Determine the Diameter to the Nearest Inch of a Large Can of Tuna Fish

Algebra I Mutual Core Regents New York State Exam - August 2015

The following are questions from the past paper Regents High School Algebra one August 2022 Examination (pdf).
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Algebra I Common Core Regents New York Land Exam - August 2015

Algebra ane - August 2022 Regents - Q #i - 12

1. Given the graph of the line represented by the equation computations. f(x) = -2x + b, if b is increased by 4 units, the graph of the new line would be shifted 4 units
   
2. Rowan has $50 in a savings jar and is putting in $5 every calendar week. Jonah has $ten in his own jar and is putting in $15 every week. Each of them plots his progress on a graph with fourth dimension on the horizontal centrality and corporeality in the jar on the vertical axis. Which statement near their graphs is truthful?
   
3. To watch a varsity basketball game, spectators must purchase a ticket at the door. The cost of an adult ticket is $three.00 and the cost of a pupil ticket is $1.50. If the number of developed tickets sold is represented by a and pupil tickets sold by s, which expression represents the amount of money nerveless at the door from the ticket sales?
   
4. Which function could represent the graph of f(x)?
   
5. The toll of a pack of chewing glue in a vending machine is $0.75. The toll of a bottle of juice in the same machine is $one.25. Julia has $22.00 to spend on chewing gum and bottles of juice for her team and she must buy seven packs of chewing gum. If b represents the number of bottles of juice, which inequality represents the maximum number of bottles she tin can purchase?
   
6. Which graph represents the solution of y ≤ 10 + 3 and y ≥ -2x - 2?
   
7. The land of Republic of benin in W Africa has a population of 9.05 million people. The population is growing at a charge per unit of iii.1% each year. Which role can exist used to find the population 7 years from now?
   
8. A typical cell phone plan has a stock-still base fee that includes a certain computations. corporeality of data and an overage accuse for information use beyond the program. A cell phone plan charges a base of operations fee of $62 and an overage charge of $xxx per gigabyte of data that exceed 2 gigabytes. If C represents the toll and one thousand represents the total number of gigabytes of data, which equation could represent this plan when more than 2 gigabytes are used?
   
9. Find the equivalent expression.
   
10. Concluding week, a candle store received $355.60 for selling twenty candles. Small candles sell for $10.98 and large candles sell for $27.98. How many large candles did the store sell?
    
11. Which representations are functions?
    
12. If f(x) = √(2x+3)/(6x-5), then f(1/ii)=
    

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Algebra 1 - Baronial 2022 Regents - Q #13 - 24 13. The zeros of the part f(x) = 3x² - 3x - vi are
fourteen. Which recursively divers part has a offset term equal to 10 and computations. a common divergence of iv?
15. Firing a piece of pottery in a kiln takes place at dissimilar temperatures for different amounts of time. The graph below shows the temperatures in a kiln while firing a slice of pottery later on the kiln is preheated to 200°F.
16. Which graph represents f(x)?
17. If f(x) = tenⁱⁱ - 2x - 8 and g(x) = 1/iv 10 - 1, for which values of x is f(x) = g(ten)?
eighteen. Alicia has invented a new app for smart phones that two companies computations. are interested in purchasing for a 2-year contract
Company A is offering her $10,000 for the first month and volition increase the corporeality each calendar month past $5000.
Visitor B is offering $500 for the first month and will double their payment each month from the previous calendar month.
Monthly payments are made at the cease of each month. For which monthly payment will company B's payment first exceed company A'south payment?
nineteen. The 2 sets of data below represent the number of runs scored by 2 different youth baseball teams over the grade of a flavour.
Squad A: 4, 8, 5, 12, three, ix, five, 2
Team B: 5, 9, eleven, iv, half dozen, eleven, ii, 7
Which set of statements about the mean and standard deviation is truthful?
20. If Lylah completes the foursquare for f(x) = x² - 12x + vii in gild to find the minimum, she must write f(ten) in the general grade f(x) = (x - a)² + b. What is the value of a for f(x)?
21. Which argument virtually these functions is true?
22. For which value of P and West is P + W a rational number?
23. The solution of the equation (x + 3)² = 7 is
24. Which trinomial is equivalent to iii(x - ii)² - two(x - 1)?

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Algebra 1 - August 2022 Regents - Q #25 - 37 25. Each day Toni records the height of a establish for her science lab. Her information are shown in the table below.
The establish continues to grow at a abiding daily rate. Write an equation to correspond h(n), the height of the institute on the nth twenty-four hour period.
26. On the set of axes beneath, graph the inequality 2x + y > ane.
27. Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their biology class.
Rachel wants to model this data with a linear function. Marc wants to apply an exponential office. Which model is the better selection? Explain why you chose this model.
28. A commuter leaves home for a business trip and drives at a abiding speed of 60 miles per hour for 2 hours. Her car gets a flat tire, and she spends 30 minutes changing the tire. She resumes driving and drives at 30 miles per hour for the remaining one hr until she reaches her destination. On the set of axes below, draw a graph that models the commuter'south distance from domicile.
29. How many real solutions does the equation x² - 2x + five = 0 have? Justify your answer.
30. The number of carbon atoms in a fossil is given by the role y = 5100(0.95)¹⁰, where x represents the number of years since existence discovered.
What is the percentage of change each year? Explain how y'all arrived at your respond.
31. A toy rocket is launched from the footing direct upward. The pinnacle of the rocket above the ground, in feet, is given by the equation h(t) = -16t² + 64t, where t is the time in seconds. Make up one's mind the domain for this function in the given context. Explain your reasoning.
32. Jackson is starting an practise program. The start day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each 24-hour interval. Write an equation for T(d), the time, in minutes, on the treadmill on day d. Find T(6), the minutes he will spend on the treadmill on mean solar day 6.
33. Graph f(ten) = 10² and g(ten) = 2x for 10 ≥ 0 on the set of axes below. Country which function, f(10) or g(10), has a greater value when x = 20. Justify your reasoning.
34. Solve for x algebraically: 7x - 3(4x - 8) ≤ 6x + 12 - 9x. If 10 is a number in the interval [four,eight], country all integers that satisfy the given inequality. Explain how you determined these values.
35. The book of a large can of tuna fish can exist calculated using the formula V = πr²h. Write an equation to find the radius, r, in terms of Five and h. Determine the bore, to the nearest inch, of a large tin can of tuna fish that has a volume of 66 cubic inches and a elevation of 3.three inches.
36. The tabular array below shows the omnipresence at a museum in select years from 2007 to 2013. State the linear regression equation represented by the data tabular array when x 0 is used to represent the year 2007 and y is used to represent the omnipresence. Circular all values to the nearest hundredth. State the correlation coefficient to the nearest hundredth and determine whether the data advise a strong or weak association.
37. A rectangular picture measures vi inches by 8 inches. Simon wants to build a wooden frame for the picture so that the framed picture takes upwards a maximum expanse of 100 square inches on his wall. The pieces of woods that he uses to build the frame all accept the aforementioned width. Write an equation or inequality that could be used to make up one's mind the maximum width of the pieces of wood for the frame Simon could create. Explain how your equation or inequality models the situation. Solve the equation or inequality to determine the maximum width of the pieces of wood used for the frame to the nearest tenth of an inch.

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