A contractor is paving 1 mile 201.25 yards of a county road. How long is this portion of the road in feet and inches?
1 answer:
A contractor is paving 1 mile 201.25 yards of a county road
Given distance is 1 mile and 201.25 yards
First we will convert 1 mile in feet.
1 mile = 5280 feet
Now we will convert 201.25 yards in feet
1 yard = 3 ft
201.25 yards = feet
So total distance in feet is = 5280+603.75 = 5883.75 feet
1 foot = 12 inches
0.75 feet = inches
This is 5883 feet and 9 inches.
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1:
notice that each part is divisible by 3
÷ 3 =
9n ÷ 3 = 3n
6 ÷ 3 = 2
so it becomes
3n can be rewritten as 2n+n
-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)
which would get you
Now that it's rewritten, you can factor out n + 2 from the equation.
<u><em>the answer is </em></u>
3(n+2)(n+1)
And you can check that by multiplying (n+2)(n+1) which is and then each of those by 3, which is
or
, our origional equation
2:
So I rewrote this as (it's the same thing, just reordered using the commutative property)
now -11x can be rewritten as -4x-7x
(remember, the two numbers should multiply to equal 28, which is our constant.)
now we can factor out x from the first expression and -7 from the second
and lastly you factor out x-4,
<u><em>which would give you</em></u>
(x-4)(x-7)
Make sure to check your work and make sure it multiplies to
3:
The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12
So if you rewrite 9 as and 4 as
, the equation becomes
now that is ugly so it can be turned into
and -12x can be rewritten as
so our equation now looks like
There's a rule that says
In our case, a=3x and b=2
<u><em>so the final answer is</em></u>