Rearrange variables - practice problems
Work with mathematical expressions. Expressions are mathematical objects where some numbers are replaced by letters - variables. For example, the area of a circle is S = π r2, where r is a variable, the radius of the circle, and S is also a variable, the area. This is how we can describe the relationship between area and radius for all circles, generally. We can modify expressions, simplify, multiply, divide, add, etc. Also known as Formula Manipulation.Number of problems found: 2921
- Ratio of acid and water
In a mixture of 60 litres, the ratio of acid to water is 2:1. If the ratio of acid to water is to be changed to 1:2, how much water must be added? - Carnival
Kevin is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $3.00. Kevin spent $18 altogether, and the number of games he played is 4 times the number of rides he went on. Write a system of equations that could be used - Two terms and d
The 8th term of an arithmetic progression is 17 and its 14th term is 29. Find the common difference. - Motorboat : current
The ratio of the speed of a motorboat to that of the current is 36:5. The motorboat travels downstream in 5 hours and 10 minutes. Find the time for the motorboat to return upstream. - ABCD rhombus
ABCD is a rhombus with sides of 10.5 cm. If the length of diagonal AC = 15.8 cm, use the cosine rule to: a. calculate the length of diagonal BD to the nearest centimetre, b. find the angles of the rhombus to the nearest degree. - Insert two > GP
If 4, 36, 324 are in a geometric progression, insert two more numbers into this progression so that it still forms a geometric progression. - Common difference 4 The 28th term of an arithmetic progression is −5. Find its common difference if the first term is 31.
- Angle of elevation 3
The angle of elevation of a pole from a point on the horizontal ground is 15°. After moving 10 m closer to the pole, the angle of elevation becomes 30°. What is the height of the pole? - Four plates
Four equal maximum-sized circular plates are cut from a square sheet of paper with an area of 784 cm². Calculate the circumference of each plate. - Square park
Amyra goes for a walk in a square park. The perimeter of the park is 1,235 m. Find the side length of the park. - GP - negative term
The first term of a geometric progression is −3 and the square of the second term equals its 4th term. Find the 7th term of the progression. - Three in a ratio
If A is 40% more than B, and B is 20% less than C, find the ratio A:C. - School - boys:girls
In a school, 10% of the boys is equal to 1/4 of the number of girls, and 10% of the number of girls is equal to 1/25 of the boys. Find the ratio of the number of boys to girls. - The sum 53 The sum of three numbers in a geometric progression is 35 and their product is 1,000. Find the numbers.
- The centroid
The centroid of a triangle ABC is at the point (3, 3, 3). If the coordinates of A and B are (3, −5, 7) and (−1, 7, −6) respectively, find the coordinates of point C. - The surface 5
The surface area of a cylinder is 6,140 cm², and the base radius is 25 cm. What is the height? - A rope for cow
Find the length of rope by which a cow must be tethered so that it can graze an area of 154 m². - The average 19 The average age of a class was 15 years. When 5 boys with an average age of 12 years and 6 months were admitted, the class average decreased by 6 months. How many students were in the class originally?
- Cu ore
An ore contains 5% copper. How much ore is required to obtain 400 grams of copper? - The Earth and Moon
The diameter of the Moon is approximately 1/4 of the diameter of the Earth. What fraction of the Earth's volume is the Moon's volume?
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