The hypotenuese of an isosceles right triangle is 16 inches. the midpoints of its sides are connected to form an inscribed triangle, and this process is repeated, creating a third triangle inscribed in the previous one. find the sum of the areas of these triangles if this process is continued infinitely.

  256/3 = 85 1/3 square inches

Step-by-step explanation:

The dimensions of the first inscribed triangle are 1/2 those of the original, so its area is (1/2)² = 1/4 of the original. The area of the original is ...

  A = (1/2)bh = (1/2)(16/√2)(16/√2) = 64 . . . . square inches

The sum of an infinite series with first term 64 and common ratio 1/4 is ...

  S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

  = 64/(1 -1/4) = 64(4/3) = 256/3 . . . . square inches

The sum of the areas of the triangles is 256/3 = 85 1/3 square inches.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

question

what is the value of the third quartile of the data set represented by this box plot? a. 19 b. 21 c. 26 d. 29

answer

c