Math Is Fun Forum

Let ABCD and BEDF be two 2 times 3 rectangles that overlap, as shown. Find the area of the overlap.

ABCD is a square. Parallel lines m, n, and p pass through vertices A, B, and C, respectively. The distance between m and n is 12, and the distance between n and p is 17. Find the area of square ABCD

Let P be a point inside rectangle ABCD such that PA = 1, PB = 7, and PC = 8. Find PD.

Please provide a solution if possible. Thanks

I am stuck on these two problems, a solution would be greatly appreciated

Triangle ABC is a right triangle with right angle at A. Suppose

Points D, E, and F are the midpoints of sides

Many Thanks

I am stuck on this problem:

When the measures of the angles of a triangle are placed in order, the difference between the middle angle and smallest angle is equal to the difference between the middle angle and largest angle. If one of the angles of the triangle has measure 23 degrees, then what is the measure in degrees of the largest angle of the triangle?

Thanks for the help

Part 1:

Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.

Part 2:

Consider the functions
\[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]
Explain why f and g are not the same function.