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3 years ago

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

Mathematics

1 answer:

VladimirAG [237]3 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 $\frac{3x - 6}{2x - 6}$

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Answer:

The percentage rate is 4.5%.

Step-by-step explanation:

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3 years ago

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2 years ago

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The length and width of a rectangle are 7 cm and (x-8) cm respectively. Find the value of x if the area with of the rectangle is

Tcecarenko [31]

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plug in the given numbers you have

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3 years ago

I need help with math homework #2 algebra

OverLord2011 [107]

Answer:

A. (0, -2) and (4, 1)

B. Slope (m) = ¾

C. y - 1 = ¾(x - 4)

D. y = ¾x - 2

E. -¾x + y = -2

Step-by-step explanation:

A. Two points on the line from the graph are: (0, -2) and (4, 1)

B. The slope can be calculated using two points, (0, -2) and (4, 1):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 -(-2)}{4 - 0} = \frac{3}{4}$

Slope (m) = ¾

C. Equation in point-slope form is represented as y - b = m(x - a). Where,

(a, b) = any point on the graph.

m = slope.

Substitute (a, b) = (4, 1), and m = ¾ into the point-slope equation, y - b = m(x - a).

Thus:

y - 1 = ¾(x - 4)

D. Equation in slope-intercept form, can be written as y = mx + b.

Thus, using the equation in (C), rewrite to get the equation in slope-intercept form.

y - 1 = ¾(x - 4)

4(y - 1) = 3(x - 4)

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4y = 3x - 12 + 4

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E. Convert the equation in (D) to standard form:

y = ¾x - 2

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