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FromTheMoon [43]
3 years ago
13

Choose all that give the correct expression for the quantity described. The difference of nine times a number x and the quotient

of that number and 5. 9x − x 5 Eight more than the quotient of twelve and a number n. n 12 + 8 The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number. x(6 − x) + 8 x Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4)
Mathematics
1 answer:
ohaa [14]3 years ago
4 0

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;

=9 \times x\\= 9x

The quotient of that number and 5.

= \frac{x}{5}

The difference between both expression;

9x - \frac{x}{5}

Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as 9x - \frac{x}{5}

2) Eight more than the quotient of twelve and a number n

Quotient of twelve and a number n is expressed as:

\frac{n}{12}

Eight more than the resulting function is;

\frac{n}{12}+8

Hence eight more than the quotient of twelve and a number n is expressed as \frac{n}{12}+8

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;

6-x

product of a number x and the quantity 'six minus the number is;

x(6-x)

quotient of eight and the number is;

\frac{8}{x}

Taking the resulting sum of the last two expression

x(6-x) + 8x

Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;

x(6-x) + 8x

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;

= 2x +(2x+2)+(2x+2+2)\\=  2x+(2x+2)+(2x+4)

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What is the sum of the first 70 consecutive odd numbers? Explain.
expeople1 [14]

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Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

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The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

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The second sum is simply the sum of N ones:

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2 years ago
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