Quadratic Equations Problems - page 11 of 30
Number of problems found: 584
- Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Dimensions of the trapezoid
One of the trapezoid bases is one-fifth larger than its height, and the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2 - Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Ratio of squares
A circle is given, and a square is inscribed. The smaller square is inscribed in a circular arc formed by the square's side and the circle's arc. What is the ratio of the areas of the large and small squares? - Points in space
There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times as many as the given points? - Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - Roots and coefficient
In the equation 2x² + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b. - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How long is its longest side? - Right-angled triangle
The right-angled triangle XYZ is similar to the triangle ABC, which has a right angle at the vertex X. The following applies: side a = 9 cm, x=4 cm, x = v-4 (v = height of triangle ABC). Calculate the unknown side lengths of both triangles. - Intersections 3
Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0 - On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - Shell area cy
The cylinder's shell area is 300 cm square, and its height is 12 cm. Calculate its volume. - The cylinder
The cylinder's surface area is 300 square meters, and its height is 12 meters. Calculate its volume. - Function 3
Function f(x)=a(x-r)(x-s) the graph of the function has an x-intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s. - Variation element increase
If the number of elements increases by two, the number of variations of the second class of these elements created by 38 increases. What is the original number of elements? - Rectangle area function
A rectangle with sides of lengths a, b (cm) has a circumference of 100 cm. The dependence of its area P (in cm2) on the number a can be expressed by the quadratic function P = sa + ta². Find the coefficients s, t. - Table side calculation
The area of the work surface of the rectangular table is 70 dm2, and its perimeter is 34 dm. Determine (in dm) the length of the shorter side of this table. - Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now. - 1 page
One 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? - 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.
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