if a graph is proportional what characteristic does it display?
If a graph is proportional, it displays a linear relationship between two variables. This means that as one variable increases or decreases, the other variable also increases or decreases in direct proportion. In other words, the graph of a proportional relationship is a straight line that passes through the origin (0,0) on a coordinate plane.
if Chase runs 5 miles in 60 minutes, how far will he run if he continues at the same rate?
If Chase runs 5 miles in 60 minutes, we can determine how far he will run if he continues at the same rate by finding the proportion.
The rate at which Chase runs can be calculated as 5 miles per 60 minutes. To find out how far he will run in, for example, 120 minutes, we can set up the proportion:
5 miles / 60 minutes = x miles / 120 minutes
To solve for x, we can cross multiply:
5 * 120 = 60 * x
600 = 60 * x
Dividing both sides by 60:
x = 600 / 60
x = 10
Therefore, if Chase continues at the same rate, he will run 10 miles.
if Chase runs 5 miles in 60 minutes, how far will he run in 3 hours if he continues at the same rate?
To find out how far Chase will run in 3 hours if he continues at the same rate of 5 miles in 60 minutes, we need to convert 3 hours to minutes.
Since there are 60 minutes in 1 hour, we can calculate:
3 hours * 60 minutes/hour = 180 minutes
Now, we can set up a proportion:
5 miles / 60 minutes = x miles / 180 minutes
To solve for x, we can cross multiply:
5 * 180 = 60 * x
900 = 60 * x
Dividing both sides by 60:
x = 900/60
x = 15
Therefore, if Chase continues at the same rate, he will run 15 miles in 3 hours.
Jimmy reads 15 pages in 5 minutes, Carlo reads 12 pages in 6 minutes, find each constant of proportionality, showing your work. Then write a sentence to compare the proportional relationships.
To find the constant of proportionality for each scenario, we divide the number of pages read by the number of minutes taken for each person.
For Jimmy, the constant of proportionality (k) can be calculated as:
k = 15 pages / 5 minutes = 3 pages/minute
For Carlo, the constant of proportionality (k) can be calculated as:
k = 12 pages / 6 minutes = 2 pages/minute
Comparing the proportional relationships, we can deduce that Jimmy reads at a faster pace than Carlo. For every minute, Jimmy reads 3 pages, while Carlo reads 2 pages. Therefore, Jimmy's rate of reading is higher than Carlo's.
what was one reason for Gengis Khan's success as a military leader?
One reason for Genghis Khan's success as a military leader was his innovative military tactics. He revolutionized warfare by introducing new strategies and organizational techniques. For example, he implemented a highly efficient messenger system called the Yam, which enabled rapid communication and coordination among his armies. He also utilized strategies such as feigned retreats and the integration of different military disciplines, such as archers, cavalry, and infantry. These innovative tactics allowed him to adapt to various combat situations, outmaneuver his enemies, and achieve military triumphs.
What was one reason for Gengis Khan's success as a military leader?
He ruthlessly destroyed all Mongol clans except his own.
He organized the Mongol army into an efficient fighting force.
He built goodwill by treating conquered people with mercy.
He divided his empire into four military districts called khanates.