Triangle ABC and triangle DEF are similar. What is the measure of side DF?

Two times a number plus three times another number equals 4. three times the first number plus four times the other number is 7. find the numbers

Circle d circumscribes abc and abe. which statements about the triangles are true? statement i: the perpendicular bisectors of abc intersect at the same point as those of abe. statement ii: the distance from c to d is the same as the distance from d to e. statement iii: bisects cde. statement iv: the angle bisectors of abc intersect at the same point as those of abe. a. i only b. i and ii c. ii and iv d. i and iii e. iii and iv

Find the maximum value of p= 4x + 5y subject to the following constraints :