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3 years ago

What is the equation of the perpendicular to y=2/3x+1 that passes through the point (12,-6)

1 answer:

7 0

Well, first off let's check what is the slope of y = 2/3x+1.... .hmmmmm, notice $\bf y=\stackrel{slope}{\cfrac{2}{3}}x+1$ , since the equation is already in slope-intercept form, we can see it has a slope of 2/3.

well then, a line perpendicular to that one, will have a negative reciprocal to it.

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\
slope=\cfrac{2}{{{ 3}}}\qquad negative\implies -\cfrac{2}{{{ 3}}}\qquad reciprocal\implies - \cfrac{{{ 3}}}{2}$

so, we're really looking for the equation of a line whose slope is -3/2 and goes through 12, -6.

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 12}}\quad ,&{{ -6}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{3}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-6)=-\cfrac{3}{2}(x-12)
\\\\\\
y+6=-\cfrac{3}{2}x+18\implies y=-\cfrac{3}{2}x+12$

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1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the

ipn [44]

Answer:

8 hours

Step-by-step explanation:

Given:

Sheyna drives to the lake with average speed of 60 mph and

$v_1 = 60\ mph$

Sheyna drives back from the lake with average speed of 36 mph

$v_2 = 36\ mph$

It took 2 hours less time to get there than it did to get back.

Let $t_1$ be the time taken to drive to lake.

Let $t_2$ be the time taken to drive back from lake.

$t_2-t_1 = 2$ hrs ..... (1)

To find:

Total time taken = ?

$t_1+t_2 = ?$

Solution:

Let D be the distance to lake.

Formula for time is given as:

$Time =\dfrac{Distance}{Speed }$

$t_1 = \dfrac{D}{60}\ hrs$

$t_2 = \dfrac{D}{36}\ hrs$

Putting in equation (1):

$\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles$

So,

$t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs$

$t_2 = \dfrac{180}{36}\ hrs = 5\ hrs$

So, the answer is:

$t_1+t_2 = \bold{8\ hrs}$

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3 years ago

A construction worker needs to determine the volume of a sandpille in a construction yard as shown

postnew [5]

Answer:
6580cm
Step-by-step explanation:
The answer is 6580cm because....
Step one First let's figure out what the smaller shape's volume is. To do so we need to multiply ( LxWxH ) so 6x5x? it does not list what the height is so we know it has the same height as the larger shape and it's height is 14cm so we will use 14cm. 6x5x14=420cm
Step two Now lets find the Volume of the larger shape. So lets do LxWxH so Lx?x14 it does not give us the length so we need to add up all of the numbers along the line. We got 7cm then 5 from the bottom of the smaller shape and 10cm. all ads up to 22cm so 20x22x14=6160
Finally we add up the following shapes Volume which are 6160+420=6580cm

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3 years ago

Help please!!!! Asap!! math whizzes!!!

Katyanochek1 [597]

Answer:

$5xy^3 \sqrt{3x}$

Step-by-step explanation:

The radical $\sqrt{75x^3y^6}$ can be simplified by breaking it down into factors and removing the perfect squares from inside the radical.

$\sqrt{75x^3y^6} =\sqrt{3*25*x^2*x*y^6} =5xy^3 \sqrt{3x}$

25 is a perfect square and is 5 outside the radical.

$x^2$ is a perfect square and is x outside the radical.

$y^6$ is a perfect square and is $y^3$ outside the radical.

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2 years ago

A jumbo chocolate bar with a rectangular shape measures 11 centimeters in length, 8 centimeters in width, and 3 centimeters in

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3 years ago

Juan y Andrés son adultos mayores y maratonistas. Hoy participaron en la maratón internacional de los Andes.El locutor que cubre

Ira Lisetskai [31]

Answer:

3 hours 8 seconds

Step-by-step explanation:

Juan and Andrés are older adults and marathoners. Today they participated in the international marathon of the Andes. The announcer who covers this sporting event reported that Juan had finished the race with a time of 3¾ hours. Tijuanito the route in ⅔ of hours more than Andrés, how long did Andrés finish the marathon ?.

It is given that,

Juan had finished the race with a time of 3¾ hours.

He takes ⅔ of hours more than Andrés.

We need to find how long did Andrés finish the marathon.

Time taken by Juan = $\dfrac{15}{4}$ hours

Time taken by Tijuanito is $\dfrac{2}{3}$ hours more than Andrés.

So, Andrés finish the marathon $\dfrac{15}{4}-\dfrac{2}{3}=3.08\ \text{hours}$ before.

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2 years ago