The width of a rectangle is 6 inches less than it’s length, and the area is 7 square inches. what are the length and width of the rectangle

So length is 7 in while width is 1 in.

Step-by-step explanation:

We are given W is 6 inches less than L which mean as an equation we have W=L-6.

We are given the area of this rectangle, LW=7.

So we have the system:

W=L-6

LW=7.

Replace the second W with what the first W equals:

LW=7

L(L-6)=7

Distribute:

Subtract 7 on both sides:

We are luck since the coefficient of L^2 is 1.  This means all we have to do is find two numbers that multiply to be -7 add at the same time add up to -6.

Those numbers are -7 and 1 since (-7)(1)=-7 and (-7)+(1)=-6.

So the factored form of our equation is:

(L-7)(L+1)=0

This gives us two equations to solve:

L-7=0  or L+1=0

L=7     or L=-1

L=-1 doesn't make sense for a length so L=7.

L=7 means the length is 7 inches.

If W=L-6 and L=7, then W=7-6=1.

The width is 1 inch since W=1.

So length is 7 in while width is 1 in.

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.