System of equations + expression of a variable from the formula - practice problems
Number of problems found: 211
- Calculate 415
Calculate the cuboid's dimensions if the sum of its edges is 19cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - Yiguo
There were an equal number of carrots, tomatoes, and cabbage in the pantry. Yiguo used 49 carrots som, some tomatoes, and some cabbages. There were 3 times as many tomatoes as cabbages left. Sixteen fewer carrots than tomatoes were left. There were 117 ca - The sum 39
The sum of the first six terms of the arithmetic sequence is 72, and the second term is seven times the fifth term. Find the first term and the AP difference. - Determine 83240
In triangle ABC, the internal angle beta is twice the size of the angle alpha, and the angle gamma is 20 degrees less than the size of the angle beta. Determine the size of all interior angles of this triangle. - Dimensions 83176
If we reduce the length of the rectangle by 2 cm and the width by 1 cm, its area will decrease by 8 cm². If we increase the length of the rectangle by 1 cm and the width by 2 cm, then its content will increase by 13 cm². What were the original dimensions - Hypotenuses 83154
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle. - Centimeters 82996
The volume of the trapezoid is 132 cm². The difference in the length of both bases is 6 cm, and the height is 2 cm longer than the shorter base. Determine the height of the trapezoid in centimeters. - Diagonals 82850
How do I find the diagonals of a rhombus if its perimeter is 80dm and one diagonal is 2x larger than the other? - Parallelogram 82626
Calculate the area of a parallelogram if we know the perimeter is 23 cm, the diagonal is 8.5 cm, and one side is 1.5 cm longer. - Rectangle 82456
The sides of the rectangle are in the ratio 5 : 8. Its perimeter measures 208 cm. Determine the content of this rectangle. - Right-angled 82416
What are the sides of a right-angled triangle with a perimeter of 45 centimeters and a volume of 67.5 cm²? - Difference 81849
Determine four numbers so that the first three form the successive three terms of an arithmetic sequence with difference d=-3 and the last three form the next terms of a geometric sequence with quotient q=one half. - Intersection 81594
Given a trapezoid ABCD and the sizes of the interior angles. Angle SDC 32° SAD angle 33° SDA angle 77° Angle CBS 29°, where S is the intersection of the diagonals. What is the size of the angle BSA? - Arithmetic 80808
The lengths of the sides of a right triangle form the first 3 terms of the arithmetic sequence. The content is 6cm². - Increases 80772
The product of two numbers we know. If we increase the first factor by 2 and decrease the second factor by two, the product increases by 4. How much does the product change if we decrease the first factor by 3 and increase the second factor by 3? - Nightmares 80568
At the dream market, she offered the Sphinx to a traveler for four dreams, seven illusions, two naps, and one nightmare. Another has seven dreams, four illusions, four naps, and two nightmares. The Sphinx always measures the same for all travelers. How ma - Two numbers 13
Two numbers are in the ratio 5:8. When 2 is added to each, the ratio of the resulting numbers is 2:3. Find the numbers. - Parallelogram 79744
A parallelogram has a perimeter of 30 cm and heights of 10 cm and 6 cm. Find the lengths of its sides. - Determine 79364
Given a general triangle ABC. Its perimeter is 30 cm, with side a=2 cm longer than side b and 5 cm shorter than side c. Determine the area of the triangle. - One-third 77724
The cuboid has a body diagonal u=25 cm, and side b is one-third longer than side a. What is the volume of the cuboid?
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