30 x−5+6y^12 z−8 = 10 x−6+6y^5 z^4 , and 30 xy^12 z−8 = 10 y^5 z^4 . Dividing both sides by 30y^12 z−8, you have
and thenand 19 . B
The slope m of a line that goes through the points (x 1 ,y 1 ) and (x 2 ,y 2 ) is given by .
The slope of PQ is . Since PQRS is a square, QR is perpendicular to PQ. When two
lines are perpendicular and the lines are not parallel to the coordinate axes (the coordinate
axes are the x-axis and the y-axis), the slopes of the lines are negative reciprocals. Since QR is
perpendicular to PQ, the slope of QR is the negative reciprocal of the slope of PQ. The slope
of QR is , which is 20 . C
When the tangent and the cotangent of an angle are both defined, the tangent and the
cotangent are reciprocals. So tan (3x) cot (3x) = 1.21 . E
Since 4 is a solution to q(x) = 0, x − 4 is a factor of q(x). Since 0 is a solution to q(x) = 0, x − 0 = x
is a factor of q(x).
So x(x − 4) is a factor of q(x).Now x(x − 4) = x^2 − 4 x. Choice (E) is correct.22 . D
Since f(x) = 5x^2 + 4, f(g(3)) = 5(g(3))^2 + 4. You know that f(g(3)) = 84. So 5(g(3))^2 + 4 = 84. Solve
this equation for g(3).