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线性建模・建立方程挑战
A polygonal chain is a connected series of line segments whose length is defined as the sum of the lengths of the line segments it is made of. A polygonal chain with a length of 33 centimeters (cm) is extended by adding line segments that each have a length of \( 8−r \) cm. Which function \( f \) represents the total length, in cm, of the extended polygonal chain after x line segments are added?
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线性建模・建立方程挑战
A chemist combines 30 grams of compound A, 45 grams of compound B, and x grams of compound C. The resulting mixture has a mass of 135 grams. What is the value of x?
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线性建模・建立方程挑战
The table gives the number of hours, \( h \), of labor and a plumber's total charge \( f\left(h\right) \), in dollars, for two different jobs.
There is a linear relationship between \( h \)and \( f\left(h\right) \). Which equation represents this relationship?
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线性建模・建立方程挑战
A carnival receives $10 for each adult admission ticket sold and $5 for each child admission ticket sold. On a particular day, the carnival received a total of $4,100 from selling adult and child admission tickets. If 220 adult admission tickets were sold on that day, how many child admission tickets were sold?
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线性建模・建立方程挑战
Hassan put up wire fencing along each edge of a rectangular garden with a length of x feet and a width of y feet. Hassan put up a total length of 44 feet of wire fencing. Which equation represents this situation?
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线性建模・建立方程挑战
A linear function \( f \) gives a company's profit, in dollars, for selling x items. The company's profit is $190 when it sells 4 items, and its profit is $670 when it sells 10 items. Which equation defines ?
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线性建模・建立方程挑战
The cost of renting a piece of construction equipment for up to 10 days is $230 for the first day and $115 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the equipment for x days, where x is a positive integer and \( x\le10 \)?
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线性建模・建立方程挑战
The roofs on the buildings of a public garden are designed to allow water to drain into the garden. The table shows the relationship between the area x, in square feet, of a roof and the amount of water \( f\left(x\right) \), in gallons, drained from the roof into the garden over a certain period of time. Which equation could define \( f \)?
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线性建模・建立方程挑战
In 2010, a skating team had a total of 37 skaters, each classified as either advanced or intermediate. From 2010 to 2020, the number of advanced skaters on the team increased by approximately 23%, and the number of intermediate skaters on the team increased by approximately 33%. The total number of skaters on the team increased by approximately 27%. Which equation best represents this situation, where a represents the number of advanced skaters on the team in 2010 and b represents the number of intermediate skaters on the team in 2010?
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线性建模・建立方程挑战
The value of y is 8 more than twice the value of x. Which equation represents y in terms of x ?
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线性建模・建立方程挑战
A park rents beach umbrellas to visitors. The park earns revenue of $15 for each beach umbrella they rent for the day. On Wednesday, the park earned $435 in profit from renting beach umbrellas after paying daily expenses of $150. How many beach umbrellas did the park rent on Wednesday? (profit = total revenue - total expenses)
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线性建模・建立方程进阶
A machine makes 8-inch, 9-inch, and 3-inch parts. During a certain day, the number of 8-inch parts that the machine makes is 4 times the number n of 9-inch parts, and the number of 3-inch parts is 30. During this day, the machine makes 100 parts total. Which equation represents this situation?
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