Answer:
10 liters of pure alcohol
Step-by-step explanation:
Create an equation where x is the number of liters of pure alcohol needed:
1x + (0.4)(20) = (20 + x)(0.6)
Simplify:
x + 8 = 0.6x + 12
Solve for x:
0.4x = 4
x = 10
So, 10 liters of pure alcohol have to be added
The first expression can be simplified by combining like terms.
First, the terms "4b" and "-3b" can be combined to form "b"
Then, the terms "-7" and "9" can be combined to form "2"
Finally, we simply put these two final terms together, to form "b+2"
Hence, 4b-7-3b+9 is equal to be + 2.
Hope this helps!
Step-by-step explanation:
For a quadratic equation y = ax² + bx + c, the vertex (the maximum or minimum point) is at x = -b/(2a).
1) y = -0.5t² + 2t + 38
The maximum is at:
t = -2 / (2 × -0.5)
t = 2
The maximum height is:
y = -0.5(2)² + 2(2) + 38
y = 40
The coordinates of the vertex are (2, 40). That means the missile reaches a maximum height of 40 km after 2 minutes.
2) y = -4.9t² + 12t + 1.6
The maximum is at:
t = -12 / (2 × -4.9)
t = 1.22
The maximum height is:
y = -4.9(1.22)² + 12(1.22) + 1.6
y = 8.95
The coordinates of the vertex are (1.22, 8.95). That means the missile reaches a maximum height of 8.95 m after 1.22 seconds.
3) y = -0.04x² + 0.88x
The maximum is at:
x = -0.88 / (2 × -0.04)
x = 11
The maximum height is:
y = -0.04(11)² + 0.88(11)
y = 4.84
The maximum height of the tunnel is 4.84 meters.
The maximum width is when y = 0.
0 = -0.04x² + 0.88x
0 = -0.04x (x − 22)
x = 22
The maximum width is 22 feet.
Answer:
x = 6
Step-by-step explanation:
6 - 2x = (5-9)x +18
6 - 2x = -4x +18
2x = 12
x = 6
Jamie completed 7/16 more than Halverson because 10/16-3/16 is 7/16
