System of equations - high school - practice problems - page 43 of 44
Number of problems found: 878
- Alloy
The first alloy is a mixture of two metals in the ratio 1:2; the second is a mixture of the same metals in the ratio 2:3. At what ratio do we have these two alloys put into the furnace to obtain a new metal alloy with a ratio of 17:27? (All three ratios c - Aircrafts
Above the town, the hall tower flew the plane at a constant speed of 510 km/h, and 15 minutes later, the second plane at a speed of 703 km/h. How long and how far from the town hall will it be for aircraft to catch up? - Sum-log
The sum of two numbers is 32, and the sum of their logarithms (base 10) is 2.2. Determine these numbers. - Scouts
The boys from the scout group traveled 5 days distance of 115 km. Every day walked 1.5 km less than the previous day. How many kilometers did scouts walk on the first day?
- 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. - Two valves
Water fills the pool with two valves for 11 days. After 7 days, the workers stopped the first and second valve fill pool for 7 days. How many days took to fill the pool of each of the valves individually? - Parabola
Find the equation of a parabola that contains the points at A[10; -5], B[18; -7], C[20; 0]. (use y = ax²+bx+c) - Two wine
In the ratio of 2:1, mixed wine solution cost 4.1 USD. In the ratio of 1:2, mixed wine solution costs 4.5 USD. How much does a liter of each wine cost? - Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
- Balls
Michal said to Martin: give me one ball, and I'll have twice as you. Martin said: give me 4, and we will have equally. How many balls does each have? - Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q, and n - number of members by their sum s_n. - 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 - Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18
- Null points
Calculate the roots of the equation: 3 |x +4| +3 |x +5| +2 |x +4| = 30 - Team
The football team has 11 players. Their average age is 20 years. During the match, one player withdraws due to injury, and the team's average age is 18. How old was the injured player? - Sequence
The arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n. - Car factory
The carmaker now produces 2 cars a day more than last year, so the production of 70312 cars will save just one full working day. How many working days were needed to manufacture 70312 cars last year? - Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm.
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