All categories

2 years ago

Simplify completely (6x² - 54x + 84 / 8x² -40 x +48) ÷ (x² + x - 56 / 2x² + 12x -32)

Mathematics

1 answer:

VladimirAG [237]2 years ago

4 0

Answer:

The answer to your question is $\frac{3(x - 2)}{2(x - 3)}$ or $\frac{3x - 6}{2x - 6}$

Step-by-step explanation:

Expression $\frac{6x^{2}- 54x + 84}{8x^{2} - 40x + 48} / \frac{ x^{2} + x - 56}{2x^{2} + 12x - 32}$

Process

1.- Change the division to a multiplication

$\frac{6x^{2}- 54x + 84}{8x^{2} - 40x + 48} x \frac{2x^{2}+ 12x - 32}{x^{2} + x - 56}$

2.- Factor

$\frac{6(x^{2}- 9x - 14)}{8(x^{2} - 5x + 6)} x \frac{2(x^{2}+ 6x - 16)}{(x^{2} + x -56)}$

$\frac{6(x + 8)(x - 2)}{8(x - 3)(x - 2)} x \frac{2(x + 8)(x - 2)}{(x + 8)(x - 7)}$

3.- Simplify (cancel the terms that are repeated in both numerator and denominator)

$\frac{2(6)(x - 2)}{8(x - 3)}$

$\frac{3(x - 2)}{2(x - 3)}$ or $\frac{3x - 6}{2x - 6}$

You might be interested in

A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment i

Tasya [4]

Answer:

(3,7) for the first line, and (12,0) for the second one.

Step-by-step explanation:

Hi Isabella,

1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:

$x_{m}=\frac{x_{1} +x_{2} } {2}, y_{m} =\frac{y_{1}+ y_{2} }{2}$

2) Each segment has two endpoints, and their midpoints, namely:

a) (1,-9) and its midpoint (2,-1)

b) (-2,18) and its midpoint (5,9)

3) Calculating. You need to be careful to not sum the wrong coordinates.

So be attentive!

The first line a

$2=\frac{1+x_{2} }{2}\\ 4=1+x_{2}\\ 4-1=-1+1+x_{2} \\ x_{2}=3\\-1=\frac{y_{2}-9}{2}\\-2=y_{2}-9\\+2-2=y_{2}-9+2\\ y_{2}=-7$

So (3,7) is the other endpoint whose segment starts at (1,-9)

The second line b endpoint at (-2,18) and its midpoint (5,9)

$5=\frac{-2+x_{2} }{2} \\ 10=-2+x_{2} \\ +2+10=+2-2+x_{2}\\ x_{2}=12 \\ \\ 9=\frac{18+y_{2} }{2} \\ 18=18+y_{2} \\ -18+18=-18+18+y_{2}\\ y_{2} =0$

So (12,0) it is the other endpoint.

Take a look at the graph below:

8 0

3 years ago

What Did the Baby Porcupine Say When It Backed into a Cactus??

Katen [24]

Answer:

Is that you, Mommy?

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

On Wednesday 72% of the customers who bought gas at a gas station made additional purchases. There were 250 customers who bought

elena-s [515]

Answer: 180 people

I hope i helped you! I wish you luck on the test!

6 0

2 years ago

A guitar string is plucked at a distance of 0.6 centimeters above its resting position and then released, causing vibration. The

liubo4ka [24]

Answer:

The equation that represents the motion of the string is given by:

$y =Ae^{-kt}\cos(2\pi ft)$ .....[1] where t represents the time in second.

Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.

Substitute the given values in [1] we get;

$y =0.6e^{-1.8t}\cos(2\pi 105t)$

$y =0.6e^{-1.8t}\cos(210\pi t)$

(a)

The trigonometric function that models the motion of the string is given by:

$y =0.6e^{-1.8t}\cos(210\pi t)$

(b)

Determine the amount of time t that it takes the string to be damped so that $-0.24\leq y \leq0.24$

Using graphing calculator for the equation

$y =0.6e^{-1.8x}\cos(210\pi x)$

let x = t (time in sec)

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that $-0.24\leq y \leq0.24$ is, 0.5 sec

4 0

3 years ago

What is the probability of losing 6 times in a row playing Heads or Tails flipping a coin?

slava [35]

The probability of losing per flip is 1/2. Multiply 1/2 by itself 6 times since the condition is asking for the probability for the person to lose 6 times in a row. 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64. The answer is 1/64.

6 0

3 years ago

Read 2 more answers