Choose all that give the correct expression for the quantity described. The difference of nine times a number x and the quotient
1 answer:
Step-by-step explanation:
We are to get the expression for the following statements;
1) The difference of nine times a number x and the quotient of that number and 5.
The product of nine and a number x is expressed as;
The quotient of that number and 5.
The difference between both expression;
Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as
2) Eight more than the quotient of twelve and a number n
Quotient of twelve and a number n is expressed as:
Eight more than the resulting function is;
Hence eight more than the quotient of twelve and a number n is expressed as
3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.
Let the number be x:
six minus the number is expressed as;
product of a number x and the quantity 'six minus the number is;
quotient of eight and the number is;
Taking the resulting sum of the last two expression
Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;
4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).
Let the first even number be 2x
The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2
the sum of three consecutive even integers is expressed as;
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Answer: 2√2 - 3
Explanation:
The expession written properly is:
To rationalize that kind of expressions, this is to eliminate the radicals on the denominator you use conjugate rationalization.
That is, you have to multiply both numerator and denominator times the conjugate of the denominator.
The conjugate of √3+√6 is √3 - √6, so let's do it:
To help you with the solution of that expression, I will show each part.
1) Numerator: (√3 - √6) . (√3 - √6) = (√3 - √6)^2 = (√3)^2 - 2√3√6 + (√6)^2 =
= 3 - 2√18 + 6 = 9 - 6√2.
2) Denominator: (√3 + √6).(√3 - √6) = (√3)^2 - (√6)^2 = 3 - 6 = - 3
3) Then the resulting expression is:
9 - 6√2
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-3
Which can be further simplified, dividing by - 3
-3 + 2√2
Answer: 2√2 - 3
Explanation:
The expession written properly is:
To rationalize that kind of expressions, this is to eliminate the radicals on the denominator you use conjugate rationalization.
That is, you have to multiply both numerator and denominator times the conjugate of the denominator.
The conjugate of √3+√6 is √3 - √6, so let's do it:
To help you with the solution of that expression, I will show each part.
1) Numerator: (√3 - √6) . (√3 - √6) = (√3 - √6)^2 = (√3)^2 - 2√3√6 + (√6)^2 =
= 3 - 2√18 + 6 = 9 - 6√2.
2) Denominator: (√3 + √6).(√3 - √6) = (√3)^2 - (√6)^2 = 3 - 6 = - 3
3) Then the resulting expression is:
9 - 6√2
-----------
-3
Which can be further simplified, dividing by - 3
-3 + 2√2
Answer: 2√2 - 3