A post office has a machine that can sort letters by zip code much more quickly than a 289 human. The machine scans the mail looking for zip codes, but is not always able to locate them . That means that every few seconds , one or more letters cannot be scanned and still need to be sorted by hand . There is a linear relationship between the number of minutes that the machine is working (x) and the typical number of letters that UNITED STATES cannot be scanned and must be sorted by hand POS Prem (V). A postal worker starts the machine at the beginning of her shift. She notices that after 15 minutes, 80 pieces of mail could not be scanned and must be hand-sorted. She notices that after 45 minutes, 170 pieces of mail could not be scanned. a. Determine the slope of this function. b. Interpret the slope using the problem context. C. Determine a function equation. d. What is the y-intercept of the function ? e . Interpret the y-intercept using the problem context . CUNY Start Algebra Core Curriculum - Fall 2022290 f. If the machine runs for 4 hours without a break, how many pieces of mail would we expert would need to be hand-sorted? bosd 8. Solve the following equation for x: x2 - x=20 low site borton a. x =10 bennear ed fort blugo b. x =4 or x =-4 c. x =5 or x =-5 d. x=5 or x =-4 e. x =4 or x =-5 Axetoo moldorg sof an 9. Solve for x. a. 11x -5 =72 b. 6x' = 48 c. 15 =-6x + 3 * d. - x2 +10= 6$400 bicycle is reduced in price by 13%. What is the sale price? 291 In order to make a profit and cover their expenses, a clothing store sells clothes for 60% more than the amount that they pay the manufacturers for the clothes. If the store paid $20 for a shirt, what would be the selling price of the shirt? 12. Determine the slope of the linear function which has the inputs and outputs shown in this table. X y 2 22 6 10 13. Determine an equation for the line that passes through the points (6, 3) and (4, -1).02 grocery store has 1200 square feet of floor space. The store then buys the neighboring building 303 ind expands by 75%. What is the amount of the increase in floor space? A rent-stabilized apartment in Manhattan rents for $2,000 per month. The landlord is permitted to raise the rent to market rates, and the rent increases 30%. The next year, the landlord raises the rent another 5%. What is the new monthly rent? saoass bluco nutwollot sift To 7. Multiply and simplify. a. - 3(x+8) b. ( m + 8 ) (m - 2) d. 5.3.98 C. (2x - 8)(3x - 2) e. 2a(a2 + 2a+ 6) f. (3x + 1ly)(3x2 -1ly)