Algebra - math word problems
Number of problems found: 2654
- 1 page
1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?
- An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
- Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
- A bottle
A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh?
- The sum
The sum of five consecutive odd numbers is 75. Find out the sum of the second and fourth of them.
- Save trees
25 tons of old paper will save 1,600 trees. How many tons of paper is needed to save the 32 trees in the park?
- Aquarium height
How high does the water in the aquarium reach, if there are 36 liters of water in it? The length of the aquarium is 60 cm and the width is 4 dm.
- Cube surfce2volume
Calculate the volume of the cube if its surface is 150 cm2.
- The tower
The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
- Finite arithmetic sequence
How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?
- Prime factors
Factor the number 6600 into the product of prime numbers.
- Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
- Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
- Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order.
- Book reading
Suzan reads a book. If she read half an hour a day, she would read it in nine days. How many minutes does he have to read a day if he wants to read it three days earlier?
We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.
- Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
- Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.