Jeanne babysits for $6 per hour she also works as a reading tutor for $10 per hour she is only allowed to work 20 hours per week this week her goal is to make at least $75. use a system of inequalities to model the scenario above let x represent babysitting hours and y represent tutoring hours.

see the explanation

Step-by-step explanation:

Let

x------> represent babysitting hours

y ------> represent tutoring hours

we now that

The system of inequalities that model the scenario is

-----> inequality A

-----> inequality B

The solution is the shaded area between the positive values of x and y

see the attached figure

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).