EOY 2020 Algebra 1
Question: 1-2
Grace wants to buy some new clothes, but she cannot afford more than $75 before the sales tax is added. The blouses she wants are priced $17 each and the pants she wants are priced $25
each. Which inequality could be used to determine b, the number of blouses, and p, the number of pants Grace can afford?

The inequality is: 17*b + 25*p <= 75

Step-by-step explanation:

If she can't afford to pay more than $75, then the price of the purchase must be less or equall to that. The expression that represents the value of the purchase is given by the number of blouses by the price of each blouse added by the number of pants multiplied by the price of each pant.

price = 17*b + 25*p

Since the price must be less or equal to 75, then:

17*b + 25*p <= 75

The inequality is: 17*b + 25*p <= 75

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).

answer: -8.2562234e+13