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3 years ago

Which two lines are parallel?

Mathematics

1 answer:

Masteriza [31]3 years ago

6 0

Answer:

3x + y = -2
2y = -6x – 8

Step-by-step explanation:

When the equations are written in the same form, the ratio of x coefficient to y coefficient is the same for parallel lines.

These equations in the same form are ...

3x +y = -2
-6x +2y = 4
6x +2y = -8

The first and last of these equations have a ratio of x-coefficient to y-coefficient of ...

(x-coefficient)/(y-coefficient) = 3/1 = 6/2

so the lines are parallel.

The second equation has a ratio that is the opposite of this.

Alternate approach

You can put each equation into slope-intercept form (solve for y). The x-coefficient is then the slope of the line. Parallel lines** have equal slopes.

y = -3x -2 **
y = 3x +2
y = -3x -4 **

_____

I find a graphing calculator to be a big help for many problems involving equations and their characteristics.

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3 years ago

Read 2 more answers

Find the constant of variation k for the direct variation

Alla [95]

Answer:

The constant of variation is k = -2 ⇒ (B)

Step-by-step explanation:

The equation of the direct variation is y = k x, where

k is the constant of variation

The constant of variation k = $\frac{y}{x}$

The given table has 4 points (-1, 2), (0, 0), (2, -4), (5, -10)

We can use one of the points [except point (0, 0)] to find the value of k

∵ (-1, 2) is a given point

∴ x = -1 and y = 2

∵ k = $\frac{y}{x}$

→ Substitute the values of x and y in the relation above

∴ k = $\frac{2}{-1}$

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3 years ago

What is 1-2sin^2x=sinx Please show steps and find all solutions in interval [0,2pi)

Svetlanka [38]

Answer:

$\large\boxed{x=\dfrac{3\pi}{2}\ \vee\ x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}$

Step-by-step explanation:

$1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}$

$\sin x=-1\to x=-\dfrac{\pi}{2}+2k\pi,\ k\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}\\\\x\in[0,\ 2\pi)$

$x=-\dfrac{\pi}{2}\notin[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+2\pi=\dfrac{3\pi}{2}\in[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+4\pi=\dfrac{7\pi}{2}\notin[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}+2\pi=\dfrac{13\pi}{6}\notin[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}+2\pi=\dfrac{17\pi}{6}\notin[0,\ 2\pi)$

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3 years ago

I am a 4 digit number larger than 2,500. No two of my digits are the same. The product of the thousands digit and the hundreds d

gulaghasi [49]

Answer:

After 5 minutes of hitting my head on a wall I found your answer... 3256

Step-by-step explanation:

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3 years ago

In the figure, find the perimeter of AABC.

erma4kov [3.2K]

Answer:C. 36

Step-by-step explanation: height is 12 base is 9

12^2+9^2= 144+81=225 sq rt of 225 =15

So 12+9+15=36

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3 years ago