Examples for secondary school students - page 178 of 237
Number of problems found: 4730
- Tangent length
There is a triangle ABC whose perimeter is 2 s (2 s = a + b + c), and the circle k (S, ρ) is the inscribed circle of the triangle. Calculate the length of the tangent of the circle k from point A. - EQ2
Solve a quadratic equation: 2x²- 2(x-7)²+5x=0 - Solve equation
Solve equation: [(a²)+3]1/2 + [(a²)-3]1/2 = 5 - Trapezoid
Trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Alfa beta gama
The triangle's interior angle beta is 10 degrees greater than the angle alpha, and the gamma angle is three times larger than the beta. Determine the size of the interior angles. - 3 masons
Three masons received 7,700 CZK. The second half received 1/2 more than the first, and the third twice more than the second mason. How much do they each have crowns? - Factory and divisions
The factory consists of three auxiliary divisions and a total of 2,406 employees. The second division has 76 employees less than the 1st division, and the 3rd division has 212 employees more than the 2nd. How many employees have each division? - Remuneration Total remuneration for workers is 47,000 CZK. The second worker received 20% more than the first and the third 4000 CZK less than the second employee. How many CZK does each receive?
- Eight palm
There grow eight palms by the sea. At the first sitting, one parrot, on the second two, on the third sits four parrots on each other, twice the previous parrots sitting on a previous palm. How many parrots are sitting on the eighth palm? - Boys and money
270 USD boys divided so that Peter got three times more than Paul, and Ivan had 120 USD more than Paul. How much was each received? - Boxes
Two hundred boxes have been straightened in three rows. The first row was 13 more than in the second, and the second was one-fifth more than in the third. How many boxes are in each row? - Tokens
The non-transparent bags contain red, white, yellow, and blue tokens. We pulled one token three times and returned it again, writing down all possibilities. - Blueberries 2
Helen and Martin collected eight liters of blueberries in two hours. How long will Helen take to collect the blueberries alone if we know that she takes 2.5 hours less than Martin? - Circle's chords
The circle has two chord lengths, 30 and 34 cm. The shorter chord is twice as far from the center as the longer one. Determine the radius of the circle. - Sweets
We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How many of these two candy types are necessary to prepare this mixture? - Resistance
Determine the bulb's resistance with the current 200 mA and is in a regular lamp (230 V). - White and black balls
There are seven white and three black balls in an opaque pocket. The balls are the same size. a) Randomly pull out one ball. What is the probability that it will be white? We pull out one ball, see its color, and return it to the pocket. Then we pull out - Cycling trip
At 8:00 AM, a group of children from a summer camp set off on a cycling day trip. After 9:00, the weather deteriorated sharply and the leader decided to send a bus along the same route to pick up the children. The bus departed at 10:00. When and at what d - Car and cyclist
The cyclist started from town at a speed of 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was the car? - Two planes
Two planes are flying from airports A and B, 420 km apart. The plane from A took off 15 minutes later and flew at an average speed of 40 km/h higher than the plane from B. Determine the average speed of these two aircraft if you know that it will meet 30
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