# Algebra - examples

- Simplify 2

Simplify expression: 5ab-7+3ba-9 - Intercept with axis

F(x)=log(x+4)-2, what is the x intercept - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - A square

A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal. - Diagonals

What x-gon has 54 diagonals? - Rectangles

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? - Three friends

Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together. - Book reading

If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book? - Three students

Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolved - 2 pipes

2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone? - The tank

The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank? - The sum 2

The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer. - The length

The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle. - 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? - Solid cuboid

A solid cuboid has a volume of 40 cm^{3.}The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - A man

A man spends 5/9 of his money on rent, and 5/16 of the remainder on electricity. If the final balance remaining is 550 find how much was spent on rent - Tank 11

When 150 litres has been drawn from a tank it is 3/8 full, how many litres will the tank hold? - 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 - Bottles

The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles? - Clothes

Danka and Janka collect clothes. Danka had 9 more than Janka, so she gave her 7. Which now has more cloth and how many?

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