Question

Factor the following expression
20u^5v8-24u^3v^2w^9

Answer 1

Graph the parabola y=2x^2+4x+4
Plot the 5 points
1)the vertex
2)two points to the left of the vertex
3)two points to the right of the vertex

Answer 2

Simplify secxcotx use algebra and fundamental trigonometric identities

Answer 3

To factor the expression 20u^5v^8 - 24u^3v^2w^9, we can first look for common factors among the terms.

The common factors among the terms are:
- 4u^3v^2, which can be factored out of both terms.

Factoring out 4u^3v^2, we get:
4u^3v^2(5u^2v^6 - 6w^9)

Thus, the expression 20u^5v^8 - 24u^3v^2w^9 can be factored as 4u^3v^2(5u^2v^6 - 6w^9).

Answer 4

To graph the parabola y = 2x^2 + 4x + 4, we can start by finding the vertex.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = 2 and b = 4 in this case.
x = -4/2(2) = -1
Substituting x = -1 into the equation, we can find the y-coordinate of the vertex.
y = 2(-1)^2 + 4(-1) + 4 = 2 - 4 + 4 = 2
Therefore, the vertex is (-1, 2).

To find two points to the left of the vertex, we can substitute x = -2 and x = -3 into the equation.
For x = -2, y = 2(-2)^2 + 4(-2) + 4 = 8 - 8 + 4 = 4
For x = -3, y = 2(-3)^2 + 4(-3) + 4 = 18 - 12 + 4 = 10
So the two points to the left of the vertex are (-2, 4) and (-3, 10).

To find two points to the right of the vertex, we can substitute x = 0 and x = 1 into the equation.
For x = 0, y = 2(0)^2 + 4(0) + 4 = 0 + 0 + 4 = 4
For x = 1, y = 2(1)^2 + 4(1) + 4 = 2 + 4 + 4 = 10
So the two points to the right of the vertex are (0, 4) and (1, 10).

Now we can plot these points on a graph:

The vertex (-1, 2) is located at the minimum point of the parabola.
Two points to the left of the vertex are (-2, 4) and (-3, 10).
Two points to the right of the vertex are (0, 4) and (1, 10).

The graph of the parabola y = 2x^2 + 4x + 4 will have a "U" shape and will pass through these points.

Answer 5

To simplify sec(x) * cot(x), we can use the fundamental trigonometric identities.

We know that:
sec(x) = 1/cos(x)
cot(x) = cos(x)/sin(x)

Substituting these values into sec(x) * cot(x), we get:
(1/cos(x)) * (cos(x)/sin(x))

The cosine terms cancel out, leaving us with:
1/sin(x)

Recall that the reciprocal of sine is cosecant, so we can rewrite 1/sin(x) as:
cosec(x)

Therefore, sec(x) * cot(x) simplifies to:
cosec(x)