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3 years ago

8

Factor the polynomial completely. 9g^2 - 30gh + 25h^2

1 answer:

Bezzdna [24]3 years ago

7 0

Answer:

Step-by-step explanation:

It's a perfect square.

It factors into (3g - 5h)^2

or (3g - 5h)(3g - 5h)

Make sure it is correctly factored.

3g*3g = 9g^2

3g * - 5h = - 15gh

-5h*3g = - 15gh

5h*5h = 25h^2

These four terms add to 9g^2 - 15gh - 15gh + 25h^2 = 9g^2 - 30gh + 25h^2 which is exactly what you started with.

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1. Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

2. Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

3. Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

Step-by-step explanation:

Slope intercept form: $y = mx + b$

where:

$y$ = y-coordinate
$m$ = slope
$x$ = x-coordinate
$b$ = y-intercept

Standard form: $Ax + By = C$

$\textsf{1. as} \ m=2: \ \ y = 2x + b$

$\textsf{at} \ (6, 8): \ \ 8 = 2(6) + b$

$\implies b = -4$

Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

$\textsf{2. as} \ \ m = \dfrac12: \ \ y = \dfrac12x + b$

$\textsf{at} \ (4, 1): \ \ 1 = \dfrac12(4) + b$

$\implies b = -1$

Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

$\textsf{3. as} \ \ m = \dfrac45: \ \ y = \dfrac45x + b$

$\textsf{at} \ (1,5): \ \ 5 = \dfrac45(1) + b$

$\implies b = \dfrac{21}{5}$

Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

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