Simplify the expression: Show your work. Write the answer in standard form (15 +6d - d²) + (-5d² - 18 + 6d) PLEASE HELP
1 answer:
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Given:
A set of composite numbers less than 12.
To find:
The set by listing and set builder methods.
Solution:
Composite number: A positive integer is called a composite number if it has at least one divisor other than 1 and itself.
Composite numbers less than 12 are 4, 6, 8, 9, 10.
By using the listing method , the given set can be expression as:
Set = {4, 6, 8, 9, 10}
The numbers 4, 6, 8, 9, 10 are greater than 1, less than 12 and non prime numbers.
By using set builder method, the given set can be expression as:
Set =
Therefore, the list and set builder notation of the given set are {4, 6, 8, 9, 10} and respectively.
Answer:
The roots of equations are as m = And n =
Step-by-step explanation:
The given quadratic equation is 2 x² + 6 x - 1 = 0
This equation is in form of a x² + b x + c = 0
Let the roots of the equation are ( m , n )
Now , sum of roots =
And products of roots =
So, m + n = = - 3
And m × n =
Or, (m - n)² = (m + n)² - 4mn
Or, (m - n)² = (-3)² - 4 ()
Or, (m - n)² = 9 + 2 = 11
I.e m - n =
Again m + n = - 3 And m - n =
Solving this two equation
(m + n) + ( m - n) = - 3 +
I.e 2 m = - 3 +
Or, m =
Similarly n =
Hence the roots of equations are as m = And n =
Answer