The price of an item has been reduced by 40 %. The original price was $82 .

Me, prove a quadrilateral with vertices g(1,-1), h(5,1), i(4,3) and j(0,1) is a rectangle using the parallelogram method and a rectangle method.

The sum of the first eight terms of an arithmetic progression is 9m + 14. the fifth term of the06 progression is 2m - 6, where m is a constant. given that the first term of the progression is 26,find the value of the common difference, d and thevalue of m.

Your vet has placed your pet on a diet. the diet is to contain at least 12 mg of fat and at least 14 mg of protein per serving. these requirements are to be obtained from two food sources. source a contains 2 mg of fat and 2 mg of protein per serving. source b contains 1 mg of fat and 3 mg of protein per serving. if source a sells for $1.28 per serving and source b sells for $1.12 per serving, how many servings of each type should be purchased to satisfy the requirements at minimal cost?