Is (2,12) a solution to the given system?
y>2x+4
y<3x+7
Yes
No
What is the solution of the system of equations shown below?
2x+2y=10
5x-2y=4
(-2,7)
(2,7)
(2,3)
(3,2)
The point (-3,11) is a solution of which of the following systems?
y≥x-2
2x+y≤5
y>x+8
3x+y>2
y>-x+8
2x+3y≥7
y≤-3x+1
x-y≥-15
Melissa keeps a jar for holding change. The jar holds 21 coins. All of the coins are quarters and nickels. The total amount in the jar is $3.85. How many quarters are in the jar?
3
7
14
21
Steve is taking a 50 question test and he answered all questions. He earned 3 points for each question he answered correctly. He lost 1 point for each question he answered incorrectly. His final test score was 102 points. The system of equations below describes the relationship between the number of questions he answered correctly (x) and the number of questions he answered incorrectly (y).
x+y=50
3x-y=102
Part of the solution of the system of equations is x=38. What does this value represent?
the number of points Steve lost from questions he answered incorrectly
the number of points Steve earned from questions he answered correctly
the number of questions Steve answered correctly
the number of questions Steve answered incorrectly
Drake is recording a new album. The record company wants him to record 14 or fewer songs and the album must be shorter than 72 minutes. He can record short songs that are about 3 minutes in length or long songs that are about 5 minutes in length. Which system of inequalities best represents the number of short songs (x) and the number of long songs (y) Drake can record for his new album?
x+y<14
3x+5y≤72
x+y≤14
3x+5y<72
x+y≤72
3x+5y<14
x+y<72
3x+5y≤14
You try first. I already took the course.
Apparently, you neglected to read and heed these instructions.
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To solve the given system of inequalities, we need to substitute the values of the given points into each inequality and check if the resulting statements are true or false.
For the first question, we substitute the point (2, 12) into the inequalities:
1. y > 2x + 4:
12 > 2(2) + 4
12 > 4 + 4
12 > 8 (True)
2. y < 3x + 7:
12 < 3(2) + 7
12 < 6 + 7
12 < 13 (True)
Since both inequalities are true, (2, 12) is indeed a solution to the given system. Therefore, the answer is "Yes".
Moving on to the second question, we need to solve the system of equations:
1. 2x + 2y = 10
2. 5x - 2y = 4
To solve it, we can use the method of substitution or elimination. Let's use elimination:
Multiply equation 1 by 5 and equation 2 by 2:
1. 10x + 10y = 50
2. 10x - 4y = 8
Subtract equation 2 from equation 1:
(10x + 10y) - (10x - 4y) = (50 - 8)
10x + 10y - 10x + 4y = 42
14y = 42
y = 3
Now substitute y = 3 into equation 1:
2x + 2(3) = 10
2x + 6 = 10
2x = 4
x = 2
Therefore, the solution to the system of equations is (2, 3). So the answer is "(2, 3)".
For the third question, we need to check if the point (-3, 11) is a solution to each system of inequalities:
1. y ≥ x - 2:
11 ≥ -3 - 2
11 ≥ -5 (True)
2. 2x + y ≤ 5:
2(-3) + 11 ≤ 5
-6 + 11 ≤ 5
5 ≤ 5 (True)
Since both inequalities are true, (-3, 11) is a solution to the given system. Therefore, the answer is "yes".
For the fourth question, we need to find the number of quarters in the jar.
Let's assume the number of quarters is q and the number of nickels is n. We have two equations based on the given information:
1. q + n = 21 (total number of coins)
2. 0.25q + 0.05n = 3.85 (total value in dollars)
To solve this system of equations, we can use substitution or elimination. Let's use elimination:
Multiply equation 1 by 0.05:
0.05(q + n) = 0.05(21)
0.05q + 0.05n = 1.05
Subtract equation 2 from the new equation:
0.05q + 0.05n - 0.25q - 0.05n = 1.05 - 3.85
-0.2q = -2.8
q = -2.8 / -0.2
q = 14
Therefore, there are 14 quarters in the jar. So the answer is "14".
For the last question, let's analyze the given information:
- Drake can record 14 or fewer songs.
- The album must be shorter than 72 minutes.
- Short songs are about 3 minutes long.
- Long songs are about 5 minutes long.
Based on this, we can set up the following inequalities:
1. x + y ≤ 14 (Drake can record 14 or fewer songs)
2. 3x + 5y < 72 (The album must be shorter than 72 minutes)
Therefore, the system of inequalities that best represents the number of short songs (x) and the number of long songs (y) Drake can record for his new album is:
x + y ≤ 14 and 3x + 5y < 72.
So the answer is "x + y ≤ 14 and 3x + 5y < 72".