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2 years ago

Solve |2x – 6| = 4x+4

Mathematics

2 answers:

Novay_Z [31]2 years ago

6 0

Answer:

-6-4=4x-2x

10=2x

x=2÷10

x=5

svp [43]2 years ago

3 0

There are 2 solutions with absolute value equations.

1. |2x-6| = 4x+4

Remove absolute value:

2x-6 =4x + 4

Subtract 4x from both sides:

-2x -6 = 4

Add 6 to both sides:

-2x = 10

Divide both sides by -2:

X = -5

2nd solution

Remove absolute value and add a negative sign to the right side:

2x-6 = -4x -4

Add 4x to both sides::

6x-6 =-4

Add 6 to both sides:

6x = 2

Divide both sides by 6:

X = 2/6

X = 1/3

The two answers are x = -5 and x = 1/3

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2 years ago

A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the

zlopas [31]

1. The function $h(t)=-16t^{2}+48t$ is a parabola of the form $ax^{2}+bx$ . The the formula for the axis of symmetry of a parabola is $x= \frac{-b}{2a}$ . We can infer from our function that $a=-16$ and $b=48$ , so lets replace those values in our formula:
$x= \frac{-b}{2a}$
$x= \frac{-48}{-2(16)}$
$x= \frac{-48}{-32}$
$x= \frac{3}{2}$
$x=1.5$
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.

2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
$0=-16t^{2}+48t$
$-16t(t-3)=0$
$t=0$ or $t-3=0$
$t=0$ or $t=3$
From our previous point we know that the ball reaches its maximum time at $t=1.5$ , which means that it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.