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2 years ago

Determine the common factor and HCF for each of the following terms.

Mathematics

1 answer:

Tamiku [17]2 years ago

8 0

Answer:

Step-by-step explanation:

1) 8y = 2 * 2 * 2 * y

12y = 2 * 2 * 3 * y

Common factors = 2 , 2 , y

HCF = 2*2y = 4y.

2) 2 b = 2 *b

3b = 3 * b

Common factor = b

HCF = b

3) 3w = 3 *w

5w² = 5 * w * w

Common factor = w

HCF = w

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

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,

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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

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

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The covertices are (±6,0), so b = 6.

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

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

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

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3 years ago