Reason + quadratic equation - problems
- MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
- Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
The root of the equation ? is: ?
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
Trolleybus line No. 207 measured 20 km. If the trolleybus go faster by 9 km/h, the way there and back would is shorter by 20 minutes. Calculate the trolleybus speed and how much time it takes a return trip.
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump?
- Do you solve this?
Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
- Euler problem
Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
- Rectangle diagonals
It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?
- Secret number
Determine the secret number n, which reversed decrease by 16.4 if the number increase by 16.4.
Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
- Triangle ABC
Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
The square of the first number is equal to three-fifths of the second number. Determine both numbers if you know that the second number is 5 times greater than the first, and neither of numbers is not equal to zero.
- Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
- Four integers
Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
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