# System of equations + expression of a variable from the formula - math problems

#### Number of problems found: 90

- In the

In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm^{2}. - 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? - Area and perimeter of rectangle

The content area of the rectangle is 3000 cm^{2}, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle. - 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. - Two-digit number

Digit sum of thinking two-digit natural number is 11. When it exchanging a sequence of digits, given a number which is 27 less than the thinking number. Find out which number I think. - 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? - 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? - Rectangles

The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle? - Rectangle field

The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m? - Lookout tower

How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now. - Rectangular triangle

The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle? - Two patches

Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide. What was the width of the - 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? - The tourist

The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone? - Two resistors

Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of - Faces diagonals

If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2 - The circumference

The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length? - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Non linear eqs

Solve the system of non-linear equations: 3x^{2}-3x-y=-2 -6x^{2}-x-y=-7

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