Answer:
1089525
Step-by-step explanation:
2985 is per day of bulbs and a year has 365 days
so we multiply bulbs by day and days in a year
which will give us 1089525
Answer:
c. (x + 3)
Step-by-step explanation:
using factor theorem
if x - 3 is a factor then p(a) = 0
p(a)= x^3 - 3x^2 - 4x + 12
a.(x-3)
p(3) = (3)^3 - 3(3)^2 - 4(3) + 12
= 27 - 27 - 12 + 12
= 0
therefore x-3 is a factor
b.(x + 2)
p(-2) = (-2)^3 - 3(-2)^2 - 4(-2) + 12
= -8 -12 + 8 + 12
,= 0
therefore x + 2 is a factor
c.(x + 3)
p(-3) = (-3)^3 - 3(-3)^2 - 4(-3) + 12
= -27 -27 + 12 + 12
= -30
therefore x + 3 is not a factor
d.(x-2)
p(2) = (2)^3 - 3(2)^2 - 4(2) + 12
= 8 -12 - 8 + 12
= 0
therefore x - 2 is a factor
The triangle BAC has two known measurements 30 and 90 so add those together and subtract by 180
30 + 90 = 120
180 - 120 = 60°
Answer: B. 1975
Step-by-step explanation:
Given: The model of population of a certain city between the years 1965 and 1995 by the radical function
![P(x)=75000\sqrt[3]{x-1940}](https://tex.z-dn.net/?f=P%28x%29%3D75000%5Csqrt%5B3%5D%7Bx-1940%7D)
To find the x year at which population is 245,000, put this in equation we get
![245000=75000\sqrt[3]{x-1940}\\\\\Rightarrow\frac{245000}{17000}=\sqrt[3]{x-1940}\\\\\Rightarrow3.266=\sqrt[3]{x-1940}\\\\\Rightarrow\ x-1940=(3.266)^3..........\text{[by taking cube on both sides]}\\\\\Rightarrow\ x-1940=34.8587\\\\\Rightarrow\ x=1940+34.8587\\\\\Rightarrow\ x=1974.8587\approx1975](https://tex.z-dn.net/?f=245000%3D75000%5Csqrt%5B3%5D%7Bx-1940%7D%5C%5C%5C%5C%5CRightarrow%5Cfrac%7B245000%7D%7B17000%7D%3D%5Csqrt%5B3%5D%7Bx-1940%7D%5C%5C%5C%5C%5CRightarrow3.266%3D%5Csqrt%5B3%5D%7Bx-1940%7D%5C%5C%5C%5C%5CRightarrow%5C%20x-1940%3D%283.266%29%5E3..........%5Ctext%7B%5Bby%20taking%20cube%20on%20both%20sides%5D%7D%5C%5C%5C%5C%5CRightarrow%5C%20x-1940%3D34.8587%5C%5C%5C%5C%5CRightarrow%5C%20x%3D1940%2B34.8587%5C%5C%5C%5C%5CRightarrow%5C%20x%3D1974.8587%5Capprox1975)
Hence, at year 1975 the population of the city is 245,000.
I was originally going to graph the two equations, but I don't have graph paper so I set the equations equal to each other.
so Mr.Reeds equation is: y=70x+4.5 and Mrs.Reeds equation is: y=85x
so if I set these equal to each other I would minus the 70x from both sides leaving me with 15x = 4.5. Now since that's done I would divide everything by 15 which will cause me to get a fraction. So once that's done I would be left with x=3/10. I hope this helped!
