Analyze the diagram below and complete the instructions that follow. find the unknown side lenght x. write your answer in simplest radical form.

I'm going to work from left to right here, starting with the base of the largest triangle and ending with x. Pay close attention to the sides I am describing since there are no distinctive values for each vertex. The base of the largest triangle is also the hypotenuse of the one next to it. We will look at that missing side as the base of the large one to solve it. Since these are all right triangles, every single side/hypotenuse we solve for will use Pythagorean's theorem. The first missing side is found by 52^2-48^2=c^2 . Simplifying we get 2704 - 2304 = c^2. c^2 = 400 so c = 20. That first missing side is 20. Now we move to the next triangle in line. we have the hypotenuse of that triangle as 20 and the base as 12. The formula to find the missing side is 20^2-12^2=c^2 and c^2=256. c = 16. 16 is the length of that whole side, but that whole side is actually the bases for those 2 small triangles. Before we can solve for x we have to find out what the base of the larger of the 2 triangles is and subtract that from 16 to find the base of the triangle with x in it. Got that? The hypotenuse is 13 and the height is 5, so the formula to find the base of that triangle is 13^2-5^2=c^2 and 169-25=c^2 so 144=c^2 and c = 12. That means that the base of the triangle with x in it is 16 - 12 which is 4. Now we have the base as 4 of that triangle and the height as 5, so we solve for x: 4^2+5^2=x^2 and 25+16=x^2 so x^2=41 and finally we have that x=\sqrt{41} . That is the simplest radical form, so that's your answer!

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

hi how are you doing today? if you ever need just tell me

step-by-step explanation: