Answer:
2°
one solution
(a) The system has no solution
Explanation:
Let the smaller angle be x. According to the given condition, the larger angle is forty-four times the smaller angle, which is 44x. Since the angles are complementary, their sum is 90°.
x + 44x = 90
45x = 90
x = 90/45
x = 2
So, the smaller angle is 2°, and the larger angle is 44 times that, which is 88°.
The given system of equations is:
20y = -24x + 40
6x + 5y = 10
To determine the nature of the system, we can compare the slopes of the two equations. If the slopes are equal and the y-intercepts are also equal, the system has infinitely many solutions. If the slopes are equal but the y-intercepts are not equal, the system has no solution. If the slopes are not equal, the system has one solution.
Let's find the slopes of the two equations:
20y = -24x + 40
Dividing by 20, we get: y = (-24/20)x + 2
6x + 5y = 10
Dividing by 5, we get: (5/5)y = (6/5)x + (10/5)
y = (6/5)x + 2
Comparing the slopes, we see that they are equal (both are 6/5), and the y-intercepts are also equal (both are 2). So, the system has infinitely many solutions. The correct answer is (b) The system has infinitely many solutions.
The given system of equations is:
19 = 4y + 12x
12x + 4y = 15
To determine the nature of the system, we can again compare the slopes of the two equations. If the slopes are equal and the y-intercepts are also equal, the system has infinitely many solutions. If the slopes are equal but the y-intercepts are not equal, the system has no solution. If the slopes are not equal, the system has one solution.
Let's find the slopes of the two equations:
19 = 4y + 12x
Dividing by 4, we get: (1/4)(4y + 12x) = 19/4
y + 3x = 19/4
12x + 4y = 15
Dividing by 4, we get: (1/4)(12x + 4y) = 15/4
3x + y = 15/4
Comparing the slopes, we see that they are equal (both are 1/3), but the y-intercepts are not equal. So, the system has no solution. The correct answer is (a) The system has no solution.