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2 years ago

Please help!!!!!!!!!!!

Mathematics

1 answer:

boyakko [2]2 years ago

4 0

Answer:

(7√6)/2

Step-by-step explanation:

The side ratios in these special triangles are ...

30°-60°-90° triangle: 1 : √3 : 2

45°-45°-90° triangle: 1 : 1 : √2

This tells you the length of the horizontal line is 7√3, and the value of x is ...

(7√3)/√2 = (7√6)/2

_____

<em>Additional comment</em>

Call the length of the horizontal line "y". Then the given ratios tell you ...

7 : y = 1 : √3 ⇒ y/7 = √3/1 ⇒ y = 7√3

and

x : y = 1 : √2 ⇒ x/y = 1/√2 ⇒ x = y/√2

When we rationalize the denominator, we get ...

x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2

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For this case we have the following equation:

$\frac {5} {6} (2x + 12) -8 = 4- (x + 1)$

We apply distributive property on the left side of the equation:

$\frac {5 * 2} {6} x + \frac {5 * 12} {6} -8 = 4- (x + 1)\\\frac {10} {6} x + \frac {60} {6} -8 = 4- (x + 1)$

We simplify the left side of the equation:

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Different signs are subtracted and the major sign is placed.

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On the right side we must take into account that:

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So:

$\frac {5} {3} x + 2 = 4-x-1\\\frac {5} {3} x + 2 = 3-x$

We add x to both sides of the equation:

$\frac {5} {3} x + x + 2 = 3\\\frac {5 * 1 + 3 * 1} {3} x + 2 = 3\\\frac {5 + 3} {3} x + 2 = 3\\\frac {8} {3} x + 2 = 3$

We subtract 2 from both sides of the equation:

$\frac {8} {3} x = 3-2\\\frac {8} {3} x = 1$

We multiply by 3 on both sides of the equation:

$8x = 3$

We divide by 8 on both sides of the equation:

$x = \frac {3} {8}$

Thus, the solution of the equation is:

$x = \frac {3} {8}$

Answer:

$x = \frac {3} {8}$

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