In this diagram, ray ea is perpendicular to ray ed and ray eb bisects angle aec. given that the measure of angle aeb=4x+1 and the measure of angle ced=3x, find x and the measure of angle bec.

 x=8

 ∠BEC =33°  

Step-by-step explanation:

Given : Ray EA is perpendicular to ray ED .

It means ∠AED= 90°  [Perpendicular amkes right angles with the line]  (1)

Also, Ray EB bisects angle AEC.

i.e. ∠AEB=∠BEC

Given that the measure of ∠AEB=4x+1  , then  ∠BEC =4x+1   ......(2)

The measure of ∠CED=3x.                               (3)

Now, ∠AED=∠AEB+∠BEC+∠CED   [From the figure below]

Then, ∠BEC =4(8)+1=33°  

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2