There are 8 students on the minibus. Five of the students are boys. What fraction of the students are boys?

Answer:

See  below

Step-by-step explanation:

Lets label the consecutive odd numbers as 2n+1 and 2n+3 where n is an integer.

We need to prove that

((2n + 3)^2 - (2n + 1)^2 is a multiple of 8.

Using the difference of 2 squares on the left side:-

(2n + 3 + 2n + 1)(2n + 3 -  (2n + 1)

=  (4n + 4)(2)

= 8n + 8  which is a multiple of 8  

Final answer:

The difference between squares of consecutive odd numbers can be expressed as 4n+4 which is a multiple of 8.

Explanation:

Let's take two consecutive odd numbers. We can express an odd number as 2n+1 where n is any integer. So, the consecutive odd number will be 2n+3 (adding 2 to the previous one).

Now, the squares of these consecutive numbers are (2n+1)² and (2n+3)² respectively.

The difference between these squares is (2n+3)² - (2n+1)². Applying the formula a² - b² = (a+b)(a-b), we get 4n+4 as the answer which is a multiple of 8 as 8 divides it without a remainder.

So the difference between the squares of consecutive odd numbers is a multiple of 8.

Learn more about Consecutive Odd Numbers here:

brainly.com/question/35983904

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Answer:

-6w-22

Step-by-step explanation:

-3(2w+6)-4=

= -6w-18-4=

= -6w-22

So,choose C (none of the above) :)

Answer:

a = 3 and b = 4

Step-by-step explanation:

Independent Equations

Lines intersect

One solution

In this case the two equations describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the equation of either line. Thus the pair (x, y) is the one and only solution to the system of equations. One solution is called "consistent". This shows two distinct non-parallel lines that cross at exactly one point. This is called an "independent" system of equations, and the solution is always some x, y-point.