Find the length of side x in simplest radical form with a rational denominator.

x=2√5

Step-by-step explanation:

1st method:

sin(30)=opposite/hypotenuse=√5/x

sin(30)x=√5

x=√5/sin(30)

x=2√5

2nd method:

cos(60)=adjacent/hypotenuse=√5/x

cos(60)x=√5

x=√5/cos(60)

x=2√5

3rd method:

This is a 30-60-90 triangle, so we can multiply the short side, √5, by 2, to get x=2√5

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5