40x - 24 - 33x - 77 = 102
40x - 33x = 102 + 24 + 77
7x = 203
x = 29
Answer:
The real solution is
.
Step-by-step explanation:
while ![\sin(\frac{\pi}{2})=1](https://tex.z-dn.net/?f=%5Csin%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%3D1)
So the equation becomes:
![-64=(2(0)+2i(1))^n](https://tex.z-dn.net/?f=-64%3D%282%280%29%2B2i%281%29%29%5En)
![-64=(0+2i)^n](https://tex.z-dn.net/?f=-64%3D%280%2B2i%29%5En)
![-64=(2i)^n](https://tex.z-dn.net/?f=-64%3D%282i%29%5En)
We know that
. So let's see what
gives us:
.
is the result we wanted.
is therefore a solution.
If you are looking to round, then you simply either round up or round down due to the term before the place you want to round (in this case, the thousands place). when you round in this case, you would round down because 4 is less than 5 (the middle point between 0 and 10) in which case would give us 60,000
Answer:
x-intercept:
A line that crosses the graph at x-axis.
i.e substitute y = 0 and solve for x.
As per the statement:
A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water
Given the graph:
![y = -2x^2+20x+400](https://tex.z-dn.net/?f=y%20%3D%20-2x%5E2%2B20x%2B400)
Substitute y = 0 we have;
![-2x^2+20x+400 = 0](https://tex.z-dn.net/?f=-2x%5E2%2B20x%2B400%20%3D%200)
⇒![-2(x^2-10x-200) = 0](https://tex.z-dn.net/?f=-2%28x%5E2-10x-200%29%20%3D%200)
⇒![x^2-10x-200 =0](https://tex.z-dn.net/?f=x%5E2-10x-200%20%3D0)
⇒![x^2-20x+10x-200 =0](https://tex.z-dn.net/?f=x%5E2-20x%2B10x-200%20%3D0)
⇒![x(x-20)+10(x-20)=0](https://tex.z-dn.net/?f=x%28x-20%29%2B10%28x-20%29%3D0)
⇒![(x-20)(x+10)=0](https://tex.z-dn.net/?f=%28x-20%29%28x%2B10%29%3D0)
By zero product property we have;
x-20 =0 and x+10 = 0
⇒x = 20 and x = -10
Therefore, the x-intercept represents the water has no larvae at −10 degrees Celsius and 20 degrees Celsius.