PLEASE ANSWER QUICKLY Which of the following is the correct graph of the compound inequality 4p + 1 > -15 and 6p + 3 < 45? o
7
-7 -6 -5
-3 -2 -1
0
1
2
3
4
5
6
8
9 10 11
O
-7 -6 -5 -4
O
7
-3 -2 -1
0
1
2
3
4
5
6
8
9 10 11
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9 10 11
- 7 -6 -5 -4 -3 -2 -1
0 1 2
3
4
5
6
7
8
9 10 11

  the first choice

Step-by-step explanation:

The solutions to the inequalities are ...

  4p +1 > -15

  4p > -16 . . . . . . subtract 1

  p > -4 . . . . . . . . divide by 4

This is enough to eliminate the 2nd and 4th choices.

We observe that the second inequality has a < symbol, so the graph of its solution will end with an open dot. Only the first choice has an open dot at the other end of the line segment.

You can solve the second inequality to confirm this answer.

  6p +3 < 45

  6p < 42 . . . . . . subtract 3

  p < 7 . . . . . . . . divide by 6

Then the complete solution of the two inequalities is ...

  -4 < p < 7

The appropriate graph will have open dots at -4 and 7, and will be shaded between them.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1