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irga5000 [103]
1 year ago
13

Which equation is made true by the opposite angles theorem?

Mathematics
1 answer:
Oksana_A [137]1 year ago
4 0

Solution

Step 1

The opposite angles of a parallelogram are equal:

Step 2

85\text{ + y  =  3y - 15}

The equation is made true by the opposite angles theorem is

85 + y = 3y - 15

or

y = 50

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\boxed{\pink{\sf (x + 3) \ is\ the \ LCM . }}

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\qquad (1)\: x^2 - 9 \\\\ \qquad (2)\:3x^3 + 81

And , we need to find the LCM , that is lowest common factor . So , let's factorise them seperately .

<u>Factorising</u><u> </u><u>x²</u><u> </u><u>-</u><u> </u><u>9</u><u> </u><u>:</u><u>-</u><u> </u>

= x^2 - 9 \\\\= x^2 - 3^2 \\\\ \red{= (x+3)(x-3)} \qquad\bf [Using \ a^2-b^2 = (a+b)(a-b) ]

<u>Factorising</u><u> </u><u>3x</u><u>³</u><u> </u><u>+</u><u> </u><u>8</u><u>1</u><u> </u>

= 3x^3 + 81\\\\= 3(x^3+27) \\\\= 3( x^3+27) \\\\ = 3(x^3+3^3) \\\\ \red{= 3 [ (x+3)(x^2+9-3x) ] } \qquad \bf{[ Using \ a^3+b^3=(a+b)(a^2+b^2-ab) ] }

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