A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p ? (A) 12 (B) 15 (C) 20 (D) 22

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.

we know that

1) the inscribed angle measures half of the arc it comprises.

so

m∠dgf= > expression

2) the opposite angles in an inscribed quadrilateral are supplementary angles

so

m∠dgf=

m∠dgf=°

substitute in the expression to find the value of arc ef

therefore

the answer is

the measure of the arc ef is

x=3y-6

step-by-step explanation:

solve for   x by simplifying both sides of the equation, then isolating the variable.