For this case we have the following functions:
y = (1/3) x + 6
y = (1/3) x + 4
We note that both lines have the same slope in this case given by:
m = 1/3
Therefore, the lines are parallel. As they are parallel, they are not cut at any point.
Thus, the system of equations has no solution.
Answer:
The system has no solution (parallel lines)
Answer:
x = 4 + sqrt(38) or x = 4 - sqrt(38)
Step-by-step explanation using the quadratic formula:
Solve for x over the real numbers:
2 (x^2 - 8 x - 22) = 0
Divide both sides by 2:
x^2 - 8 x - 22 = 0
x = (8 ± sqrt((-8)^2 - 4 (-22)))/2 = (8 ± sqrt(64 + 88))/2 = (8 ± sqrt(152))/2:
x = (8 + sqrt(152))/2 or x = (8 - sqrt(152))/2
sqrt(152) = sqrt(8×19) = sqrt(2^3×19) = 2sqrt(2×19) = 2 sqrt(38):
x = (2 sqrt(38) + 8)/2 or x = (8 - 2 sqrt(38))/2
Factor 2 from 8 + 2 sqrt(38) giving 2 (sqrt(38) + 4):
x = 1/22 (sqrt(38) + 4) or x = (8 - 2 sqrt(38))/2
(2 (sqrt(38) + 4))/2 = sqrt(38) + 4:
x = sqrt(38) + 4 or x = (8 - 2 sqrt(38))/2
Factor 2 from 8 - 2 sqrt(38) giving 2 (4 - sqrt(38)):
x = 4 + sqrt(38) or x = 1/22 (4 - sqrt(38))
(2 (4 - sqrt(38)))/2 = 4 - sqrt(38):
Answer: x = 4 + sqrt(38) or x = 4 - sqrt(38)
Answer:
The volume of the sphere is eight times the volume of hemisphere
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x-----> volume of the hemisphere
y-----> volume of the sphere
in this problem we have
substitute
that means------> The volume of the sphere is eight times the volume of hemisphere
12*14=168*4=672 dollars the answer to the equation.