Isolating a variable in the formula - practice problems - page 2 of 144
To isolate a variable in a formula, use inverse operations to systematically undo surrounding mathematical operations. For example, in 2x + 3 = 7 , subtract 3 from both sides ( 2x = 4 ), then divide by 2 ( x = 2 ). Maintain balance by applying each operation to both sides of the equation. For complex formulas, follow the order of operations (PEMDAS/BODMAS) in reverse, handling addition/subtraction before multiplication/division.Number of problems found: 2866
- Four numbers 3
What least number must be added to each of the numbers 6,15,20 and 43 to make them proportional? - The angle 9
The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 m towards the foot of the tower to a point B, the angle of elevation increases to 60°. Find the height of the tower and the distance of the tower - Surface = volume
If the volume and the surface area of a sphere are numerically the same then find its radius. - GP - terms
Which term of the G.P., 2, 8, 32, ... up to n terms is 131072? - Triangle 90
Triangle made by 6 cm 4.5 cm and 7.5 cm. what angles does it make? - 765 chairs
765 chairs are arranged in rows in such a way that the number of chairs in each row is equal to the number of rows. How many chairs needs to be removed to complete this arrangement? - Susan 5
Susan has a water tank in his back garden that can hold up to 750L in water. At the start of a rainy day (at 0:00) there is 165L in the tank, and after a heavy day’s rain (at 24:00) there is 201 L in the tank. Assuming that the rain fell consistently duri
- The boat
A boatman goes 2 km against the stream in 40 minutes and returns to the same spot in 30 minutes. What is his rate of rowing in still water? - A plane 3
A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hr from the usual speed. Find its usual speed. - Three inscribed objects
A circle is inscribed in a square. An equilateral triangle of side 4√3 is inscribed in that circle. Find the length of the diagonal of the square. - Expression - two variables
The formula with two variables is given: y=5*x+38. Solve for x. - Two cubes 2
Two cubes each of volume 125 cm³ are joined end to end. Find the surface area of the resulting cuboid . - Repeating to infinity
How do I express 0.99999999… as a fraction? (nine repeating) Another questions: Can you write .9999 repeating as a fraction? How do you turn 0.9 repeating into a fraction? - Angle of elevation
From a point A on the ground, the angle of elevation of the top of a 20 m tall of a building is 45°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from A is 60°. Find the length of the flagstaff and th - A long train
A train passes a standing man in 6 sec and 210 m long platform in 16 s . Find the length and the speed of the train.
- Antecedent and consequent
In a ratio which is equal to 5:8, if the antecedent is 40, then find the consequent. - Direct proportional If m is proportional to n and m=5 when n=4, then what is the value of m when n=18?
- Two circles 3
Two circles are inscribed in a square whose side is 4 cm. Find the radius of the smaller circle. - The radius 3
The radius of a solid circular cylinder decreases by 20% and its height increases by 10% . Find the percentage change its : (a) volume (b) curved surface area. - Common work
39 men can repair a road in 12 days working 5 hours a day. How many days will be required to complete the work by 30 men working 6 hours a day?
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