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3 years ago

Select the postulate that is illustrated for the real numbers.

Mathematics

2 answers:

Inessa05 [86]3 years ago

4 0

The answer is the additive identity postulate.

Rom4ik [11]3 years ago

3 0

Answer:

The additive identity postulate

Step-by-step explanation:

6 + 0 = 6

Any number added with zero, we get the same number.

That is, a + 0 = a, where "a" is any real number.

Let's take a = 9, we get

9 + 0 = 9

Let's check out a few more examples:

-9 + 0 = -9

2/3 + 0 = 2/3

22 + 0 = 22

You can see any number added with 0, we get the same number.

Here 0 is additive identity, this is called additive identity postulate.

We are given 6 + 0 = 6 which illustrated by "The additive identity postulate."

Therefore, answer is "The additive identity postulate"

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Which statements about the hyperbola are true? Check all that apply. A. There is a focus at (0,−10). B. There is a focus at (0,

hichkok12 [17]

Answer:

A. There is a focus at (0,−10).

Step-by-step explanation:

Assume the hyperbola is like the one below.

The hyperbola is vertical and centred on the y-axis, so its general equation is

$\dfrac{y^{2}}{a^{2}} - \dfrac{x^{2}}{b^{2}} = 1$

The vertices of your parabola are (0,±8) so a = 8.

The covertices are (±6,0), so b = 6.

Calculate c

$\begin{array}{rcl}a^{2} + b^{2} & = & c^{2}\\8^{2} + 6^{2} & = & c^{2}\\64 + 36 & = & c^{2}\\100 & = & c^{2}\\c & = & \mathbf{10}\\\end{array}$

A. Foci

The foci are at (0, ±c) = (0, ±10)

TRUE. There is a focus at (0,-10).

B. Foci

The foci are at (0,±10).

False. There is no focus at (0,12)

C. and D. Asymptotes

The equations for the asymptotes are

$y = \pm\dfrac{a}{b}x = \pm\dfrac{8}{6}x = \pm\dfrac{4}{3}x$

So, y = ±x are not asymptotes.

False.

E. and F. Directrices

The equations of the directrices are

y = ±a²/c = ±64/10 = ±6.4

y = 6.4 is a directrix.

E is false. x = cannot be a directrix

F is uncertain. Your equation for the directrix is incomplete.

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