Equations practice problems - page 72 of 212
An equation is a statement that asserts the equality of two expressions, which are connected by the equals sign =. Solving an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation.Number of problems found: 4228
- Fulfilled 29001
Race A can fulfill the order in 12 days, and race B the same order in 18 days. How many days will the order be fulfilled if both plants work together? - 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 - Delivered 28881
They delivered the same number of cans of stuffed cabbage leaves and leche with sausage to the store. On the first day, they sold 10 cans of cabbage leaves and 85 cans of leche. So there were six times more cans of cabbage leaves than cans of leche. How m - Magic bag
The number of tolars in the magic bag doubled each time the prince crossed the bridge. But then the devil always conjured 300 tolars for him. When this happened for the third time, the prince had twice as much as he had in the beginning. How many tolars d
- Traveling 28813
The ship set sail at 6 A.M. and traveled at a speed of 16 km per hour. At 8:30 A.M., a speedboat was sent behind her, traveling 24 miles per hour. When will the boat catch up? - One-third 28793
Mom baked cheese and poppy seed buns. One-third of them, 26 buns, were poppy. How many buns did mom bake? - 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]. - Train delay
Due to a breakdown, the train lost 16 minutes standing on the track behind Brno. He "eliminated" this delay so that after the start, the 80 km long section went at a speed 10 km/h higher than originally planned. What speed was it, and what was it supposed - Sow barley
Farmers wanted to sow barley within 13 days. Due to the excellent weather, they exceeded the daily plan of sowing by 2 ha and therefore finished sowing grain in 12 days. How many hectares of land did they sow with barley?
- Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the square's side and the circle's arc. What is the ratio of the areas of the large and small squares? - Three-quarters 28581
Jarek went for a one-day strawberry picking. In the morning, he collected two-fifths of the required amount; in the afternoon, he collected 5 kilograms less than in the morning, and in total, he collected three-quarters of the required amount. How many ki - Personally 28573
At 9:00 a.m., a truck left town A at an average speed of 50 km/h to town B, 290 km from town A. In 1 hour and 20 minutes, a car drove behind him at an average speed of 75 km/h. At what time and distance from city B will the passenger truck catch? - Together 28411
Worker A will dig a trench in 12 days. Worker B will dig a trench in 18 days. How many days will it take them together?
- Individual 28401
In the first and second years, there are 58 pupils in a pile. In the first and third years, there are 57 pupils. In the second and third years, there are 59 pupils. How many students are there: a) In all of them, to the dromedary, b) In individual classes - Points in space
There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - Roots and coefficient
In the equation 2x² + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b. - Speeds 28051
A car will depart from place A at 1 PM at a speed of 72 km/h. At the same time, a truck speeds up 68 km/h from point B, which is 315 km away from point A. When and where will they meet?
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