The question is incomplete:
Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p
=
s^2+9s-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
Answer:
s>42
Reyna needs to sell more than 42 T-shirts.
Step-by-step explanation:
Given that you have to find the amount of T-shirts that should be sold to earn a profit of more than $2,000, you have to find the amount required to earn $2,000 by replacing p with 2,000 and solving for s:
s^2+9s-142=2000
s^2+9s-2142=0
(s+
)^2-2142-(
)^2=0
(s+
)^2=2142+(
)^2
(s+
)^2=2142+![\frac{81}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B81%7D%7B4%7D)
(s+
)^2=![\frac{8649}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B8649%7D%7B4%7D)
![\sqrt{(s+\frac{9}{2})^2 } =\sqrt{\frac{8649}{4} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28s%2B%5Cfrac%7B9%7D%7B2%7D%29%5E2%20%7D%20%3D%5Csqrt%7B%5Cfrac%7B8649%7D%7B4%7D%20%7D)
s+
=![\frac{93}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B93%7D%7B2%7D)
s=![\frac{93}{2}- \frac{9}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B93%7D%7B2%7D-%20%5Cfrac%7B9%7D%7B2%7D)
s=![\frac{186-18}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B186-18%7D%7B4%7D)
s=![\frac{168}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B168%7D%7B4%7D)
s=42
According to this, Reyna needs to sell more than 42 T-shirts to earn a profit of more than $2,000.
X-intercept mean y=0
2/5x+1/10(0)=2
2/5x=2
X= 5
X-intercept = (5,0)
Y-intercept means x= 0
2/5(0)+1/10y=2
1/10y=2
y=20
Y-intercept = (0,20)