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3 years ago

What is the equation of the line (in slope-intercept form) that passes through the given point and is

1 answer:

6 0

keeping in mind that perpendicular lines have negative reciprocal slopes, hmmmm what's the slope of the equation above anyway?

$\bf x+y=6\implies y = \stackrel{\stackrel{m}{\downarrow }}{-1}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-1}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{1}\implies 1}}$

so we're really looking for the equation of a line whose slope is 1 and runs through (-5,-6).

$\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-6})~\hspace{10em} \stackrel{slope}{m}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{1}[x-\stackrel{x_1}{(-5)}] \\\\\\ y+6=1(x+5)\implies y+6=x+5\implies y=x-1$

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A boat sails for 5 hours at 30 mph in a direction 164°56'. How far south has it sailed (to the nearest mile)?

Valentin [98]

Total distance covered = 5 x 30 = 150 miles
Angle of travel with respect to south pole = 180 - 164°56' = 15°4'

Let the distance southwards covered be x, then
cos 15°4' = x/150
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Therefore, the distance covered southwards = 145 miles to the nearest mile.

5 0

2 years ago

The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect

ki77a [65]

Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

$Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}$

Now the points A(−3, 4) and B(7, 2)

$AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}$

$AB = \sqrt{(10)^{2} +(-2)^{2}}$

$AB = \sqrt{100+4}$

$AB = \sqrt{104}$

$AB = 2\sqrt{26}\units$

Thus

$CD= 2\sqrt{26}\units$

Now the points

A (−3, 4) , D (−4, −1)

$AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}$

$AD = \sqrt{(-1)^{2} +(-5)^{2}}$

$AD = \sqrt{1 + 25}$

$AD = \sqrt{26}\units$

Thus

$BC = \sqrt{26}\units$

Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

$Length = 2\sqrt{26}\ units$

$Breadth = \sqrt{26}\ units$

$Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})$

$Perimeter\ of\ rectangle = 2(3\sqrt{26})$

$Perimeter\ of\ rectangle = 6\sqrt{26}$

$\sqrt{26} = 5.1 (Approx)$

$Perimeter\ of\ rectangle = 6\times 5.1$

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

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2 years ago

Find m angle QSRIf m angle TSQ=15x , m angle TSR=173^ , and m angle QSR=10x-2

Serggg [28]

${\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}$

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$\Large\color{red}{{\underline{\mathfrak {{꧁"Carry\:on\: learning"꧂ }}}}}$

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2 years ago

Y+4=-2(x-1) slope intercept form

lys-0071 [83]

To convert this equation into slope intercept form simply distribute the number of -2 and put it in

Y = mx + b form

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Y = -2X - 2

I believe this is the solution in slope intercept form.

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3 years ago

The slope of the line whose equation is 3y + 2x =1 is

frez [133]

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slope : - 2/3

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2 years ago