What is the distance between points S and T?
2 answers:
Answer: 16 units
Step-by-step explanation:
The distance between any two points and
on a number line is given by :-
From the given picture, there is a number line where point S is at -2 and point T is at 14.
Then, the distance between points S and T will be :_
Hence, the distance between points S and T = 16 units
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1)
An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.
For the first answer choice, clearly
does not pass the first criterion so we look at the second choice.
Let's come back to
and 
.
doesn't meet our first criterion, and let's skip 
for now.
It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are
. For now, it's just helpful to know these and recognize them.
So we can check off
and .
2)
For this next question, we know that
. Clearly this isn't irrational. Likewise, 
isn't irrational. 
, which is rational, leaving only 
. By process of elimination, this is the correct answer. Indeed, 
is an irrational number.
3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.
But it can be written as a fraction because its pattern repeats, unlike for an irrational number.
Let's say
. Would you agree that 
? (We choose to multiply by 100 because there are two decimals that repeat. For 1, choose 10, for 3 choose 1,000, and so on.)
Now, let's subtract x from 100x and solve.
Voila!
An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.
For the first answer choice, clearly
Let's come back to
It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are
So we can check off
2)
For this next question, we know that
3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.
But it can be written as a fraction because its pattern repeats, unlike for an irrational number.
Let's say
Now, let's subtract x from 100x and solve.
Voila!
Answer:
<em>There are 12 boys and 18 girls</em>
Step-by-step explanation:
<u>Equations</u>
There are 30 students in a class. Let's call:
x = number of boys
Since the sum of boys and girls is 30:
30 - x = number of girls
The ratio of boys to girls is 2:3, thus:
Crossing denominators:
3x = 2(30 - x)
Operating the parentheses:
3x = 60 - 2x
Adding 2x:
5x = 60
Dividing by 5:
x = 60/5 = 12
x = 12
There are 12 boys and 30-12=18 girls