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Khurshid A.

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Trigonometry

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Question:

The area of a right triangle is 50. One of its angles is 45 degree. Find the lengths of the sides and hypotenuse of the triangle.

Khurshid A.

Answer:

The triangle is right and the size one of its angles is 45 degree; the third angle has a size 45 degree and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse. Area = (1/2)x^2 = 50 , solve for x: x = 10 We now use Pythagoras to find H: x^2 + x^2 = H^2 Solve for H: H = 10 sqrt(2)

Basic Math

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Question:

What are the values of the real numbers a, b and c if the equation - 4 x(x + 5) - 3(4x + 2) = a x^2 + b x + c is true for all values of x?

Khurshid A.

Answer:

Expand the left side of the given equation and group like terms. - 4x^2 - 20x - 12 x - 6 = a x^2 + b x + c - 4x^2 - 32x - 6 = a x^2 + b x + c The two polynomials on each side of the equation are equal if the corresponding coefficients (of the same power of x) are equal. Hence Answer: a = - 4 , b = - 32 and c = - 6

Algebra

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Question:

Find the slope of the line passing through the points (-1, -1) and (2, 2).

Khurshid A.

Answer:

Given the points (-1, -1) and (2, 2), the slope m is given by m = (y2 - y1) / (x2 - x1) = (2 - -1) / (2 - -1) = 1

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