2. 24-7p=10
-7p=-14
p=2
3. x+(x+1)+(x+2)=72
3x+3=72
3x=69
x=23
4. x+(x+2)+(x+4)=48
3x+6=48
3x=42
x=14
7. 40-2x=8
-2x=-32
x=16
8. 1/2x+4=12
1/2x=8
x=16
The factors of 32 is 1,2,4,8,16, and 32.
Given that R(ABCDE) is in Boyce-Codd normal form.
And AB is the only key for R.
Definition
A relational nontrivial Schema R is in BCNF if FD (X-A) holds in R, Super key of R. whenever then X is
a
Given that AB is the only key for R.
ABC E (Yes).
check if ABC is a Super key. AB is a key, ABC is A B C E is in BONE a super key.
2) ACE B
(NO). no Check if ACE As there is ACE is not a Super key? AB in Super key. ACE.
ACE B
is
Boyce-Codd Normal Form not in BENE (NO)
3) ACDE → B (NO)
check if is a super key. ACDE
As ACDE there is not any AB Tn ACDE. a super key.
ACDEB is not in BCNF.
4) BS → C → (NO)
As there is no AB in BC ~. B(→ not in BCNF
BC is not a super key.
5) ABDE (Yes).
Since AB is a key.
ABO TS a super key.
.. ABDE → E is in BCNF
Let R(ABCDE) be a relation in Boyce-Codd Normal Form (BCNF). If AB is the only key for R, identify each of these FDs from the following list. Answer Yes or No and explain your answer to receive points.
1. ABC E
2. ACE B
3. ACDE B
4. BC C
5. ABD E
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Answer: x³-21x+20=0
Step-by-step explanation:
To find which polynomial has 1, 4, -5 as the roots, all we have to do is equal each root to 0 and multiply all factors together.
1 is (x-1)=0
4 is (x-4)=0
-5 is (x+5)=0
Now, we just multiply them together.
(x-1)(x-4)(x+5)=0 [FOIL]
(x²-4x-x+4)(x+5)=0 [combine like terms]
(x²-5x+4)(x+5)=0 [FOIL]
x³+5x²-5x²-25x+4x+20=0 [combine like terms]
x³-21x+20=0
Now we know x³-21x+20=0 is the polynomial with those roots.
