System of equations + quadratic equation - math problems
Number of problems found: 88
- Two simple
Two simple fraction 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 feet 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?
- 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 content. 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.
- 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 hire a guide. Everyone will pay the same amount. If there are two less 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.
- Sequences AP + GP
The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.
- The cylinder
In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm2 and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
- Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm2 and volume V = 192 cm cubic. Calculate its radius and height.
- Two grandmothers
Two grandmothers went to sell eggs at the market, and they had a total of 100. When they sold all the eggs, they made the same money. The first grandmother says to the second: "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmot
- Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence.
The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.
- Area and perimeter of rectangle
The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
- Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
- Dimensions of the trapezoid
One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2
- Intersections 3
Find the intersections of the circles x2 + y2 + 6 x - 10 y + 9 = 0 and x2 + y2 + 18 x + 4 y + 21 = 0
- Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more of them were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now.
- An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
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