And I need help with these too please! I need to find the area of the shaded region please
1 answer:
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Answer:
option: B () is correct.
Step-by-step explanation:
We are given the solution set as seen from the graph as:
(-4,2)
1)
On solving the first inequality we have:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>-2 and x<4
so we have the region as:
(-2,4)
Case 2:
and
i.e. x<-2 and x>4
Hence, we did not get a common region.
Hence from both the cases we did not get the required region.
Hence, option 1 is incorrect.
2)
We are given the second inequality as:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>2 and x<-4
Hence, we do not get a common region.
Case 2:
and
i.e. x<2 and x>-4
Hence the common region is (-4,2) which is same as the given option.
Hence, option B is correct.
3)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x>-2 and x>4
Hence, the common region is (4,∞)
Case 2:
and
i.e. x<-2 and x<4
Hence, the common region is: (-∞,-2)
Hence, from both the cases we did not get the desired answer.
Hence, option C is incorrect.
4)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x<2 and x<-4
Hence, the common region is: (-∞,-4)
Case 2:
and
i.e. x>2 and x>-4.
Hence, the common region is: (2,∞)
Hence from both the case we do not have the desired region.
Hence, option D is incorrect.
Answer:
Step-by-step explanation:
3a²*2a³ = (2*3)(a² *a³)=
Answer:
The first three terms of the geometry sequence would be ,
, and
.
The sum of the first seven terms of the geometric sequence would be .
Step-by-step explanation:
<h3>1.</h3>Let denote the common difference of the arithmetic sequence.
Let denote the first term of the arithmetic sequence. The expression for the
th term of this sequence (where
is a positive whole number) would be
.
The question states that the first term of this arithmetic sequence is . Hence:
- The third term of this arithmetic sequence would be
.
- The thirteenth term of would be
.
The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let denote the ratio of the geometric sequence in this question.
Ratio between the second term and the first term of the geometric sequence:
.
Ratio between the third term and the second term of the geometric sequence:
.
Both and
are expressions for
, the common ratio of this geometric sequence. Hence, equate these two expressions and solve for
, the common difference of this arithmetic sequence.
.
.
.
Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be ,
, and
, respectively.
These three terms (,
, and
, respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be
.
Let and
denote the first term and the common ratio of a geometric sequence. The sum of the first
terms would be:
.
For the geometric sequence in this question, and
.
Hence, the sum of the first terms of this geometric sequence would be:
.