We are given the function –2x – 4 + 5x = 8 and is asked in the problem to solve for the variable x in the function. In this case, we can first group the like terms and put them in their corresponding sides:
-2x + 5x =8+4
Then, do the necessary operations.
3x = 12
x = 4.
The variable x has a value of 4.
<u><em>Answer:</em></u>
A. (3x²-4x-5)(2x⁶-5)
<u><em>Explanation:</em></u>
<u>The fundamental theorem of Algebra states that:</u>
"A polynomial of degree 'n' will have exactly 'n' number of roots"
We know that the degree of the polynomial is given by the highest power of the polynomial.
Applying the above theorem on the given question, we can deduce that the polynomial that has exactly 8 roots is the polynomial of the 8th degree
<u>Now, let's check the choices:</u>
<u>A. (3x²-4x-5)(2x⁶-5)</u>
The term with the highest power will be (3x²)(2x⁶) = 6x⁸
Therefore, the polynomial is of 8th degree which means it has exactly 8 roots. This option is correct.
<u>B. (3x⁴+2x)⁴</u>
The term with the highest power will be (3x⁴)⁴ = 81x¹⁶
Therefore, the polynomial is of 16th degree which means it has exactly 16 roots. This option is incorrect.
<u>C. (4x²-7)³</u>
The term with the highest power will be (4x²)³ = 64x⁶
Therefore, the polynomial is of 6th degree which means that it has exactly 6 roots. This option is incorrect
<u>D. (6x⁸-4x⁵-1)(3x²-4)</u>
The term with the highest power will be (6x⁸)(3x²) = 18x¹⁰
Therefore, the polynomial is of 10th degree which means that it has exactly 10 roots. This option is incorrect
Hope this helps :)
Answer:
Step-by-step explanation:
Given
Required
Determine the probability of red then blue jelly? i.e. P(R and B)
From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean
So, we have:
This is then solved further as:
The probability has a denominator of Total - 1 because the number of jelly beans reduced by 1 after the picking of the red jelly bean
The equation becomes:
