Quadratic equation + system of equations - practice problems - page 2 of 8
Number of problems found: 149
- A speedboat
A speedboat goes 900 km against a current of 25 km/hr. Its trip took 10 minutes longer than it would have taken to travel with the current. What is the speedboat's speed in still water? - Determine 73454
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - Calculate 70804
The garden is a right triangle fenced with a 364 m fence length. The shorter slope of the triangle is 26 m long. Calculate the area of this garden. - Consecutive 69904
The three numbers that make three consecutive members of an arithmetic sequence have a sum of 60 and a product of 7500. Find these numbers.
- Intended 63664
Farmers had to sow 200 hectares of fields. They reduced the planned sowing time by two days while planting 5 hectares more each day than intended. How many days did the sowing last? - An integer
An integer is 17 more than five times another. If the product of the two integers is -6, then find the integers. - The same book
Alexander and Blanka bought the same book that had 240 pages. Blanka read four pages more a day than Alexander. Blanka read it before Alexander. Alexander read the book both weekend days longer. Using an equation or system of equations, calculate how many - 11990 perimeter RT
A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length. - The ratio 7
The ratio of the sides of two squares is 4:5 if the sum of their areas is 180 cm². Find the sides of the two squares.
- Two simple
Two simple fractions have the product of 3/10. When the smaller fraction is divided by the bigger fraction, the quotient is 5/6. What are the two fractions in simplest form? - One leg
One leg of a right triangle is 1 foot longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle. - Two workers
One worker makes a part 4 hours and the second 9 hours later than they would make the same part together. How long does it take for each worker to make the part himself? - Consecutive 46781
We get three consecutive GP members if we subtract the same number from 33, 45, and 63. Determine this GP and calculate its fifth member. - Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base.
- The block
The block, the edges formed by three consecutive GP members, has a surface area of 112 cm². The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block. - Perpendicular 41811
Calculate the area of a right triangle whose longer perpendicular is six dm shorter than the hypotenuse and three dm longer than the shorter perpendicular. - The sides
The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle. - The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - Tourists
Tourists hire a guide. Everyone will pay the same amount. If there are two fewer of them, they will pay 14 crowns more, and if there are three more, they will pay 14 crowns less. How many tourists are there and how much have the guides paid?
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