Let triangle MNP right angled at M , altitude MH . a) Prove that AHNM is similar to AMNP.
b) Prove the relation MH? = NH. PH.
c) Take an arbitrary point E on edge MP ( E is different from M ; P ), draw a point F on edge MN such that FHE = 90° , EF intersects MH at point I. Prove that ANPH is similar to AMEH and FMI = FEH .
d ) Determine the position of point E on MP so that the area AHEF reaches the minimum value .

Give the functions f(x) = |x + 2| - 3, what is the domain? a,b,c, or d all real numbers x > 2 x < -2 all real numbers and x cannot equal to 2

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.

Point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places?