If AB = CD, then 3x+4 is equal to 4x-1
3x + 4 = 4x - 1
Add one to both sides to cancel out.
3x + 5 = 4x
Subtract 3x from both sides to cancel out.
5 = x
Now, substitute the 5 in place of the x in the equation for AB (3x+4)
3(5) + 4
15 + 4
19
Final Answer: B) 19
First, factor out a 3.
3(x² - 9)
In any quadratic ax² + bx + c, we can split the bx term up into two new terms which we want to equal the product of a and c.
In this case, we have x² + 0x - 9. (the 0x is a placeholder)
We want two numbers that add to 0 and multiply to get -9.
Obviously, these numbers are 3 and -3.
Now we have 3(x² + 3x - 3x - 9).
Let's factor.
3(x(x+3)-3(x+3))
<u>3(x-3)(x+3)</u>
There are multiple shortcuts which you could make here, FYI:
Instead of splitting the middle, if your a value is 1, you can go straight to that step (x+number)(x+other number).
Whenever you have a difference of squares, like a²-b², that factors to (a+b)(a-b).
Step 1
find the perimeter of a <span>single enclosure
perimeter of a square=4*b
where b is the long side of a square
area square=b</span>²
area square=2025 ft²
b²=2025-------> b=√2025-----> b=45 ft
<span>so
perimeter=4*45-------> 180 ft
step 2
</span>find the perimeter of a two individual enclosure
<span>perimeter=4*20+3*40------> 200 ft
area=20*40*2------> 1600 ft</span>²
<span>
therefore
fencing singular enclosure < fencing two individual enclosure
180 ft < 200 ft
</span>area singular enclosure > area two individual enclosure
2025 ft² > 1600 ft²<span>
the answer is the option
</span><span>a The singular enclosure would minimize cost because it requires 180 feet of fencing.</span><span>
</span>
Substitute answers in, a = 3 and b = 2.
(3^2 - 2^2)/(3+2)
= (9-4)/5
= 5/5
= 1
