Answer:
x = 1/4
y = -1/2
z = 9/4
Step-by-step explanation:
Here we have a system of 3 equations with 3 variables:
4*x + 2*y + 1 = 1
2*x - y = 1
x + 3*y + z = 1
The first step to solve this, is to isolate one of the variables in one of the equations, let's isolate "y" in the second equation:
2*x - y = 1
2*x - 1 = y
Now that we have an expression equivalent to "y", we can replace this in the other two equations:
4*x + 2*(2*x - 1) + 1 = 1
x + 3*(2*x - 1) + z = 1
Now let's simplify these two equations:
8*x - 1 = 1
7*x - 3 + z = 1
Now, in the first equation we have only the variable x, so we can solve that equation to find the value of x:
8*x - 1 = 1
8*x = 1 + 1 = 2
x = 2/8 = 1/4
Now that we know the value of x, we can replace this in the other equation to find the value of z.
7*(1/4) -3 + z = 1
7/4 - 3 + z = 1
z = 1 + 3 - 7/4
z = 4 - 7/4
z = 16/4 - 7/4 = 9/4
z = 9/4
Now we can use the equation y = 2*x - 1 and the value of x to find the value of y:
y = 2*(1/4) - 1
y = 2/4 - 1
y = 1/2 - 1
y = -1/2
Then the solution is:
x = 1/4
y = -1/2
z = 9/4
Answer:
t_a = 7 s
t_w = 5 s
Step-by-step explanation:
Given:
- The average speed in air v_a = 16 m/s
- The average speed in water v_w = 3 m/s
- The total distance D = 127 m
- The total time T = 12 s
Find:
How long did the stone fall in air and how long did it fall in the water?
Solution:
- Lets time taken by stone to drop through air as t_a = t_a.
- The time taken in water would be t_w = (12 - t_a)
- The total distance covered can be calculated as:
D = v_a*t_a+ v_w*(12 - t_a)
127 = 16*t_a + 3*(12 - t_a)
Simplify and solve for t:
91 = 16*t_a - 3t_a
13*t_a = 91
t_a = 7 s
t_w = 5 s
Answer:
-18/3
Step-by-step explanation:
My advice is don't smoke and make sure you don't keep the two close together. Hope this helped,
Answer:
2:5
Step-by-step explanation:
Total marbles: 10
red: 2
yellow: 5
2:5
