Given:
Expression is
To prove:
If r is any rational number, then is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,
It can be written as
Now,
3, -2 and 4 are rational numbers by property 1.
is rational by Property 3.
are rational by Property 3.
is rational by property 2.
So, is rational.
Hence proved.
When going down on a Cartesian coordinate system, you are moving in the negative direction, so-7
Answer:
c= 125/2
h= 3
/2
Step-by-step explanation:
Answer: The polynomial 3x2 is of one variable with a degree of 2.
The polynomial x2y + 3xy2 + 1 is of two variables a with a degree of 3.
Step-by-step explanation: For this case we have the following polynomials:
3x2
x2y + 3xy2 + 1
We have then:
For 3x2:
Classification: polynomial of one variable:
Degree: 2
For x2y + 3xy2 + 1:
Classification: polynomial of two variables
Degree: 2 + 1 = 3
<h3>
Answer: Sometimes true</h3>
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Explanation:
-8+d is positive only when d > 8
Here's why
-8+d > 0
-8+d+8 > 0+8 .... add 8 to both sides
d > 8
So if Jessica said "d is greater than 8", then her claim would always be correct.
However, her claim is sometimes true.
Two counter examples could be when d = 1 and d = 2.
If d = 1, then -8+d = -8+1 = -7 which isn't positive.
If d = 2, then -8+d = -8+2 = -6 which also isn't positive.
Basically if d is anything smaller than 8, then you'll have -8+d be negative.
If d is something larger than 8, say d = 9, then -8+d = -8+9 = 1 which is finally positive.
