explaining
Algebra
Simplify (2x^2)(4x^3y^2)
(2x2)(4x3y2)(2x2)(4x3y2)
Multiply x2x2 by x3x3 by adding the exponents.
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2x5(4y2)2x5(4y2)
Rewrite using the commutative property of multiplication.
2⋅4(x5y2)2⋅4(x5y2)
Multiply 22 by 44.
8x5y2
Answer:
One solution (-1,2)
Step-by-step explanation:
Since these two linear equations have different slopes, different y-intercepts, and are indeed linear, these equations will only have one crossing when graphed, and hence one solution.
To find that solution, we can simply set the equations equal to each other.
y = -x + 1
y = 2x + 4
-x + 1 = 2x + 4
-3 = 3x
-1 = x
Now plug that value back into one of the equations:
y = -x + 1
y = -(-1) + 1
y = 2
So now you know the crossing for these two equations occurs at (-1,2).
Cheers.
Answer:
Remember that the maximum rate of change of f at a point u is the length of the of the gradient vector evaluate in u, and the direction in which it occurs is in direction of the gradient vector evaluate in u.
The gradient vector of f is
Then, the maximum rate of change is
in the direction of (5,8).
X²-4x+18=0
x= 4 ± √(16-4*1*18) / 2
x=4±√(16-72) /2
x= 4 ± √-56 /2
x = 4±2i√14 / 2
x= 2±√14 * i
Answer:
C)
Step-by-step explanation:
Note that one of the lines is simply y=-1 for any x, so we can dismiss the only answer without y=-1. That rejected answer is A)
Now let's notice, that the other line is decreasing y when increasing x. That tells us that in the equation y = ax + b, a has to be negative. This brings us to reject option D).
What is the y of that line for x = 0? Because y = ax + b, for x = 0 we will get the value of b. This is called the intercept. The line is at y=4 for x=0, so we know that the b in the equation must be positive 4. This fits answer C, but rejects answer B). And so, we have found that C) is the only possible answer.
