Nicky wants to surround an 11 in. by 5 in. painting with a frame that is w inches wide. Which quadratic function represents the combined area A of the picture and the frame?

The isosceles triangle has two sides of equal length, a, that sre longer than the length of the base ,b. the equation 2a+b=15.7 can be used to find the sides length. if one of the longer sides is 6.3 centimeters what is the length of the base

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Find the sum of 4x^{2} -4+6 and -7^{2} +3x+1