Equations practice problems - page 245 of 251
Number of problems found: 5001
- Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - Rectangle
In rectangle ABCD with sides |AB|=19, |AD|=19, a perpendicular is drawn from point A to diagonal BD, meeting it at point P. Determine the ratio r = (|PB|)/(|DP|). - College
A dormitory has 73 rooms and 254 students. Some rooms are triple occupancy and some are quadruple occupancy. How many of each type of room are there, given that all rooms are fully occupied? - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the centre S[x₀, y₀] and the radius r of the circle. - Freedom
In the city are 2/4 of women married for 4/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number. - Pine
How much of a mixed forest will a ranger cut down, given the following instructions: "We are cutting down only pine trees, which currently make up 97% of our mixed forest. After the cutting, pine trees should constitute 92% of all remaining trees." - Trapezoid MO
Right-angled trapezoid ABCD has a right angle at vertex B. Given that |AC| = 12, |CD| = 8, and the diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Motion problem
One car travels from Martina to Levíc at 89 km/h. Another car travels from Levíc to Martina at 71 km/h. How many minutes before they meet will the two cars be 29 km apart? - Beer
After drinking three 10° beers in a short time, there are 5.2 g of alcohol in the blood of an adult weighing 5 kg. How much is this in per mille? - Ravens
In the tale of the Seven Ravens, there were seven brothers, each born exactly 4 years after the previous one. When the eldest was 4 times older than the youngest, their mother put a curse on all of them. How old were the seven brothers when their mother c - Class
When Pythagoras was asked how many students attended his school, he replied: "Half of the students study mathematics, a quarter study music, a seventh remain silent, and there are three girls." How many students did Pythagoras have at his school? - Motion
If you go at speed 6.2 km/h, you come to the station 52 minutes after leaving the train. If you bike to the station at speed 23 km/h, you come to the station 51 minutes before its departure. How far is the train station? - Radians
Convert 90° to radians. Write the result as a multiple of π. - Discount
A ladies' sweater was discounted twice: first by 8%, then by 8% of the new price. Its final price was 66 €. Determine the original price of the sweater. - Hypotenuse and height
In a right triangle is length of the hypotenuse c = 195 cm and height hc = 70 cm. Determine the length of both triangle legs. - Four pupils
Four pupils divided 765 euro so that the second received 50% less than the first, the third received 1/2 euro less than the fourth, and the fourth received 50 euro less than the first. How much did each of them receive? - Motion
A car and a bus set off toward each other from two locations 232 km apart. The car started at 6:20 at an average speed of 67 km/h. The bus started at 8:40 at an average speed of 74 km/h. When did they meet? How many kilometres had the bus travelled at the - Peroxide
How many litres of distilled water must a pharmacist add to 300 ml of 32.7% hydrogen peroxide solution to obtain a 2.8% gargling solution? - Vinegar
We need to dilute 36 litres of 9.1% vinegar solution to a 4.5% solution. How much water must be added? - Camp
Children are at a summer camp. 1/2 of them went on a trip, 1/5 went swimming, and 33 children remained in the room. How many children are at the camp?
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