Equations practice problems - page 93 of 240
Number of problems found: 4793
- 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? - Quarantine cupcakes
Mr. Honse was baking quarantine cupcakes. Mrs. Carr made twice as many as Mr. Honse. Ms. Sanchez made 12 cupcakes, more than Mr. Honse. Suppose they put all their cupcakes together (which they can't because. of quarantine!), they would have 108 cupcakes. - Distance 27971
The distance between K & L is 150 km. At 8 AM, a car left place K at a speed of 40 km/h. At 9 AM, a second car drove towards him from location L at 75 km/h. At what time will they meet, and how far from L will it be? - Remaining
Petra went on a 4-day trip to Vienna with her aunt. On the first day of the trip, she spent a quarter of her pocket money, on the second day, two-fifths of the remaining money, on the third day, she spent a third of the entire amount of pocket money, and - One press
One press will produce one truck of respirators in 3.5 days and the second in 10 days. How long does it take to fill a truck while working together? - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How long is its longest side? - Lottery - eurocents
Tereza bets in the lottery and finally wins. She went to the booth to have the prize paid out. An elderly gentleman beside him wants to buy a newspaper but is missing five cents. Tereza is in a generous mood after the win, so she gives the man five cents - Traveling 27833
The truck drove at an average speed of 20 km/h and left Prague toward Liberec. At the same time, a bus left with him, traveling at an average speed of 30 km/h, and it arrived in Liberec 2 hours earlier than the truck. What is the distance between Prague a - Right-angled triangle
The right-angled triangle XYZ is similar to the triangle ABC, which has a right angle at the vertex X. The following applies: side a = 9 cm, x=4 cm, x = v-4 (v = height of triangle ABC). Calculate the unknown side lengths of both triangles. - Cleaning 27663
During the pool cleaning, two drains and one inlet were opened. The first outflow would empty the pool in 6 hours, the second outflow would fill it in 9 hours, and the inflow would fill it in 12 hours. How long will it take to empty if the drains are open - Intersections 3
Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0 - Concentration 27551
We need a 4% solution of H2O2 (hydrogen peroxide) for the disinfection solution. We only have a 40% solution available. How much water must we add to 100ml of the original solution to obtain the desired concentration? - Between 27501
Dan and Honza live 4 km from each other. They agreed to meet on the way between the two homes. Dan went out at 2 p.m. at a speed of 5 km/h. Honza rode towards him on a bicycle at 15 km/h. What time did they meet, and how far did John travel? - Beer tapping
When checking compliance with the beer tapping, it was found that 60% of the offered beers were underfilled. The others were fine. Thus, instead of 0.5 l, the volume was 4.4 deciliters on average. What was the volume of one average underfilled beer? - Original 27411
The tourist section planted 145 trees, 16% more than planned. What was the original plan? - Calculate 27351
There were goats and chickens in the yard. The total number of heads was 15, and the total number of legs was 40. Calculate the number of hens. Every animal has all its legs. - Readers
Readers borrowed 220 books from the library during the first three days. On the second day, readers borrowed half as many books as on the first day and, at the same time, 20 fewer books than on the third day. Depending on the quantity x, express the numbe - Three workshops
One workshop can complete the task in 48 days, the second in 30 days, and the third in 20 days. In how many days would the task be completed if all workshops worked?
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