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3 years ago

The perimeter of a rectangle is 44. The length is 5 less than double the width. What is the length?

Mathematics

1 answer:

OleMash [197]3 years ago

4 0

$44 = 2x - 5 \\ \frac{39}{2} = \frac{2x}{2} \\ 19.5 = x \\$

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Rewrite the equation y−2=−3/2(x+6) in standard form.

navik [9.2K]

For this case we have that by definition, the standard form of the equation of the line is given by:

$ax + by = c$

We have the following equation:

$y-2 = - \frac {3} {2} (x + 6)$

We manipulate the equation algebraically:

$y-2 = - \frac {3} {2} x- \frac {3 * 6} {2}\\y-2 = - \frac {3} {2} x \frac {18} {2}\\y-2 = - \frac {3} {2} x-9\\y-2 + 9 = - \frac {3} {2} x\\y-7 = - \frac {3} {2} x\\2 (y-7) = - 3x\\2y-14 = -3x\\3x + 2y = 14$

Finally, the equation is:

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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,

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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4 years ago