Write an equivalent ratio to 6/24?
Car goes 420miles on a 10gallon tank. What is unit rate of miles per gallon?
Dog runs 200 miles in 4 days. Write an equation to find miles in 14days.
What 2 things must a graph do to be a proportional relationship?
Milly reads 20pages in 4 minutes. Sara reads 12pages in 3 minutes. Find each constant of proportionality and write a direct variation equation then.
1) An equivalent ratio to 6/24 is 1/4.
2) The unit rate of miles per gallon can be found by dividing the total miles (420 miles) by the total gallons (10 gallons).
Therefore, the unit rate is 42 miles per gallon.
3) To find the equation to calculate miles in 14 days, you can set up a proportion using the ratio of miles to days. The ratio is 200 miles in 4 days, so we can write the equation as:
200 miles / 4 days = x miles / 14 days.
4) Two things a graph must do to be a proportional relationship are:
- The graph must go through the origin (0,0), meaning that when x and y are both 0, the relationship still holds true.
- The graph must be a straight line. This indicates that the relationship has a constant rate or ratio between the two variables.
5) To find the constant of proportionality for Milly, we divide the number of pages read (20) by the number of minutes (4). The constant of proportionality is 5, and the direct variation equation is y = 5x.
For Sara, the constant of proportionality can be found by dividing the number of pages read (12) by the number of minutes (3). The constant of proportionality is 4, and the direct variation equation is y = 4x.
To find an equivalent ratio to 6/24, divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 6 and 24 is 6, so dividing both by 6 gives the ratio 1/4.
The unit rate of miles per gallon can be found by dividing the total miles by the total gallons. In this case, the car goes 420 miles on 10 gallons, so the unit rate is 420 miles per 10 gallons, which simplifies to 42 miles per gallon.
To find the equation to calculate miles in 14 days, use the unit rate of miles per day. The dog runs 200 miles in 4 days, so the unit rate is 200 miles per 4 days, which simplifies to 50 miles per day. Thus, the equation would be miles = 50 * days.
A graph must have two properties to represent a proportional relationship: firstly, it must pass through the origin (0,0), meaning when x = 0, y must also equal 0. Secondly, the graph must have a constant slope, which means that as x increases by a constant amount, y also increases by a constant amount.
To find the constant of proportionality and write a direct variation equation for the given data, divide the number of pages by the number of minutes for each person. For Milly, the constant of proportionality is 20 pages divided by 4 minutes, which equals 5 pages per minute. So the direct variation equation is y = 5x. For Sara, the constant of proportionality is 12 pages divided by 3 minutes, which also equals 4 pages per minute. So, the direct variation equation for Sara would be y = 4x.
To find an equivalent ratio to 6/24, you can simplify the given ratio by dividing both the numerator and denominator by their greatest common divisor, which is 6 in this case.
Dividing 6 by 6 gives you 1, and dividing 24 by 6 gives you 4. Therefore, an equivalent ratio to 6/24 is 1/4.
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To find the unit rate of miles per gallon in the given scenario, you need to divide the total number of miles by the total number of gallons.
In this case, the car goes 420 miles on a 10-gallon tank. So, the unit rate of miles per gallon can be found by dividing 420 miles by 10 gallons:
420 miles ÷ 10 gallons = 42 miles per gallon.
Therefore, the unit rate of miles per gallon for the car is 42 miles.
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To find an equation to calculate the number of miles a dog runs in 14 days based on the given information, you can use the concept of a constant rate.
The dog runs 200 miles in 4 days, which means it has a constant rate of 200 miles per 4 days.
To find the rate per day, you can divide both sides of the equation by 4:
200 miles ÷ 4 days = 50 miles per day.
The dog runs 50 miles per day. To find the number of miles the dog will run in 14 days, you can multiply the rate per day (50 miles) by the number of days (14):
50 miles/day × 14 days = 700 miles.
Therefore, the equation to find the number of miles in 14 days would be: Miles = 50 days × Number of Days.
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For a graph to represent a proportional relationship, it must satisfy two conditions:
1. The graph must pass through the origin (0, 0). This means that when both the x and y values are zero, it represents the starting point or initial state of the relationship.
2. The graph must form a straight line. This indicates that the relationship between the two variables is constant and consistent regardless of the values chosen.
If both of these conditions are met, the graph represents a proportional relationship.
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To find the constant of proportionality and write a direct variation equation, you first need to determine the ratio of pages read to minutes taken for each person.
For Milly, the ratio is 20 pages for 4 minutes, which is simplified as 20/4 or 5 pages per minute.
For Sara, the ratio is 12 pages for 3 minutes, simplified as 12/3 or 4 pages per minute.
The constant of proportionality represents the ratio of the dependent variable (number of pages) to the independent variable (number of minutes). In this case, that ratio is 5 pages per minute.
Therefore, the direct variation equation can be written as: Pages = 5 × Minutes, where the number of pages read is equal to 5 times the number of minutes.
You can use the same process to find the constant of proportionality for Sara, which is 4 pages per minute.