5. (10 points) a pythagorean triple is a triple a, b, cof positive integers satisfying the pythagorcan theorem ab2 = 2. a pythagorean triple is called primitive if gcd(a, b, c) = 1 recall from assignment 1 that if a2 +b2 = 2, then a and b cannot both be odd. let a, b, c be a primitive pythagorean triple. then a and b cannot both be even, since otherwisc c is also even and gcd(a, b, c) 2. hence, exactly adopt the convention that a is odd and b is even (and thus c is odd) one of a and b is odd and the other is even. we (a) let s and t be odd integers such that s> t 2 1 and gcd(s, t) = 1. prove that b a= 2 2 forms a primitive pythagorean triple a, b, c (b) let and y be positive integers such that gcd(r, ) 1, and suppose that their product xy is a square. prove that both r and y are squares. (hint. usc the fundamental theorem of arithmetic.) (c) let a, b, c be a primitive pythagorean triple where a, b, c e z, a and c are even. prove that there exist odd integers s and t where s > t> 1and gcd(s, t) = 1 such that a, b,c and show that c+b and c-b are both squares and relatively prime.) (d) find all (not just primitive) pythagoran triples a, b, c of positive integers where odd, and bis 2-b2(cb) (c - b) given by the formulas above. (hint. write a2 are c c 15 =

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

3.how is solving radical equations different than solving linear equations?

step-by-step explanation:

answer: plz put a pic in so i can answer it

step-by-step explanation:

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.