An accountant for a company is creating part of the fiscal budget for next year. She has $50,000 to allocate for salaries, insurance, and general expenses. Based on previous financial statements, she expects to spend eight times as much on salaries as on insurance. Also, general expenses historically cost 20% of the amount spent on salaries and insurance combined. a. Write a system of equations for the amount allocated to each category. (Make certain to clearly define any variables you use.) b. Write the system of equations as a matrix equation AX = B. c. Use an inverse matrix to solve the system of equations. How much is allocated to each category?

people employed | 1.10698 million people

yearly change | -26600 people (-2%)

workforce fraction | 0.8% (1 in 118)

median wage | $59430 per year (US dollars per year)

median wage yearly change | +$2370 per year (US dollars per year) (+4%)

50% range | $(45900 to 78210) per year

80% range | $(36720 to 102380) per year

Step-by-step explanation:

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).