What are the asymptotes of the following graph?

Mathematics

1 answer:

allochka39001 [22]3 years ago

5 0

Answer:

y = ±(1/3)x

Step-by-step explanation:

The asymptotes of this hyperbola will contain the diagonals of the green rectangle. The green rectangle at the center of this hyperbola has corners that have a run from its center of 3 for a rise of ±1, so the slope of the line from its center to the corner is rise/run = ±1/3. The center is at (0, 0), so the equations of the asymptotes are

y = ±(1/3)x

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What's the value of m?

Dmitry [639]

Keeping in mind that a perpendicular line to another, will have a negative reciprocal slope, hmmmmm so what's the slope of the equation above anyway?

$\bf y=16-\cfrac{x}{3}\implies \stackrel{\textit{slope-intercept form}}{y = -\cfrac{x}{3}+16}\implies y=\stackrel{slope}{-\cfrac{1}{3}}x+16
\\\\\\
\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}}
{\stackrel{slope}{-\cfrac{1}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{1}}\implies 3}$

7 0

4 years ago

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Let a, b, c, and d be nonzero real numbers. If the quadratic equation ax (cx + d) = –b (cx + d) is solved for x, which of the fo

gayaneshka [121]

Answer:

$x_1=-\frac{b}a,x_2=-\frac{d}c$

Step-by-step explanation:

Solving for x:

$ax(cx + d) =-b(cx +d)\\ax(cx + d)+b(cx+d)=0\\(ax+b)(cx+d)=0$

In this form is easy to identify the factors of the quadratic function: $(ax+b)(cx+d)$ . The two solutions are the values that make each of the factors equals to zero.