Quadratic equation + system of equations - practice problems - page 2 of 8
Number of problems found: 150
- Calculate 78714
Calculate the size of the base and side of an isosceles triangle if the side is 1 cm longer than the base and the height to the base is 2 cm shorter than the side. - 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.
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