# Tutor profile: Charles M.

## Questions

### Subject: Geometry

Johnny is building a triangular gate, Gate B. On a previous project he built a triangular gate, Gate A, where all of the angles were equal. On his current gate project, Gate B, one of the angles of the gate is 14 degrees less than one of the angles of the previous gate, Gate A. Gate B also has another angle that is 16 degrees less than ne of the angles of the previous gate, Gate A. Find all of degrees of all three angles of Gate B. Also the two shorter sides of the gate a 5 ft. and 7 ft. What is the length of the longest side?

-First draw Gate A as a triangle with three congruent angles. *This makes Gate A an equilangular triangle, which means that all three angles are 60 degrees. (Triangle Sum Theorem) *This means that the two given angles of Gate B are $$x-14$$ and $$x-16$$, where x is 60 degrees. *This means that the two angles of Gate be are 46 degrees and 44 degrees. *Since the two angles added together is 90 degrees, this means that the third angle of Gate B is 90 degrees. (Triangle Sum Theorem) *This means Gate B is a right triangle. *Therefore the Pythagorean Theorem can be used to find the length of the longest side (the hypotenuse), $$a^2+b^2 = c^2$$. This means that $$5^2 + 7^2 = c^2$$ $$ 25+49=74$$ $$ c^2=74$$ $$ \sqrt{c^2} $$ = $$\sqrt{74} $$ $$c = \sqrt{74} $$ is the hypotenuse

### Subject: Basic Math

$$ 3x^2 + 4x - 6x + 2x = 27 $$

$$ 3x^2 + 4x - 6x + 2x = 27 $$ = $$ 3x^2 + 0 = 27 $$ $$ 3x^2 = 27 $$ $$ x^2 = 27 / 3 $$ or $$ x^2 = \frac{27}{3} $$ $$x^2 = 9$$ $$ \sqrt{x^2} $$ = $$ \sqrt{9} $$ $$ x = 3 $$

### Subject: Algebra

If $$ x = -2 $$ And $$ 2x + 4 - 6 + 3x = b $$ And $$ 3x + 5b - 4 = y $$ And $$ 2b + y - 4y + 5x + 4 = g $$ What is g?

If $$ x = -2 $$ $$ 2x + 4 - 6 + 3x = b, then 2(-2) + 4 - 6 + 3(-2) = -4 + 4 - 6 + (-6) = -4 + 4 - 6 - 6 = -12 $$ Then $$ b = -12 $$ 3x + 5b - 4 = y, then 3(-2) + 5 (-12) - 4 = -6 + (-60) - 4 = -6 - 60 - 4 = -70 Then $$ y = -70 $$ 2b + y - 4y + 5x + 4 = g, then 2(-12) + (-70) - 4(-70) + 5(-2) + 4 = -24 - 70 + 280 - 10 + 4 = 180 Then final answer is $$ g = 180 $$

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