Y - 12x = 0
y = 12x
Comparing it with the formular for direct variation y = kx => k = 12
y varies directly with x and the constant of variation is 12.
Hello from MrBillDoesMath!
Answer: Suppose the function is f(x). The statement means that either:
1) f(c) >= f(x) for x in the interval [a,b]
or
2) f(c) <= f(x) for x in the interval [a,b]
That is, the value of f(c) is larger (or smaller, take your choice) than the value of f(x) for all other x in the interval. Equivalently, f(c) is the largest (or smallest) value of f(x) in the interval.
Regards, MrB
Given:
Width of the rectangular yard = x feet
Length of the rectangular yard = x+4 feet
Perimeter of the rectangular yard is:
Perimeter of the yard = 84 feet
To find:
The length of the rectangular yard.
Solution:
Perimeter of the yard is 84 feet.
Divide both sides by 4.
So, the width of the rectangular yard is 19 feet.
Length = 
Length = 
The length of the rectangular field is 23 feet.
Therefore, the correct option is B.
No they won’t be.Consider the linear combination (1)(u – v) + (1) (v – w) + (-1)(u – w).This will add to 0. But the coefficients aren’t all 0.Therefore, those vectors aren’t linearly independent.
You can try an example of this with (1, 0, 0), (0, 1, 0), and (0, 0, 1), the usual basis vectors of R3.
That method relied on spotting the solution immediately.If you couldn’t see that, then there’s another approach to the problem.
We know that u, v, w are linearly independent vectors.So if au + bv + cw = 0, then a, b, and c are all 0 by definition.
Suppose we wanted to ask whether u – v, v – w, and u – w are linearly independent.Then we’d like to see if there are non-zero coefficients in the linear combinationd(u – v) + e(v – w) + f(u – w) = 0, where d, e, and f are scalars.
Distributing, we get du – dv + ev – ew + fu – fw = 0.Then regrouping by vector: (d + f)u + (-d +e)v + (-e – f)w = 0.
But now we have a linear combo of u, v, and w vectors.Therefore, all the coefficients must be 0.So d + f = 0, -d + e = 0, and –e – f = 0. It turns out that there’s a free variable in this solution.Say you let d be the free variable.Then we see f = -d and e = d.
Then any solution of the form (d, e, f) = (d, d, -d) will make (d + f)u + (-d +e)v + (-e – f)w = 0 a true statement.
Let d = 1 and you get our original solution. You can let d = 2, 3, or anything if you want.
Your answer is:
(125 - 8x^3) / (25 + 10x + 4x^2) = - ((2x - 5) * (4x^2 + 10x + 25)) / (4x^2 + 10x + 25) = - (2x - 5) = - 2x + 5
The correct result would be - 2x + 5.
