Answer:
As explained
Step-by-step explanation:
given that D = 2A + B + 3C and S = {A, B, C, D}, C = A − B
for {A, B, D} to be linearly dependent implies that A B and D will have values that not dependent on the sample space C.
if C = A -B is substituted in the original equation, the generated equation, 5A -2B will have values each as against C which is linearly independent.
Also, D will have values that are linearly dependent.
This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon.
Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s:
2.6s + 7.3
Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:
1.5s + 12.4
To determine when both balloons are at the same height, we set the two equations equal to each other:
2.6s + 7.3 = 1.5s + 12.4
Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation:
1.1s + 7.3 = 12.4
Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation:
1.1s = 5.1
Last, we divide both sides by 1.1. So s = 4.63.
This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation:
2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33
1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33
After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
Answer:
24
Step-by-step explanation:
2+2+2 = 6*2 = 12*2 = 24
Answer:
y=3/2and x =2
Step-by-step explanation:
Answer:
one solution
Step-by-step explanation:
* Lets start to solve the question
- The 1st equation x - y = -4
- The 2nd equation 3x + y = 8
- We will use the elimination method to solve this system of equation
∵ x - y = -4 ⇒ (1)
∵ 3x + y = 8 ⇒ (2)
- Add the two equation (1) and (2) to eliminate y
∴ x + 3x = -4 + 8
∴ 4x = 4
- Divide both sides by 4
∴ x = 1
- Substitute the value of x in equation (1) or equation (2) to find
the value of y
- We will use equation (1)
∴ 1 - y = -4
Subtract 1 from both sides
∴ -y = -5
- Divide both sides by -1
∴ y = 5
∴ The solution is (1 , 5)
* The system has one solution
