71
175
180
Are the correct answers I just took the test/
Answer:
<h2>k = - 58</h2>
Step-by-step explanation:
Since (x + 8) and (3x + 2) are factors of the polynomial it means that if either one of them is equated to zero and substituted into the polynomial will give us zero
Using x + 8
We have
x + 8 = 0
x = - 8
Substitute the value of x into the polynomial
- 6x³ - 55x² + kx - 16
That's
- 6(-8)³ - 55(-8)² + k(-8) - 16 = 0
-6(-512) - 55(64) - 8k - 16 = 0
Expand
3072 - 3520 - 8k - 16 = 0
Simplify
- 464 - 8k = 0
8k = -464
Divide both sides by 8
k = - 58
Hope this helps you
Answer:
13. x = 4
14. x = -16
15. x = 11
Step-by-step explanation:
Answer:
See answer below
Step-by-step explanation:
The statement ‘x is an element of Y \X’ means, by definition of set difference, that "x is and element of Y and x is not an element of X", WIth the propositions given, we can rewrite this as "p∧¬q". Let us prove the identities given using the definitions of intersection, union, difference and complement. We will prove them by showing that the sets in both sides of the equation have the same elements.
i) x∈AnB if and only (if and only if means that both implications hold) x∈A and x∈B if and only if x∈A and x∉B^c (because B^c is the set of all elements that do not belong to X) if and only if x∈A\B^c. Then, if x∈AnB then x∈A\B^c, and if x∈A\B^c then x∈AnB. Thus both sets are equal.
ii) (I will abbreviate "if and only if" as "iff")
x∈A∪(B\A) iff x∈A or x∈B\A iff x∈A or x∈B and x∉A iff x∈A or x∈B (this is because if x∈B and x∈A then x∈A, so no elements are lost when we forget about the condition x∉A) iff x∈A∪B.
iii) x∈A\(B U C) iff x∈A and x∉B∪C iff x∈A and x∉B and x∉C (if x∈B or x∈C then x∈B∪C thus we cannot have any of those two options). iff x∈A and x∉B and x∈A and x∉C iff x∈(A\B) and x∈(A\B) iff x∈ (A\B) n (A\C).
iv) x∈A\(B ∩ C) iff x∈A and x∉B∩C iff x∈A and x∉B or x∉C (if x∈B and x∈C then x∈B∩C thus one of these two must be false) iff x∈A and x∉B or x∈A and x∉C iff x∈(A\B) or x∈(A\B) iff x∈ (A\B) ∪ (A\C).
