What is the simplest form of this expression -x(7x+2)+x^2
2 answers:
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Answer:
OR {5, 6, 7, 8, .....}
Step-by-step explanation:
First of all, let us have a look at the interval shown on the number line and try to understand it properly.
The number line shows positive numbers starting from 3 that means numbers indicated will be positive numbers.
The number highlighted starts from 5 and there is filled circle at 5.
So, 5 is included in the interval.
The arrow is from 5 towards 8 and so on..
That means Numbers greater than or equal to 5 are represented by the interval.
So, writing as an inequality
Let represents one of the numbers.
Hence, inequality can be written as:
Using the set notation:
OR
{5, 6, 7, 8, .....}
Answer:
The smallest possible value for the third term of the geometric progression is 1.
Step-by-step explanation:
Given : A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression.
To find : What is the smallest possible value for the third term of the geometric progression?
Solution :
The arithmetic progression is given by
First term a=9
Second term - 2 is added to second term i.e.
Third term - 20 is added to the third term i.e.
The geometric progression is given by
First term a=9
Second term -
Third term
r is the common ratio which is second term divided by first term,
So,
or third term divided by second term,
So,
Equating both the r,
Cross multiply,
Solving by middle term split,
Substituting the value of d in the third term,
Third term
When d=-14,
Third term
When d=10,
Third term
Therefore, The smallest possible value for the third term of the geometric progression is 1.