In trapezoid abcd the lengths of the bases are ad=7 and bc=5, and the length of diagonal ac is 6. the diagonals are perpendicular. find the measure of ∠bda, in degrees.

  ∠BDA = 30°

Step-by-step explanation:

If E is the point of intersection of the diagonals, ∆AED ~ ∆CEB. Then ...

  AE/AD = CE/CB

  AE/7 = CE/5 . . . . . . . .substitute given values for AD, BC

We also know that AE +CE = 6, so we have ...

  5·AE = (6-AE)·7 . . . . . substitute for CE and cross multiply

  12·AE = 42 . . . . . . . . . add 7·AE

  AE = 42/12 = 3.5 . . . . divide by 12

All of the angles at E are right angles, so angle BDA has the trig ratio ...

  sin(∠BDA) = AE/AD = 3.5/7 = 1/2

  ∠BDA = arcsin(1/2) = 30°

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week