Question

Which ordered pairs make both inequalities true? Select two options. y < 5x + 2 y > One-halfx + 1 On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 2, 0) and (0, 1). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 3) and (0, 2). Everything to the right of the line is shaded. (–1, 3) (0, 2) (1, 2) (2, –1) (2, 2)

Answer 1

Which line is a direct quotation from an external source?

“This is quite clearly mid-range pottery, simple earthenware of a sort that many quite modest British households were then able to afford.”

“But the owners of this particular set must have had serious social aspirations, because all three pieces have been decorated with a drape of lacy hallmarked silver.”

“The historian Celina Fox explains that tea-time had become a very smart event . . .”

“In the 1840s the Duchess of Bedford introduces the ritual of afternoon tea, because by this time dinner had become so late, seven-thirty to eight o’clock . . .”

Explanation:

Which line is a direct quotation from an external source?

“This is quite clearly mid-range pottery, simple earthenware of a sort that many quite modest British households were then able to afford.”

“But the owners of this particular set must have had serious social aspirations, because all three pieces have been decorated with a drape of lacy hallmarked silver.” Which line is a direct quotation from an external source?

“This is quite clearly mid-range pottery, simple earthenware of a sort that many quite modest British households were then able to afford.”

“But the owners of this particular set must have had serious social aspirations, because all three pieces have been decorated with a drape of lacy hallmarked silver.”

“The historian Celina Fox explains that tea-time had become a very smart event . . .”

“In the 1840s the Duchess of Bedford introduces the ritual of afternoon tea, because by this time dinner had become so late, seven-thirty to eight o’clock . . .”

“The historian Celina Fox explains that tea-time had become a very smart event . . .”

“In the 1840s the Duchess of Bedford introduces the ritual of afternoon tea, because by this time dinner had become so late, seven-thirty to eight o’clock . . .”

Answer 2

3. (1, 2) and 4. (2, -1).

Explanation:

To determine which ordered pairs make both inequalities true, we need to find the points that satisfy both y < 5x + 2 and y > (1/2)x + 1.

Let's consider each option:

1. (–1, 3):

- For y < 5x + 2: 3 < 5(-1) + 2 → 3 < -3 + 2 → 3 < -1 (False)

- For y > (1/2)x + 1: 3 > (1/2)(-1) + 1 → 3 > -1/2 + 1 → 3 > 1/2 (True)

2. (0, 2):

- For y < 5x + 2: 2 < 5(0) + 2 → 2 < 2 (False)

- For y > (1/2)x + 1: 2 > (1/2)(0) + 1 → 2 > 1 (True)

3. (1, 2):

- For y < 5x + 2: 2 < 5(1) + 2 → 2 < 5 + 2 → 2 < 7 (True)

- For y > (1/2)x + 1: 2 > (1/2)(1) + 1 → 2 > 1/2 + 1 → 2 > 3/2 (True)

4. (2, –1):

- For y < 5x + 2: -1 < 5(2) + 2 → -1 < 10 + 2 → -1 < 12 (True)

- For y > (1/2)x + 1: -1 > (1/2)(2) + 1 → -1 > 1 + 1 → -1 > 2 (False)

5. (2, 2):

- For y < 5x + 2: 2 < 5(2) + 2 → 2 < 10 + 2 → 2 < 12 (True)

- For y > (1/2)x + 1: 2 > (1/2)(2) + 1 → 2 > 1 + 1 → 2 > 2 (False)

From the options provided, the ordered pairs that make both inequalities true are:

- (1, 2)

- (2, -1)