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What is the relationship between area of a circle and its radius squared for a series of circles with large increasingly large radii?
The area of a circle is directly proportional to the square of its radius. If two circles have radii R1 and R2 , then the ratio of their areas is ( R1/R2 )2
What is the relationship between perimeters and areas of similar figures?
Whatever the ratio of perimeters of the similar figures, the areas will be in the ratios squared. Examples: * if the figures have perimeters in a ratio of 1:2, their areas will have a ratio of 1²:2² = 1:4. * If the figures have perimeters in a ratio of 2:3, their areas will have a ratio of 2²:3² = 4:9.
Which Best describes the relationship between (x plus 1) and the polynomial x2 - x - 2?
No it’s not a factor
What is an algebraic or numerical sentence that shows that 2 quantities are equal is a?
It is an identity.
How is the perimeter and area of a square related?
There is no direct relationship. The perimeter is proportional to the length of the side (if you increase the side by a factor of 10, the perimeter will also increase by a factor of 10); the area is proportional to the square of the side length (if you increase the length of a side by a factor of 10, the area will increase by a factor of 100).If you know the perimeter, divide it by 4 and then square the result, to get the area (A = (P/4)2); if you know the area, take the square root and then multiply by 4 to get the perimeter (P = root(A) x 4).There is no direct relationship. The perimeter is proportional to the length of the side (if you increase the side by a factor of 10, the perimeter will also increase by a factor of 10); the area is proportional to the square of the side length (if you increase the length of a side by a factor of 10, the area will increase by a factor of 100).If you know the perimeter, divide it by 4 and then square the result, to get the area (A = (P/4)2); if you know the area, take the square root and then multiply by 4 to get the perimeter (P = root(A) x 4).There is no direct relationship. The perimeter is proportional to the length of the side (if you increase the side by a factor of 10, the perimeter will also increase by a factor of 10); the area is proportional to the square of the side length (if you increase the length of a side by a factor of 10, the area will increase by a factor of 100).If you know the perimeter, divide it by 4 and then square the result, to get the area (A = (P/4)2); if you know the area, take the square root and then multiply by 4 to get the perimeter (P = root(A) x 4).There is no direct relationship. The perimeter is proportional to the length of the side (if you increase the side by a factor of 10, the perimeter will also increase by a factor of 10); the area is proportional to the square of the side length (if you increase the length of a side by a factor of 10, the area will increase by a factor of 100).If you know the perimeter, divide it by 4 and then square the result, to get the area (A = (P/4)2); if you know the area, take the square root and then multiply by 4 to get the perimeter (P = root(A) x 4).
How are proportional quantities described by equivalent ratios?
Proportional quantities are described by equivalent ratios because they maintain a constant relationship between two quantities. For example, if two ratios, such as 1:2 and 2:4, are equivalent, they represent the same relationship, meaning that as one quantity increases, the other does so in a consistent manner. This property allows for scaling up or down while preserving the ratio, demonstrating how proportional relationships function in various contexts, such as cooking, finance, or geometry.
What is the name of equivalent ratios?
Equivalent ratios are often referred to as "proportional ratios." These are ratios that express the same relationship between two quantities, even though the numbers may differ. For example, the ratios 1:2 and 2:4 are equivalent because they represent the same proportional relationship.
Which set of values describes two quantities that are in a proportional relationship?
Two quantities are in a proportional relationship if they maintain a constant ratio or rate. For example, if you have the values (2, 4) and (3, 6), the ratio of the first quantity to the second is the same for both pairs: 2:4 simplifies to 1:2, and 3:6 also simplifies to 1:2. Thus, any pair of values that can be expressed as k times the other (where k is a constant) indicates a proportional relationship.
What is the proportional relationship between 6 12 and 48?
It is: 1 2 and 8
What are two ratios that name the same number?
Two ratios that name the same number are 1:2 and 2:4. Both ratios represent the same relationship between the quantities, as they can be simplified to the same fraction, 1/2. This demonstrates that different ratios can express the same proportional relationship.
What is the 2 quantities that have a constant rate or ratio?
Proportional
What is a pair of ratios?
A pair of ratios consists of two proportional relationships that compare two quantities. For example, if the ratio of apples to oranges is 3:2, it can be expressed as the pair of ratios 3:2 and 3/2. These ratios indicate that for every three apples, there are two oranges, maintaining a consistent relationship between the two quantities.
What is proportional side lengths?
it is a relationship between the sides with respect to size, In maths it is a relationship between four numbers or quantities in which the ratio of the first pair equals the ratio of the second pair
What makes 2 quantities proportional?
Two quantities are proportional if they maintain a constant ratio to each other, meaning that when one quantity changes, the other changes in a consistent way. This relationship can be expressed mathematically as ( y = kx ), where ( k ) is the constant of proportionality. If you can multiply or divide one quantity to obtain the other without altering the ratio, they are proportional. For example, if doubling one quantity results in the doubling of the other, they are proportional.
What is two ratios that describe the same relationship?
Two ratios that describe the same relationship are 1:2 and 2:4. Both ratios represent the same proportional relationship, as they can be simplified to the same fraction (1/2). This means that for every 1 part of one quantity, there are 2 parts of another, and for every 2 parts of the first quantity, there are 4 parts of the second. Thus, they convey the same comparative relationship between the two quantities.
How can the term of a ratio be described as?
The term of a ratio can be described as the individual components or values that make up the ratio. For example, in the ratio 3:2, the terms are 3 and 2, representing the quantities being compared. Terms can also be referred to as the antecedent (the first term) and the consequent (the second term) in a ratio. Each term provides insight into the proportional relationship between the quantities involved.
When are 2 quantities proportional when it comes to a table or graph?
1) It has to go through the origin (0,0). 2) It has to be consistent.
