Answer:
The system is consistent; it has one solution ⇒ D
Step-by-step explanation:
A consistent system of equations has at least one solution
- The consistent independent system has exactly 1 solution
- The consistent dependent system has infinitely many solutions
An inconsistent system has no solution
In the system of equations ax + by = c and dx + ey = f, if
- a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutions
- a = d, b = e, and c ≠ f, then the system is inconsistent and has no solution
- a ≠ d, and/or b ≠ e, and/or c ≠ f, then the system is consistent independent and has exactly one solution
In the given system of equations
∵ -2y + 2x = 3 ⇒ (1)
∵ -5y + 5x = 12 ⇒ (2)
→ By comparing equations (1) and (2)
∵ -2 ≠ -5
∵ 2 ≠ 5
∵ 3 ≠ 12
→ By using the 3rd rule above
∴ The system is consistent independent and has exactly one solution
∴ The system is consistent; it has one solution
You can draw a diagram of the situation, representing it by a right triuangle.
In the right triangle the hypotenuse is the distance indicated by the radio signal, 1503 m, and the angle is 41°.
The opposed leg to 41° is the height of the ballon.
Then you can use the sine trigonometric function.
sine (41°) = opposed leg / hypotenuse = x / 1503 m => x = 1503m * sine(41°)
=> x = 986m.
Answer: 986m
Answer:
8:20
Step-by-step explanation:
Answer:
There are 9 adults
Step-by-step explanation:
3:5 = x:15
3/5 = x/15
3(15) = 5x
5x = 45
x = 9 adults
3:5 = 9:15
Answer:
C
Step-by-step explanation:
We can notice that the balance beam has in one side 7 balls and in the other one 5 balls and a square
The balance beam is balenced
Let x be the square mass
- x+5 = 7 substract five from each side
- x+5-5 = 7-5
- x = 2
The solution is 2
C fits perfectly what we prooved
