On a coordinate plane, 2 lines are shown. The first solid straight line has an equation of y greater-than-or-equal-to negative one-fifth x + 1, has a negative slope, and goes through (negative 5, 2) and (0, 1). Everything above the line is shaded. The second dashed solid line has equation y less-than 2 x + 1, has a positive slope, and goes through (negative 2, negative 3) and (0, 1). Everything to the right of the line is shaded.

Which ordered pairs make both inequalities true? Check all that apply.

(–2, 2)

(0, 0)

(1,1)

(1, 3)

(2, 2)

Given that ot =5, xt=12, and ox= 13 is xy tangent to circle o at t? explain.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Agroup of student volunteers participates in a study designed to assess several behavioral interventions for improving output in a repetitive task. prior to the beginning of the study, all volunteers unknowingly observed, and their output is measured. at the beginning of the study, prior to any intervention, the volunteers perform the same task under the observation of a study administrator, and their overall output increases. which of the following terms describes this phenomenon? a. simpson's paradox b. hawthorne effect are d. novelty effect d. pygmalion effect e. observer-expectancy effect