$x + y =3\implies y=-x+3\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1}\implies 1}}$

3 0

2 years ago

Rationalize the denominator of square root of negative 49 over open parentheses 7 minus 2 i close parentheses minus open parenth

navik [9.2K]

The answer is the option d, which is: d) $\frac{-77+21i}{130}$

The explanation for this problem is shown below:

1. Smplify the denominator and rewrite the numerator in this form:

$\frac{7i}{7-2i-4-9i} \\\frac{7i}{3-11i}$

2. Multiply the denominator and the numerator by the conjugated $(3+11i)$ and simplify the expression, as following:

$\frac{7i(3+11i)}{(3-11i)(3+11i)} \\ \frac{21i+77i^{2}}{121+9} \\ \frac{-77+21i}{130}$

3. As you can see, you obtain the expression shown in the option mentioned above.

3 0

4 years ago

ABC is an equilateral triangle, solve y

kirill115 [55]

Answer:

y is 60⁰

because all sides are equal

3 0

3 years ago

Read 2 more answers

Write the equation of the line that goes through each set of points (-1,6),(3-2)

Mariana [72]

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-1, 6) and (3, -2). Substitute:

$m=\dfrac{-2-6}{3-(-1)}=\dfrac{-8}{4}=-2\\\\y-6=-2(x-(-1))\\\\y-6=-2(x+1)\qquad\text{use distributive property}\\\\y-6=-2x-2\qquad\text{add 6 to both sides}\\\\y=-2x+4\qquad\text{add 2x to both sides}\\\\2x+y=4$

<h3>Answer:</h3><h3>y - 6 = -2(x + 1) <em>point-slope form</em></h3><h3>y = -2x + 4 <em>slope-intercept form</em></h3><h3>2x + y = 4 <em>standard form</em></h3>

4 0

3 years ago