Which ordered pairs are solutions to the inequality 2y−x≤−6 ?

Response

The first diagram displays angles 1 and 2 as vertical angles.

Clarification

In all four diagrams, the initial one illustrates the vertically opposite angles.

Angles 1 and 2 are classified as vertically opposite because they face each other.

These angles maintain equal measurement when two lines intersect, resulting in four angles where two pairs of vertically opposite angles are formed.

In contrast, all other figures depict angles 1 and 2 as adjacent angles.

Answer:

a. i) Please refer to the attached graph representing the equation $10·x + $12·y = $300

ii) The intercepts indicate the maximum number of short-sleeve (at the x-intercept) and long-sleeve shirts (at the y-intercept) that can be ordered.

Step-by-step explanation:

The details provided are as follows:

Cost of each short-sleeve shirt = $10

Cost of each long-sleeve shirt = $12

Total budget available = $300

The equation for total spending is given by $10·x + $12·y = $300

Where;

x = Number of short-sleeved shirts

y = Number of long-sleeved shirts

Rearranging the equation into slope-intercept form, we have:

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Attached is the graph produced using Microsoft Excel

The coordinates that can be used for graph plotting are as follows:

x, y

(0, 25)

(5, 20.83)

(15, 12.5)

(20, 8.33)

(25, 4.17)

(30, 0)

The x-intercept denotes the quantity of short-sleeve shirts purchasable with a $300 budget, while the y-intercept signifies the quantity of long-sleeve shirts achievable under the same budget.