Answer: x = - 7/12
Step-by-step explanation:
-3x + 2 - 5x - 7 = 4x + 2
=> -8x - 5 = 4x + 2
=> -12x = 7
=> x = - 7/12
Answer:
Orinal number of cats= 171
Step-by-step explanation:
Giving the following information:
Decrease in population= 30%
Current population= 120
<u>To calculate the original number of cats, we need to use the following formula:</u>
Orinal number of cats= current population / (1 - decrease)
Orinal number of cats= 120 / (1 - 0.3)
Orinal number of cats= 171
Answer:

Step-by-step explanation:
This problem can be solved by using the expression for the Volume of a solid with the washer method
![V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_a%5Eb%5BR%28x%29%5E2-r%28x%29%5E2%5Ddx)
where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).
Before we have to compute the limits of the integral. We can do that by taking f=g, that is

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)
x1=0.14
x2=8.21
and because the revolution is around y=-5 we have

and by replacing in the integral we have
![V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_%7Bx1%7D%5E%7Bx2%7D%5B%28lnx%2B5%29%5E2-%28%5Cfrac%7B1%7D%7B2%7Dx%2B3%29%5E2%5Ddx%5C%5C)
and by evaluating in the limits we have

Hope this helps
regards
<span>t's call P the number of art brushes that Monique has.
Chelsea has 11xP (that is 11 times as many as Monique)
Together they have:
P + 11xP = 12xP
That means 12xP = 60 (60 is the number of art brushes they have together)
In order to find how much is P, we need to divide:
60 Ă· 12 = 5 brushes
P = 5 ; that means has Monique 5 art brushes.
Chelsea has 11 times as many art brushes as Monique:
11 x 5 = 55 brushes</span>
3.21 it should be at least