The sequence of transformations, RO,90° ° rx-axis, is applied to ΔXYZ to produce ΔX''Y''Z''. If the coordinates of Y'' are (3, 0
2 answers:
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Answer:
Step-by-step explanation:
Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form
The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.
Filling in the equation with a vertex of (0, 0) which is our h and k respectively:
which simplifies to
and multiplying both sides by -1:
. This is not standard form, but it matches what your equation is in the choices. So to sum up:
The focus is located at (0, -3) and the first choice is true.
The parabola opens upside down and the second choice is not true.
The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.
We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.
So the fifth choice is not true.
The factorization of the expression of 43x³ + 216y³ is
(7x + 6y)(49x² - 42xy + 36y²)
Step-by-step explanation:
The sum of two cubes has two factors:
1. The first factor is +
2. The second factor is ( )² - (
) (
) + (
)²
Ex: The expression a³ + b³ is the sum of 2 cubes
The factorization of a³ + b³ is (a + b)(a² - ab + b²)
∵ The expression is 343x³ + 216y³
∵ = 7x
∵ = 6y
∴ The first factor is (7x + 6y)
∵ (7x)² = 49x²
∵ (7x)(6y) = 42xy
∵ (6y)² = 36y²
∴ The second factor is (49x² - 42xy + 36y²)
∴ The factorization of 43x³ + 216y³ is (7x + 6y)(49x² - 42xy + 36y²)
The factorization of the expression of 43x³ + 216y³ is
(7x + 6y)(49x² - 42xy + 36y²)
Learn more:
You can learn more about factors in brainly.com/question/10771256
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