Answer in fraction form: -17/4 < x < 11/4
Answer in decimal form: -4.25 < x < 2.75
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Work Shown:
|4x+3| - 9 < 5
|4x+3| < 5+9 .... adding 9 to both sides
|4x+3| < 14
-14 < 4x+3 < 14 .... see note at the bottom
-14-3 < 4x < 14-3 .... subtracting 3 from all sides
-17 < 4x < 11
-17/4 < x < 11/4 .... divide all sides by 4
-4.25 < x < 2.75
This says that x is between -4.25 and 2.75, but x is not equal to either endpoint.
Note: I used the rule that |x| < k becomes -k < x < k where k is a positive real number.
Answer:
Step-by-step explanation:
The limit is:
so, you have an indeterminate result. By using the l'Hôpital's rule you have:
by replacing, and applying repeatedly you obtain:
hence, the limit of the function is -1/14
7).Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.
8).In set theory, the union of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero sets and it is by definition equal to the empty set.
9).The intersection of two or more given sets is the set of elements that are common to each of the given sets. The intersection of sets is denoted by the symbol '∩'. In the case of independent events, we generally use the multiplication rule, P(A ∩ B) = P( A )P( B ).
10).Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set. ... Sets are usually represented using a roster form or a set builder form.
Step-by-step explanation:
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Answer:
Higher
Step-by-step explanation:
Answer:
If the n-th term of a sequence be , t(n) equal to 
then the 5-th term is 27 but if the n-th term is (2n -n) then the 5-th term is 5.
Step-by-step explanation:
If the n-th term of a sequence be , t(n) =
then, the 5-th term is given by, t(5) = 
= 32 - 5
= 27
If the n-th term of a sequence be , t(n) = 2n - n = n
then, the 5-th term is given by, t(5) = 5
