Reduce these fractions to the simplest form: 21/42= *

a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

Step-by-step explanation:

The equation of a line:

$y=mx+b$

We have

$m=\dfrac{2}{3}$

substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}$

Convert the equation:

$y=\dfrac{2}{3}x+b$ |subtract $y$ from both sides

$\dfrac{2}{3}x-y+b=0$ |multiply both sides by 3

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

$(0,\ 0)\to x_0=0,\ y_0=0$

substitute:

$d=4$

$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

$4=\dfrac{|3b|}{\sqrt{13}}\qquad|$ |multiply both sides by $\sqrt{13}$

$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |divide both sides by 3

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

4 0

3 years ago

You owe $1,853.42 on a credit card with a limit of $3,000.00 at a rate of 15.5% APR. You pay $400.00 the first 2 months and then

Assoli18 [71]

Answer:

the answer is the 2nd one :)

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

Beth is particularly susceptible to getting strep throat. If she is infected with one streptococcus pygenes bacterium. And it ha

Neko [114]

Add a snowman amen amen Carmen caravanserais consisted

6 0

3 years ago

Complete the equation of the line through (−8,8), and (1,-10 ). Use exact numbers. Help me please my dog just died and I want to

katrin2010 [14]

Answer: (Mayadc821 wrote this anwser check theyre account for more)

Since you know the x and y values, you just have to plug these into the linear slope-intercept equation:

y = mx + b

-10 = m(1) + b

m + b = -10

b = -10 - m

Now that we have a value for b, we can plug this into the other equation:

8 = m(-8) + b

8 = -8m + (-10 - m)

8 = -9m -10

18 = -9m

m = -2

Now that we know what m is equal to, we can plug this into our first equation to get an answer for b:

b = -10 - m

b = -10 -(-2)

b = -10 + 2

b = -8

Our final equation is y = -2x - 8

6 0

3 years ago

Need the (x) & (y) value

Katen [24]

Answer:

x=0

y=6

Step-by-step explanation:

Two equations with two unknowns can be solved. Use the three steps given below.

In general you can save time if you use the simplest expression for step 1. You can choose either expression to start with x =.. or you can rewrite it, so it starts with y =...

FOLLOW THESE STEPS:

1. Rewrite the first expression so it starts with y =...

2. Then use that expression and substitute it in the other expression, to find the value for x.

3. Use that value found in step 2. and substitute it in the rewritten expssion you created in step 1. Solve this last expression and you'll get the value for y.

Step 1.

-6y + 11x = -36

-6y = -11x -36

multiply left and right of the = sign by -1

6y = 11x + 36

divide left and right of the = sign by 6

y = 11x/6 + 36/6

y = 11/6x + 6

Step 2.

-4 * ( y ) + 7x = -24

-4 * ( 11/6x + 6 ) + 7x = -24

( -44/6x - 24 ) + 7x = -24

-44/6x + 7x = -24 + 24

You can see immediately that ...x = 0

Just for fun of it ....

-44/6x + 42/6x = 24 - 24

(-44+42)/6x = 0

-2/6x = 0

-1/3x = 0

multiply left and right of the = sign by -3

3/3x = 0 * -3

x = 0

Step 3.

y = 11/6( x ) + 6. and substitute x = 0 gives:

y = 11/6( 0) + 6

y = 0 + 6

y = 6

3 0

3 years ago