Hallar las coordenadas de un punto P (x, y) que divida el segmento que determinan P1 (x1,y1) y P2 (x2,y2) en la relación r = P1P / PP2 a) P1 (4,-3), P2 (1,4), r = 2/1
b) P1 (5,3), P2 (-3,-3), r = 1/3
c) P1 (-2,3), P2 (3,-2), r = 2/5
d) P1 (0,3), P2 (7,4), r = - (2/7)
e) P1 (-5,2), P2 (1,4), r = - (5/3)
f) P1 (2,-5), P2 (6,3), r = 3/4

ab will be equal to

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752