Quadratic equation + system of equations - practice problems - page 7 of 8
Number of problems found: 150
- Parabola 3
Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. f: y=x²+bx+c - Welcomed 3453
The product of two numbers is equal to their sum. One of the numbers is four times larger than the other. Find these numbers. They welcomed that none of them were equal to zero. - The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy? - Calculate 3339
A1 + a3 = 15 a1 + a2 + a3 = 21 Calculate a1 and q (quotient of the geometric sequence).
- Rectangle vs square
One side of the rectangle is 1 cm shorter than the side of the square. The second side is 3 cm longer than the side of the square. The square and rectangle have the same area. Calculate the length of the sides of a square and a rectangle. - Difference 3113
The difference between the two numbers is 82. The first number is eight, less than the square of the second number. Specify these numbers. - Grandfather's 2876
To the question: How old are your two grandchildren? The grandfather answers: if I add their sum to the product of the numbers that determine their age, I get 14. How many years have grandfather's grandchildren? Think only for years. - Two pipes
One pipe fills one-fifth volume 20 minutes before my second one. The two pipes together will fill the tank in two hours. How long will fill the tank of each pipe separately? - Quadratic function
Write the equation of the quadratic function, which includes points A (-1, 10), B (2, 19), C (1,4)
- Garden
The garden has a rectangular shape, a circumference of 130 m, and an area of 800.25 m². Calculate the dimensions of the garden. - Friends
Some friends had to collect the sum of 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - Water reservoir
The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later. For how long is filled by each separately? - RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm, you will reduce the hypotenuse by 4 cm. Determine the length of these legs. - The hall
The hall had a rectangular ground plan, one dimension 20 m longer than the other. After rebuilding, the length of the hall declined by 5 m, and the width increased by 10 m. The floor area increased by 300 m². What were the original dimensions of the hall?
- Right angled triangle
The hypotenuse of a right triangle is 17 cm long. When we decrease the length of the legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs. - Sum-log
The sum of two numbers is 32, and the sum of their logarithms (base 10) is 2.2. Determine these numbers. - Trains
From station 130 km away started passenger train and after 1.9 hours after the express train, which travels 27 km an hour more. Express train finish journey 5 minutes early. Calculate the average speed of these two trains. - Circle
The circle touches two parallel lines, p, and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r²
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