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Step-by-step explanation:

her wage is $4.00 + s*0.5 so 7.25-4> s*.5== 3.25 > s*.5 == 6.5 > s

4+.50n>7.25 where n represents the # of students in each class. She would need at least 7 kids in each class to exceed minimum wage.

Step-by-step explanation: the class she teaches is 1 hour long and minimum wage is based on each hour. So if she worked for minimum wage, she would make 7.25 per hour. each class she teaches is also 1 hour long. She gets paid 4 dollars for teaching a one hour class, plus 50 cents for each student. Since she wants to make more than min. Wage the inequality would look like this: 4+.50n>7.25 because I set the amount she makes teaching the class to be greater than minimum wage. N represents the number of students in each class. If we solve for n then we get n>6.5. Obviously she can’t have 6.5 kids in a class so we round up to 7 kids. She would need at least 7 kids in each class to exceed minimum wage.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is