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11 Questions

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Mathematics: Algebra and Geometry

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Questions and Answers

If the volume of a pyramid is directly proportional to the square of its slant height, and the volume of a pyramid with a slant height of 5 cm is 125 cubic cm, what is the volume of a pyramid with a slant height of 7 cm?

196 cubic cm

A rectangle has a length that is 3 cm more than its width. If the area of the rectangle is 24 square cm, what are the dimensions of the rectangle?

The length is 6 cm and the width is 3 cm

If the surface area of a cone is directly proportional to the square of its radius, and the surface area of a cone with a radius of 3 cm is 36π square cm, what is the surface area of a cone with a radius of 5 cm?

100π square cm

What is the effect of scaling the dimensions of a rectangle by a factor of 2 on its perimeter, area, and volume?

The perimeter is multiplied by 2, the area is multiplied by 4, and the volume is not applicable to a rectangle Signup and view all the answers

If the product of two binomials is (x + 2)(x + 5) = x^2 + 7x + 10, what are the values of x that satisfy the equation?

x = -2 or x = -5 Signup and view all the answers

What is the role of the constant of variation in a direct variation relationship?

The constant of variation (k) is a measure of how strongly the variables are related, and a larger constant of variation indicates a stronger relationship between the variables. Signup and view all the answers

How does the graph of a direct variation equation y = kx appear?

The graph of a direct variation equation is a straight line passing through the origin. Signup and view all the answers

What is the difference between direct variation and inverse variation?

Direct variation is a type of variation where the dependent variable (y) is directly proportional to the independent variable (x), whereas inverse variation is a type of variation where the dependent variable (y) is inversely proportional to the independent variable (x). Signup and view all the answers

What is an example of a real-world situation where inverse variation is used to model the relationship between two variables?

One example is the relationship between the pressure and volume of a gas, where the pressure is inversely proportional to the volume. Signup and view all the answers

What is the variation equation for inverse variation?

The variation equation for inverse variation is y = k/x, where k is the constant of variation. Signup and view all the answers

What is an application of direct variation in real-world situations?

One application of direct variation is in modeling the relationship between the cost and quantity of goods, where the cost is directly proportional to the quantity. Signup and view all the answers