In order to figure out whether Luis or Isabella skates farther to get to school, we have to create a common denominator between the two fractions that represent the distance that each person walks.
The least common denominator of 3 and 4 is 12. This means that we have to change both fractions into equal fractions with denominators of 12.
To figure this out, we must set up a proportion.
2/3 = x/12
To solve this proportion, we must cross-multiply the fractions. We get:
24 = 3x
If we divide both sides by the coefficient of x which is 3, to get the variable x alone, we get:
x = 8
Therefore, 2/3 = 8/12, so Luis skates 8/12 mile from his home to school.
If we do the same process for the 2/4 mile to get to school for Isabella, we get 6/12, because both fractions are equal to 1/2.
Therefore, we know that Luis skates 8/12 mile to school and Isabella skates 6/12 mile to get to school. Because they have the same denominator, we can just compare the numerators. We know that 8 is greater than 6, thus Luis skates farther to get to school.
The amount of butterscotch chips needed by proportional reasoning according to the task content is; 75oz.
<h3>What is the quantity of butterscotch chips needed according to the task content?</h3>
It follows from the task content that the proportion premise given is that; 3 times as many chocolate chips as butterscotch chips is required.
On this note, it follows that when 25oz of chocolate chips is needed, the number of butterscotch chips needed will be; 3 × 25oz
= 75oz of butterscotch chips.
Read more on proportions;
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Answer:
The value of m is 1000 for r=5
Step-by-step explanation:
Given that m is proportional to the cube of r
It can be written as:
When the proportionality symbol is removed a proportionality constant is introduced in the equation.
Let k be the proportionality constant
Given
r=3,m=216
Putting the values
The equation will now become
Putting r = 5
Hence,
The value of m is 1000 for r=5
Question
x+5/x+2 - x+1/x²+2x
Answer:
= (x² - 4x - 1)/[x (x+2)]
= (x² - 4x - 1)/[x² + 2x]
Step-by-step explanation:
x + 5/x + 2 - x + 1/x² + 2x
We factorise the second denominator to give us :
x + 5/x + 2 - x + 1/x(x + 2)
We find the L.C.M of both denominators which is x(x+2).
[x(x + 5)-(x + 1)] / (x (x + 2))
Expand the bracket
=[x² +5x - x -1] / [x (x + 2)]
=(x² - 4x - 1) / [x (x + 2)]
= (x² - 4x - 1)/ [x (x + 2)]
= (x² - 4x - 1) / [x² + 2x]
Thw answer is 571430 because 28 rounds to 30
