Given that 3y = x + 6 and y = kx + 12 are perpendicular, find the value of k

Mathematics

1 answer:

fenix001 [56]3 years ago

6 0

k = -3

Step-by-step explanation:

Let's rewrite the equations in their slope-intercept forms:

$y = \frac{1}{3}x + 2\:\:\:\:\:\:\:(1)$

$y = kx + 12\:\:\:\:\:(2)$

In order for Eqn(2) to be perpendicular to Eqn(1), the slope of Eqn(2) must be the negative reciprocal of that of Eqn(1). Therefore, $k = -3$ .

You might be interested in

Urgent please help..

Vadim26 [7]

Answer:

Step-by-step explanation:

$\text{The yellow area is half of the area of the square minus the area of the circle.}\\ \\ A_s=6^2=36\\ \\ A_c=\pi r^2=\pi 3^2=9\pi \\ \\ A_y=\frac{1}{2}(36-9\pi)\approx 3.9in^2$

7 0

3 years ago

Read 2 more answers

HELP MEEE RNNNNNNNNNNNNN

dolphi86 [110]

As this rectangle has it's sides parallel to x axis and y axis

it is easy to find the length of it's sides by counting the number of blocks on each sides.

Let us first find co ordinates of all four points

we would calculate them left and right and up down direction from the origian ( the cross point of x and y axis )

A : it is 2 unit left 2 unit up ( -2 , +2 )

B is 5 unit right 2 unit up ( +5 ,+2)

C is 5 unit right 2 unit down ( +5,-2)

D is 2 unit left 2 unit down ( -2,-2)

Let us now find the distance AB : A is 2 unit left B is 5 unit right so length AB= 2+5 = 7

Let us now find distance AD : A is 2 unit up and D is 2 unit down

so length AD= 2+2= 4

Answer should be 7 x 4 units

5 0

3 years ago

Read 2 more answers

What is the quotient written in scientific notation? 6 x 10^24 /8 x 10^8

Artist 52 [7]

When you divide 6x10^24 by 8x10^8 you end up with $\frac{6}{8} x10^{16}$

This simplifies to $0.75x10^{16}$

Now this number is not written in scientific notation as it does not have its first digit before the decimal, so we must move the decimal of this one to the right.

To do that you must multiply the number by 10.

This means that the exponet of 10 must decrease by 1.

This makes the answer $7.5x10^{15}$