Find the first five multiples of 9

Answer:

y = -4

Step-by-step explanation:

Assuming the problem is , it would be nice if we could convert both sides of this equation to the same base; that way, we could compare the exponents directly in an equation of their own. Fortunately, 8 and 16 are both powers of 2 -- and , we can rewrite the original equation by substituting those in:

When you have an exponent raised to another exponent, you multiply those exponents together, so we can simplify our equation by distributing a 3 in the left exponent and a 4 in the right:

With both of our bases the same, we can now simply compare their exponents directly to solve for y:

We know that the perimeter of a rectangle is twice the length, plus twice the width.  

P = 2L + 2W  

We also know that the perimeter is 156.  

P = 156  

Finally, we know that the width is 12 less than the length.  

W = L - 12.  

The next thing that we do is substitute the information that we have into the original equation:  

P = 2L + 2W  

156 = 2L + 2(L - 12)  

From this point we start to solve  

156 = 2L + 2L - 24 <---we multiplied the '2' through the parenthesis  

156 + 24 = 2L + 2L - 24 + 24  

180 = 2L + 2L <--- getting like terms on same sides  

180 = 4L <---combining like terms  

180/4 = 4L/4 <--- getting like terms on same sides  

45 = L <---now we have a value for L  

Now we take the known value for L and substitute it in to our equation for W  

W = L - 12  

W = 45 - 12  

W = 33  

So now we have Length = 45 and Width = 33.

w = l - 12

156 = 2l + 2w

Since we have a value of w, we can plug that into the variable w to find the exact value of l.

156 = 2l + 2(l - 12)

Distributive property.

156 = 2l + 2l - 24

Combine like terms.

156 = 4l - 24

Add 24 to both sides.

180 = 4l

Divide both sides by 4.

l = 45

Now that we have the exact value of l, we can find the exact value of w.

w = l - 12

w = 45 - 12

w = 33

We now know the width is equal to 33 cm, and the length is equal to 45 cm. (This is your answer.)

We can verify by plugging these values into the second equation.

156 = 2l + 2w

156 = 2(45) + 2(33)

156 = 90 + 66

156 = 156 √ this is correct.