Answer:
You can find the point of intersection of the line with the y-axis and the the point of intersection of the line with the x-axis. See the graph attached.
Step-by-step explanation:
Find the intersection with the y-axis. Substitute 
into the equation and solve for y:
≈3.33
Find the intersection with the x-axis. Substitute 
into the equation and solve for x:
Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)
Answer:
<em>It will take 12 hours to fill the tank</em>
Step-by-step explanation:
Proportions
Tap A fills a tank in 4 hours. It means each hour it fills 1/4 of the tank.
Tap B fills the tank in 3 hours. Each hour it fills 1/3 of the tank.
Tap C empties the tank when full in 2 hours. Each hour it empties 1/2 of the tank.
Each hour, the tank gets filled by:
Since the tank fills 1/12 of its capacity in one hour, it follows that it will take 12 hours to fill the tank
Answer:
x = 21/8
Step-by-step explanation:
Step 1: Write equation
x - 11 = 3 - 7(x - 1)
Step 2: Solve for <em>x</em>
<u>Distribute -7:</u> x - 11 = 3 - 7x + 7
<u>Combine like terms:</u> x - 11 = 10 - 7x
<u>Add 7x on both sides:</u> 8x - 11 = 10
<u>Add 11 on both sides:</u> 8x = 21
<u>Divide both sides by 8:</u> x = 21/8
Step-by-step explanation:
Explanation:
The trick is to know about the basic idea of sequences and series and also knowing how i cycles.
The powers of i will result in either: i, −1, −i, or 1.
We can regroup i+i2+i3+⋯+i258+i259 into these categories.
We know that i=i5=i9 and so on. The same goes for the other powers of i.
So:
i+i2+i3+⋯+i258+i259
=(i+i5+⋯+i257)+(i2+i6+⋯+i258)+(i3+i7+⋯+i259)+(i4+i8+⋯+i256)
We know that within each of these groups, every term is the same, so we are just counting how much of these are repeating.
=65(i)+65(i2)+65(i3)+64(i4)
From here on out, it's pretty simple. You just evaluate the expression:
=65(i)+65(−1)+65(−i)+64(1)
=65i−65−65i+64
=−65+64
=−1
So,
i+i2+i3+⋯+i258+i259=-1
