Algebra - problems - page 69
- Body diagonal
The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
- Paper squares
The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
- Sides of triangle
Triangle has circumference 42 cm. Side a is 2 times shorter than side b and sice c is 2 cm longer than side a. Determine the sizes of sides of a triangle.
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
- Variance and average
Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx).
9 workers dig a canal 120 meters long for eight hours. For how long would be dig five workers canal 200 meters long?
- The pool
The pool has a volume of 40 m3 and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
- Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this.
8 employees complete the contract for 65 hours. After 17 hours, 3 employees had to leave for another job. How many more hours will the job on contract be fulfilled?
- Alcohol mixture
Three liters of 96 percent alcohol we set up a certain amount of distilled water to form a 54-percent alcohol. How many liters of distilled water were used?
- Isosceles trapezoid
Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
- Price saleoff
Shoes standing y euros. At first they were discounted by 12% and then 50% of the new amount. After this double cheapening the cost was exactly 22 euros. Determine the original price of shoes.
- Two trains
There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway
- Tailor master
There are less than 50m of textile in the tailoring workshop. When cutting on a blouse (consumption 1.5m), no textile is left. When using a cloth (consumption of 3.2m), no textile is left. How many meters of textile are in a tailor's workshop?
- Unknown amount of money
Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis.
- Comparing salaries
Spouses compared salaries. Mrs. Janka found that a 20% higher salary than Mr Jaroslav. Together earned € 1,430. How much they earn each of them?
- Water colors
Painting workshop attend 10 students. Eight students painted water colors and nine painted with tempera colors. How many students painted water colors and tempera at the same time?
- Unknown number
Determine the unknown number, which double of its fourth square is equal the fifth its square.
Tomas spent 60% of his savings for his weekly vacation. He was 32 € left. How many euros did he have before vacation?
- PC disks
Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks?