3x^2-16x=x^2-30
-x^2 -x^2
2x^2-16x=-30
+30 +30
2x^2-16x+30=0
2x-6=0 or x-5=0
x=3 or x=5
A. 3,5
If you need an explanation, I can provide one. Hope it helped! If it didn't tell me what went wrong or what confused you.
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)
Answer:
38.72%
Step-by-step explanation:
Estimated attendance = 1,000
The actual value of attendance = 1,632
We need to find the percent error of Shaun's estimate. Using the formula as follows :
![\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100](https://tex.z-dn.net/?f=%5C%25%3D%5Cdfrac%7B%7C%5Ctext%7Bactual%20value-estimated%20value%7D%7C%7D%7B%5Ctext%7Bactual%20value%7D%7D%5Ctimes%20100)
Put all the values,
![\%=\dfrac{1632-1000}{1632}\times 100\\\\=38.72\%](https://tex.z-dn.net/?f=%5C%25%3D%5Cdfrac%7B1632-1000%7D%7B1632%7D%5Ctimes%20100%5C%5C%5C%5C%3D38.72%5C%25)
So, the percent error of Shaun's estimate is 38.72%.
Answer: -49
Step-by-step explanation:
Adding a positive number will make the negative number smaller. I am bad at explaining:(
Answer:
x= 1
QS = 10 cm
QRS = 40cm
Step-by-step explanation:
4x + 1 = 5x
x= 1 cm
QS = 4x + 1 + 5x
= 9x + 1
= 9 + 1
= 10cm
QRS perimeter
QS + RQ + RS but ( RQ = RS)
= 10 + 15 + 15
= 40cm