Answer:
-60
Step-by-step explanation:
The objective is to state whether or not the following limit exists
.
First, we simplify the expression in the numerator of the fraction.
![3(2x-1)^2 -75 = 3(4x^2 - 4x +1) -75 = 12x^2 - 12x + 3 - 75 = 12x^2 - 12x -72](https://tex.z-dn.net/?f=3%282x-1%29%5E2%20-75%20%3D%203%284x%5E2%20-%204x%20%2B1%29%20-75%20%3D%2012x%5E2%20-%2012x%20%2B%203%20-%2075%20%3D%2012x%5E2%20-%2012x%20-72)
Now, we obtain
![12(x^2-x-6) = 12(x+2)(x-3)](https://tex.z-dn.net/?f=12%28x%5E2-x-6%29%20%3D%2012%28x%2B2%29%28x-3%29)
and the fraction is transformed into
![\frac{3(2x-1)^2 - 75}{x+2} = \frac{12(x+2)(x-3)}{x+2} = 12 (x-3)](https://tex.z-dn.net/?f=%5Cfrac%7B3%282x-1%29%5E2%20-%2075%7D%7Bx%2B2%7D%20%3D%20%20%5Cfrac%7B12%28x%2B2%29%28x-3%29%7D%7Bx%2B2%7D%20%3D%2012%20%28x-3%29)
Therefore, the following limit is
![\lim_{x \to -2} \frac{3(2x-1)^2 - 75}{x+2} = \lim_{x \to -2} 12(x-3) = 12 \lim_{x \to -2} (x-3)](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20-2%7D%20%20%5Cfrac%7B3%282x-1%29%5E2%20-%2075%7D%7Bx%2B2%7D%20%3D%20%5Clim_%7Bx%20%5Cto%20-2%7D%20%2012%28x-3%29%20%3D%2012%20%5Clim_%7Bx%20%5Cto%20-2%7D%20%28x-3%29)
You can plug in
in the equation, hence
![12 \lim_{x \to -2} (x-3) = 12 (-2-3) = -60](https://tex.z-dn.net/?f=12%20%5Clim_%7Bx%20%5Cto%20-2%7D%20%28x-3%29%20%3D%2012%20%28-2-3%29%20%3D%20-60)
Macroeconomics focuses on C) government level.
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of an economy as a whole rather than individual markets.
Answer:
13 pencils.
Step-by-step explanation:
Let x be the pens and y be the pencils
Given:
Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.
Total pens and pencils is 22
So,
----------------(1)
And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.
------------(2)
solve equation 1 and equation 2 for x and y.
From equation 1.
![x+y=22](https://tex.z-dn.net/?f=x%2By%3D22)
----------------(3)
put y value in equation 2.
![0.75x+0.4(22-x)=11.95](https://tex.z-dn.net/?f=0.75x%2B0.4%2822-x%29%3D11.95)
![0.75x+0.4\times 22-0.4x=11.95](https://tex.z-dn.net/?f=0.75x%2B0.4%5Ctimes%2022-0.4x%3D11.95)
![0.75x+8.8-0.4x=11.95](https://tex.z-dn.net/?f=0.75x%2B8.8-0.4x%3D11.95)
![0.75x-0.4x=11.95-8.8](https://tex.z-dn.net/?f=0.75x-0.4x%3D11.95-8.8)
![0.35x=3.15](https://tex.z-dn.net/?f=0.35x%3D3.15)
![x=\frac{3.15}{0.35}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3.15%7D%7B0.35%7D)
![x=9](https://tex.z-dn.net/?f=x%3D9)
Now substitute x value in equation 3.
![y=22-9](https://tex.z-dn.net/?f=y%3D22-9)
![y=13](https://tex.z-dn.net/?f=y%3D13)
So, he buy 13 pencils.
Answer:
x = 3/2
Step-by-step explanation:
2(x + 5) = 6x + 4
Open bracket first
2 × x + 2×5 = 6x + 4
2x + 10 = 6x + 4
Rewrite equation
6x + 4 = 2x + 10
Subtract 2x from both sides
6x - 2x + 4 = 2x - 2x + 10
4x + 4 = 10
Subtract 4 from both sides
4x + 4 - 4 = 10 - 4
4x = 6
Divide both sides by 4
4x/4 = 6/4
x = 6/4
Divide both denominator and numerator by 2
x = (6/4) ÷ 2
x = 3/2
I hope this was helpful, please rate as brainliest
Answer:
2+n/5
Step-by-step explanation:
sum=plus
quotient=divide
number=n