Rearrange variables - math word problems - page 14 of 145

Number of problems found: 2899

Determine the area
Determine the area of trapezoid ABCD, given that AB = 6 cm, the area of triangle ABC = 15 cm², the area of triangle BCD = 20 cm², and AB ∥ CD.
Average 110
The average of five numbers is 1.3. What is their sum? What is the arithmetic mean of the numbers 0.04, 0.014, and 0.21? The arithmetic mean of four decimal numbers is 2.5. Three of these numbers are 1.8, 0.65, and 3.1. What is the fourth number?
In an electrical 3
In an electrical circuit, R₁ = 4,000 Ω, R₂ = 8,000 Ω, and R₃ = 6,000 Ω are connected in series. The power supply has a voltage of 100 V. Calculate the voltage across R₁, R₂, and R₃.
RR trapezoid
Given an isosceles trapezoid ABCD with bases |AB| = 36 m and |CD| = 200 dm, and leg |BC| = 10 m. Calculate the area and perimeter of the trapezoid and the length of diagonal AC.
Dependent variables
A printer prints k sheets in n seconds (k, n ∈ ℕ). Express the number of sheets that the printer prints in 5 minutes in terms of k and n.
Animals - pasture
There are 195 animals in total on the pasture: sheep, goats, and calves. There are half as many sheep as goats and twice as many calves as goats. How many sheep are there on the pasture?
Finding the Second Number
The arithmetic mean of two numbers is 10. One of the numbers is 2. What is the other number?
Ratio 52
The ratio of the surface area of a cube to its volume is 2:1. Calculate: a) the edge length of the cube in cm, b) the volume of the cube in cm³, c) the surface area of the cube in cm².
Trapezoid 83
Trapezoid ABCD is composed of five triangles. Points E and G divide segment AB in the ratio 2:4:3 (in this order) into three segments. Point F is the midpoint of segment AD. Triangle AEF is isosceles and right-angled. Triangles GBC and CDG are right-angle
In trapezoid 3
In trapezoid ABCD, the following elements are given: lengths of the parallel sides a = 20 cm and c = 11 cm, angle α = 63°36', and angle β = 79°36'. Calculate the lengths of the other two sides and the sizes of the remaining angles.
Students in a Class
The ratio of boys to girls in a class is 3:5. How many students are there in the class if there are 15 girls?
Missile 3
A missile penetrated an embankment to a depth of 1.2 m. What was its speed when it hit the surface of the embankment, if the missile's movement through the ground lasted 0.021 seconds and the motion was uniformly decelerated?
Determine 23
Determine in cm² the area of rectangle ABCD, whose longer side is a = 20 cm and whose diagonal is 10 cm longer than its shorter side.
Diagonal 2
What is the area in square metres of a rectangular garden whose diagonal is 50 m long and whose width is 27 m? Round the result to the nearest whole number.
Rhombus - ratio
In a rhombus, the ratio of a side to the height drawn to that side is 4:1, and its area is 49 cm². Calculate the length of the side and the height drawn to that side.
Two cubes 3
Two cubes made of plasticine have single-digit integer edge lengths differing by 1 cm. Can a single larger cube with an integer edge length be made from the same total amount of plasticine?
Suitcase - rod
The boot of a car has the shape of a cuboid with dimensions 1.6 m × 1.2 m × 0.5 m (width × depth × height). Determine the longest thin rod that can be placed flat on the bottom of the boot.
Equilateral cone
A cup has the shape of a right circular cone whose slant height equals the diameter of its base (i.e. the axial cross-section is an equilateral triangle). It is supposed to hold 0.2 litres of liquid when filled to 1 cm below the rim. Calculate its diamete
Solving for x Proportion
Find x such that: a) 2:5 = 8:x; b) x:28 = 4:7.
Regular 4BH
A regular quadrilateral prism has a volume of 864 cm³ and its total surface area is twice the area of its base. Determine the length of its space diagonal.

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