What are the next three terms 4, 7/4,-1/2,-11/

{-29/4, -19/2, -47/4}

Step-by-step explanation:

Note that this is a decreasing arith. seq.  Each term is smaller than the previous term, the result of the subtraction of 2 1/4 (equivalent to 9/4).  

The fourth term is -11/4; subtracting 9/4 results in -20/4, or -5.

The fifth term is -20/4; subtracting 9/4 results in -29/4.

The 6th term is -29/4; subtracting 9/4 results in -38/4, or -19/2.

The 7th term is -38/4; subtracting 9/4 results in -47/4.

Thus, the "next three terms" following the first four terms are {-29/4, -19/2, -47/4}

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240