Determine whether the lines are parallel, perpendicular, or neither.
9x + 3y = 12
15x + 5y = 21
Question 9 options:
A)
neither
B)
parallel
C)
perpendicular
To determine whether the lines are parallel, perpendicular, or neither, we can compare their slopes. We can rewrite the equations in slope-intercept form (y = mx + b) to find the slopes.
9x + 3y = 12
3y = -9x + 12
y = (-9/3)x + 12/3
y = -3x + 4
15x + 5y = 21
5y = -15x + 21
y = (-15/5)x + 21/5
y = -3x + 21/5
The slopes of both lines are -3, meaning they have the same slope. Therefore, the lines are parallel.
The answer is B) parallel.
To determine if two lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The given equations are:
1) 9x + 3y = 12
2) 15x + 5y = 21
We can rewrite the equations in slope-intercept form (y = mx + b) by solving for y:
1) 3y = -9x + 12
y = (-9/3)x + 4
y = -3x + 4
2) 5y = -15x + 21
y = (-15/5)x + 21/5
y = -3x + 21/5
From the equations, we can see that both equations have the same slope, which is -3. Therefore, the lines are parallel.
Hence, the answer is:
B) parallel
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
Given the equations of the lines:
9x + 3y = 12 ...........(1)
15x + 5y = 21 ...........(2)
We need to rearrange the equations to slope-intercept form (y = mx + b) where m is the slope:
1) Equation (1):
9x + 3y = 12
3y = -9x + 12
y = (-9/3)x + (12/3)
y = -3x + 4
2) Equation (2):
15x + 5y = 21
5y = -15x + 21
y = (-15/5)x + (21/5)
y = -3x + (21/5)
Now we can compare the slopes. The slope of the first line is -3 and the slope of the second line is also -3.
Since the slopes of the two lines are equal (-3 = -3), the lines are parallel.
Therefore, the answer is B) parallel.
The average attendance, A, at a minor league baseball park can be modeled by the equation
A = 30w + 6,000
where w is the number of games the team won the previous year. What will the average attendance be next year if the team wins 93 games this year?
Question 10 options:
A)
5907
B)
3210
C)
8790
D)
9720
To find the average attendance next year, we need to substitute the number of games won this year (w = 93) into the equation A = 30w + 6000:
A = 30(93) + 6000
A = 2790 + 6000
A = 8790
Therefore, the average attendance next year if the team wins 93 games this year will be 8790.
The answer is C) 8790.