46:31 A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller
number and 1. How many solutions are possible for this situation?
VA
O Infinitely many solutions exist because the two situations describe the same line.
O Exactly one solution exists because the situation describes two lines that have different slopes and different y-
intercepts
O No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
O Exactly one solution exists because the situation describes two lines with different slopes and the same y-
intercept

mental cunning

explanation:

he is often referred to as a man of twists and turns

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft