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3 years ago

An expression is shown below:

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

5 0

Answer:

(a) $3y(x^3+4x-3x^2-12)$

(b) $3y(x^2+4)(x-3)$

Step-by-step explanation:

Given the expression: $3x^3y + 12xy - 9x^2y -36y$

If we consider the terms: $3x^3y ,12xy,9x^2y,36y$ in the expression. The common terms are 3 and y.

Therefore the greatest common factor of the terms is 3y.

Factoring this out, we obtain:

$3x^3y + 12xy - 9x^2y -36y=3y(x^3+4x-3x^2-12)$

Next, we factor the expression completely

$3x^3y + 12xy - 9x^2y -36y\\=3y(x^3+4x-3x^2-12)\\$Rearranging we obtain:\\=3y(x^3-3x^2+4x-12)\\=3y[x^2(x-3)+4(x-3)]\\=3y(x^2+4)(x-3)$

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2. Which equation is equivalent to 2 + 4x = 5 - 3(x + 1)? A. 2 + 4x = 2x - 3 B. 2 + 4% = 5 - 3 -3. C. 6x = 5-(+ 1). D. 2 + 4 = 2

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5

weeeeeb [17]

Answer:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

Step-by-step explanation:

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.

Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:

y - y1 = m(x - x1)

y - 2 = (-4/5) * (x + 3)

$y-2=\frac{-4}{5} (x+3)$

Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:

y = mx + b

y = (-4/5)x + b

Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:

y = (-4/5)x + b

2 = (-4/5) * (-3) + b

2 = 12/5 + b

b = -2/5

So, the y-intercept is -2/5. Then the slope-intercept form is:

$y=\frac{-4}{5} x-\frac{2}{5}$

Thus, our two equations are:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

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Read 2 more answers