Respuesta :
We can write the expression above as the following function:
[tex]f(r)=(r-4)^{3}[/tex]
So let's examine the expressions that are true for this exercise.
1. There are three factors of [tex]r-4[/tex]:
This is true because we can write the function [tex]f(r)[/tex] as follows:
[tex]f(r)=(r-4)(r-4)(r-4)[/tex]
So you can see that in fact there are three factors.
2. The expression is equal to 1 over 12 factors of r.
This is false. It is obvious that this is impossible. There is no any way to get the same expression by applying this statement.
3. Adding the exponents will create an equivalent expression.
This is true because we can write the function as follows:
[tex]f(r)=(r-4)^{1+1+1}[/tex]
So adding one three times we can get the same function, that is:
[tex]1+1+1=3[/tex]
Therefore this is an equivalent expression because:
[tex]f(r)=(r-4)^{1+1+1}=(r-4)^{3}[/tex]
4. Multiplying the exponents will create an equivalent expression.
This is true.You can get the following expression:
[tex]f(r)=(r-4)^{\frac{2}{3}\times \frac{9}{2}}[/tex]
By multiplying the exponents we have:
[tex]\frac{2}{3}\times \frac{9}{2}=3[/tex]
Therefore this is an equivalent expression because:
[tex]f(r)=(r-4)^{\frac{2}{3}\times \frac{9}{2}}=(r-4)^{3}[/tex]
5. The expression simplifies to.
The expression is simplified, that is, it has been factorized. Therefore there is no a way to simplify this function but:
[tex]f(r)=(r-4)^{3}[/tex]
[tex]f(r)=(r-4)^{3}[/tex]
So let's examine the expressions that are true for this exercise.
1. There are three factors of [tex]r-4[/tex]:
This is true because we can write the function [tex]f(r)[/tex] as follows:
[tex]f(r)=(r-4)(r-4)(r-4)[/tex]
So you can see that in fact there are three factors.
2. The expression is equal to 1 over 12 factors of r.
This is false. It is obvious that this is impossible. There is no any way to get the same expression by applying this statement.
3. Adding the exponents will create an equivalent expression.
This is true because we can write the function as follows:
[tex]f(r)=(r-4)^{1+1+1}[/tex]
So adding one three times we can get the same function, that is:
[tex]1+1+1=3[/tex]
Therefore this is an equivalent expression because:
[tex]f(r)=(r-4)^{1+1+1}=(r-4)^{3}[/tex]
4. Multiplying the exponents will create an equivalent expression.
This is true.You can get the following expression:
[tex]f(r)=(r-4)^{\frac{2}{3}\times \frac{9}{2}}[/tex]
By multiplying the exponents we have:
[tex]\frac{2}{3}\times \frac{9}{2}=3[/tex]
Therefore this is an equivalent expression because:
[tex]f(r)=(r-4)^{\frac{2}{3}\times \frac{9}{2}}=(r-4)^{3}[/tex]
5. The expression simplifies to.
The expression is simplified, that is, it has been factorized. Therefore there is no a way to simplify this function but:
[tex]f(r)=(r-4)^{3}[/tex]
The statements that can be used to describe the expression (r-4)³ are given by:
- Option 1: There are three factors of (r-4).
- Option 3: Adding the exponents will create an equivalent expression.
What are factors of an expression?
When an expression is written as a result of product of some terms, then those terms are called factors of that expression.
An expression is factor of itself and 1 of course.
Checking all the options one by one for their correctness, we get:
- Option 1: There are three factors of (r-4).
We can rewrite (r-4)³ as:
[tex](r-4)^3 = (r-4)\times (r-4) \times (r-4)[/tex]
So, when we write three factors of (r-4), we get the resultant expression as (r-4)³. Thus, this option is correct.
- Option 2: The expression is equal to 1 over 12 factors of r.
False because.
1/(factors of r) = 1/r ≠ (r-4)³
- Option 3: Adding the exponents will create an equivalent expression.
True, because:
[tex](r-4)^3 = (r-4)^{1+1+1}[/tex]
- Option 4: Multiplying the exponents will create an equivalent expression.
False, because:
[tex](r-4)^3 \neq (r-4)^{1 \times 1 \times 1} = (r-4)[/tex]
(unless r ain't 4,or 3, it is going to be false)
(in option 3rd and 4th, we assumed the exponent of (r-4),(r-4),(r-4) is in consideration. which are 1, 1, and 1.)
- Option 5: The expression simplifies to something.
False. because the expression is already simplified. Modifying it anymore will just make it look more complex.
Thus, the statements that can be used to describe the expression (r-4)³ are given by:
- Option 1: There are three factors of (r-4).
- Option 3: Adding the exponents will create an equivalent expression.
Learn more about simplification here:
https://brainly.com/question/26437497
