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1 year ago

6

Simplify : p^2-p-12/p^2-10p+24

1 answer:

Elza [17]1 year ago

7 0

Step-by-step explanation:

$= \frac{ {p}^{2} - p - 12 }{ {p}^{2} - 10 + 24} \\$

$= \frac{ {p}^{2} - (4 - 3)p - 12 }{ {p }^{2} - (6 + 4)p + 6 \times 4} \\$

$= \frac{ {p}^{2} - 4p + 3p - 4 \times 3 }{ {p}^{2} - 6p - 4p + 6 \times 4 } \\$

$= \frac{p(p - 4) + 3(p - 4)}{p(p - 6) - 4(p - 6)} \\$

$= \frac{(p + 3)(p - 4)}{(p - 4)(p - 6)} \\$

$= \frac{p + 3}{p - 6} \\$

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3 years ago

Mr. Mole left his burrow and started digging his way down at a constant rate. Time (minutes) Altitude (meters) 666 -20.4−20.4min

Juli2301 [7.4K]

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Step-by-step explanation:

We have been given Mr. Mole left his burrow and started digging his way down at a constant rate.

We are also given a table of data as:

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6 -20.4

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First of all, we will find Mr. Mole's digging rate using slope formula and given information as:

$m=\frac{y_2-y_1}{x_2-x_1}$ , where,

$y_2-y_1$ represents difference of two y-coordinates,

$x_2-x_1$ represents difference of two corresponding x-coordinates of y-coordinates.

Let $(6,-20.4)$ be $(x_1,y_1)$ and $(9,-27.6)$ be $(x_2,y_2)$ .

$m=\frac{-27.6-(-20.4)}{9-6}$

$m=\frac{-27.6+20.4}{3}$

$m=\frac{-7.2}{3}$

$m=-2.4$

Now, we will use slope-intercept form of equation to find altitude of Mr. Mole's burrow.

$y=mx+b$ , where,

m = Slope,

b = The initial value or the y-intercept.

Upon substituting $m=-2.4$ and coordinates of point $(6,-20.4)$ , we will get:

$-20.4=-2.4(6)+b$

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$-20.4+14.4=-14.4+14.4+b$

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Since in our given case y-intercept represents the altitude of Mr. Mole's burrow, therefore, the altitude of Mr. Mole's burrow is $-6$ meters.

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3 years ago

Read 2 more answers