Algebra - problems - page 81
- Two rectangles
I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calcu
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
- The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
- The tank
The tank had 9 inflows to be filled in 21 days. After 9 days, 3 trips out. How many days did the remaining 6 tributaries fill the tank?
Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send?
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
- Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?
- Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
- Car driver
The car driver is in town A and is scheduled to be in town B at a specified hour. If it travels at an average speed of 50km/h, it will arrive in city B 30 minutes later. But if he travels at an average speed of 70km/h, he would arrive half an hour earlier
1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes?
- Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
- Quadrangular pyramid
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
More than 30 and less than 60 dinosaurs have met at the pond. A quarter of them bathed and 1/7 saws and the rest gripped. How many were at the pond? How many were there?
- Exponential equation
Determine the value of having y in the expression (3^y): (4^-1)=36.Y is a natural number greater than zero.
- The train
The train passed the observer in the 20s and passed through a 1500m tunnel in 2 minutes. Calculate the speed (km/h) and train length.
- Inscribed circle
Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
- Rate or interest
At what rate percent will Rs.2000 amount to Rs.2315.25 in 3 years at compound interest?
- CuSO4 mixture
How many grams of solid CuSO4 we have to add to 450g of 15% CuSO4 solution to produce a 25% solution?