 are correct.

For more suhc questions on rectangles visit:

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