Examples for secondary school students - page 133 of 230
Number of problems found: 4582
- Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has an area of 10 cm². Find the area of the or - Peroxide
How many ml should we pour 30% of peroxide (H2O2) into 100ml H2O to give a 20% solution? - GP members
The geometric sequence has ten members. The last two members are 2 and -1. Which member is -1/16? - Cuboid walls
Suppose the areas of three adjacent faces of a cuboid are 8 cm², 18 cm², and 25 cm². Find the volume of the cuboid. - Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm. - Isosceles triangle
The leg of the isosceles triangle is 5 dm, and its height is 20 cm longer than the base. Calculate base length z.
- Account operations
My PHP 90,000 savings in a bank earns 6% interest in a year. If I deposit an additional PHP 10,000 at the end of 6 months, how much money will be left if I withdraw PHP 25,000 after a year? - Flowers 2
Cha cruz has a garden. The ratio of roses to tulips is 2:5, and the ratio of roses to orchids is 7:6. Cha Cruz wonders what the ratio of tulips to orchids is. If Cha Cruz has 183 plants, how many of each kind are there? - Boys to girls
The ratio of boys to girls at a party is 3:5. If six more boys arrived and four girls left the party, the ratio of boys to girls would be 5:6. How many people were at the party initially? - Associative law multiplication
You obtain a 20% discount in a warehouse, but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first) - Inverse matrix
Find out the inverse using Gauss elimination or the reduction method. A=[2/3. 1 -3. 1/3] - Calculate
Calculate the resulting speed of both vehicles after the accident of a car with a mass of m1 = 1.5 tons traveling at a speed of 100 km/h and a truck with a mass of m2 = 40 tons traveling at a speed of 90 km/h, if it is a head-on acci - Trigonometric formula
Determine the value of the function tg x (tangent) when cotan x = -0.8 (cotg or cotangent); x holds in the second quadrant) - SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The viewer can see the PQ line at a 107°22' viewing angle. The observer's distance from P is 271 m. Find the viewing angle of P and the observer.
- The pond
We can see the pond at an angle of 65°37'. Its endpoints are 155 m and 177 m away from the observer. What is the width of the pond? - Sphere from tree points
Equation of sphere with three-point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Square root 2
If the square root of 3m² +22 and -x = 0, and x=7, what is m? - Expressions 3
If k(x+6)= 4x² + 20, what is k(10)=? - Octane value
I loaded 10L 95 octane gasoline and 5L 100 octane gasoline. What is the resulting octane value of the gasoline in the tank?
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