77. The mass of a radioactive sample is given by M(t)=M(0) 10-4, where t is the time in years, M, is the initial mass, and k is a constant. If 400 grams of
this material decays to 40 grams in 10 years, what is the value of k?

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step-by-step explanation:

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(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