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Veronika [31]
1 year ago
6

Simplify : p^2-p-12/p^2-10p+24​

Mathematics
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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Simplify and write answer without parentheses
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Apply the power 2 to the numerator and denominator, separately:

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The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and
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5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120

Let's find h with the quadratic formula:

\fbox {Quadratic formula:}  \frac{-b\pm\sqrt{b^2-4ac}}{2a}

h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation  

\fbox {Pythagorean equation:} <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17

H = 17

If we decrease the base and the height by 2 centimeters, we have  

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3

H' \approx 14.3

So, the hypotenuse decreases H - H' \approx 17 - 14.3 = 2.7

3 0
3 years ago
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