System of equations + expression of a variable from the formula - practice problems - page 6 of 11
Number of problems found: 211
- Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Difference 7873
Find the first term and the difference of the sequence for which it holds: a1 + a6 = 39; a10 - a4 = 18
- Isosceles triangle
In an isosceles triangle, the arm's length and the length of the base are in a ratio of 3 to 5. What is the length of the arm? - Rectangular plot
The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the plot's perimeter is 36m. Find the area of the diagonal of the plot. - Divisors 7779
Two numbers are guessing. The second number is five times greater than the first number, and the square of the first number is equal to 3/5 of the second number. Find the sum of the two numbers and all its divisors. - Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle? - Rectangle 7768
The base of a cuboid is a rectangle. The ratio of its length to width is 3:2. The length of the rectangle of the base is in the ratio of 4:5 to the height of the block. The sum of the lengths of all the edges of the block is 2.8m. Find: a) the surface of
- Two cyclists 2
At the same time, two cyclists left towns A and B at constant speeds. The first one goes from town A to town B, and the second one from town B to town A. At one point during the trip, they met. After they met, the first cyclist arrived at town B in 36min, - Circumference 7655
The triangle has a circumference of 35 cm. One side is four times longer than the other and, at the same time, 1 cm longer than the third. Determine the sides of the triangle. - Calculate 7653
The block volume is 900cm3, and the surface is 600cm². The area of one wall is 60cm². Calculate the length of edges a, b, and c. - Grandfather 7622
My grandfather says, "My son and I are 100 years old, my son and my grandson are 62 years old, and my grandson and I are 80 years old together." How old is your grandfather? - Circumference 7615
The sides of the rectangle are in a ratio of 3:5. Its circumference is 48 cm. Calculate the length of its diagonal.
- Calculate 7572
At eight in the morning, a cyclist went from city K to city L. He stayed in city L for 4.25 hours and returned home at 3:00 p.m. Calculate the distance between cities K and L if the cyclist traveled to city L at a speed of 12 km/h and from city L to city - Pupils
There are 32 pupils in the classroom, and girls are two-thirds more than boys. a) How many percents are more girls than boys? Round the result to a whole percentage. b) How many boys are in the class? c) Find the ratio of boys and girls in the class. Writ - Differing 7391
The product of two numbers differing by four does not change when we decrease the larger number by two and increase the smaller number by one. What are the numbers? - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7 - Employed 7292
Mr. Janda's factory employs three times as many men as women. There are 190 fewer women employed in this factory than men. How many men and women are employed in this factory?
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