$6x+3y=12\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x-6x+3y=12-6x\\\\3y=12-6x\qquad\text{divide both sides by 3}\\\\\dfrac{3y}{3}=\dfrac{12}{3}-\dfrac{6y}{3}\\\\\large\boxed{y=4-2y}\\\\===================$

$2p-k=3\qquad\text{subtract}\ 2p\ \text{from both sides}\\\\2p-2p-k=3-2p\\\\-k=3-2p\qquad\text{change the signs}\\\\k=-3+2p\\\\\large\boxed{k=2p-3}\\\\===================$

$6v-2w=10\qquad\text{subtract}\ 6v\ \text{from both sides}\\\\6v-6v-2w=10\\\\-2w=10-6v\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2w}{-2}=\dfrac{10}{-2}-\dfrac{6v}{-2}\\\\w=-5+3v\\\\\large\boxed{w=3v-5}\\\\===================$

5 0

3 years ago

PLEEAASE HELP MEEEEEE

Gre4nikov [31]

$\mathsf{1.\; \frac{x - 6}{2} = x + 13}$

⇒ x - 6 = 2x + 26

⇒ x = -32

⇒ This Equation has One Solution

So, It matches with A in Column B

2. 2 + 6x - 7 = 8 + 2x - 10 + 4x

⇒ 6x - 5 = 6x - 2

As, They are Equations of Parallel Lines. They never meet each other.

⇒ This Equation has No Solution

⇒ So, It matches with B in Column B

3. 15x + 25 = 15x + 10

As, They are Equations of Parallel Lines. They never meet each other.

⇒ This Equation has No Solution

⇒ So, It matches with B in Column B

4. 16 + 8x = 4(2x + 4)

⇒ 16 + 8x = 16 + 8x

As, Both Equations are Same. They Represent the Same Line.

⇒ This Equation has Infinite Number of Solutions

⇒ So, It matches with C in Column B

8 0

3 years ago

Can someone please help me with this

Nesterboy [21]

Answer:

m∠Q = 121°

m∠R = 58°

m∠S = 123°

m∠T = 58°

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Create an expression for the sum of all the angles and equate it to 360, then solve for x:

∠Q + ∠T + ∠S + ∠R = 360

⇒ 2x + 5 + x + 2x + 7 + x = 360

⇒ 6x + 12 = 360

⇒ 6x = 360 - 12 = 348

⇒ x = 348 ÷ 6 = 58

So now we know that x = 58, we can calculate all the angles:

m∠Q = 2x + 5 = (2 x 58) + 5 = 121°

m∠R = x = 58°

m∠S = 2x + 7 = (2 x 58) + 7 = 123°

m∠T = x = 58°

5 0

2 years ago