System of equations + expression of a variable from the formula - practice problems - page 4 of 11
Number of problems found: 211
- Dimensions of the trapezoid
One of the trapezoid bases is one-fifth larger than its height, and the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2 - Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4]. - Triple and quadruple rooms
Up to 48 rooms, some of which are triple and some quadruple, accommodated 173 people so that all beds are occupied. How many triple and how many quadruple rooms were there? - Coins
The money - coins are minted from the hardest bronze, which contains copper and tin in a ratio of 41:9. How much copper and tin are in 2kg of bronze money?
- In the
In the rectangle ABCD, the distance of its center from line AB is 3 cm greater than from line BC. The circumference of the rectangle is 52 cm. Calculate the area of the rectangle. Express the result in cm². - Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now. - A bottle
A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh? - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Three-quarters 25931
Jarek went strawberry picking for a day. In the morning, he collected two-fifths of the required amount; in the afternoon, he collected 5 kg less than in the morning. In total, he collected three-quarters of the required amount. How many kilograms of stra
- Determine 25341
In a two-digit number, the number of tens is three more than the number of ones. If we multiply the original number by a number written with the same digits but in the reverse order, we get the product 3 478. Determine the actual number. - The rectangle
The rectangle has a circumference of 32 m. One side is 2 m longer than the other side. Calculate the side lengths of this rectangle. - The circumference
The circumference and width of the rectangle are in a ratio of 5:1. Its area is 216cm². What is its length? - Side lengths
In the triangle ABC, the height to side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b. - Wire fence
The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure?
- In a
In a triangle, the aspect ratio a: c is 3: 2, and a: b is 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides. - 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? - Trapezoid 20873
In the trapezoid ABCD (AB II CD) is α = 57 °, γ = 4β. Calculate the size of all interior angles. - Substitution 19793
Calculate in arithmetic sequence a1, d, s7, if: a1 + a4 + a6 = 71 a5 - a3 - a2 = 2 Hint: Use the substitution method when solving the system. Pay due attention to the "minus" signs in the second equation of the system. - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block.
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