(Note: this is hard to explain without graphing. You might want to graph both of these lines just to make sure I did this correctly. :))
Y = -4(x) is the y = mx + b where m = slope and b = the y intercept.
So the slope of line A is -4 / 1 and the y intercept is 0. (If it's 0 there is no point in writing it down, so it was left out of the equation.)
The slope of line B with be equal to the slope of line A, so we can fill that in our equation. y = -4 x + ??
We know that y increases as x decreases.
Now we just need to scale 8, -3 down until x = 0.
(8 - 4, -3 + 1) = (4, -2)
(4 - 4, -2 + 1) = (0, -1)
y = -4x -1 is your final answer. Hope that helps! :)
Answer:
Area of a circle is denoted by: πr^2 where r is the radius of the circle. = 16/2 = 8 feet.
Step-by-step explanation:
Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.
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Explanation:
We have this sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
which is geometric with the following properties
- a = first term = 1
- r = common ratio = 1/2 = 0.5
Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.
Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.
That infinite sum is
S = a/(1-r)
S = 1/(1-0.5)
S = 1/0.5
S = 2
So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.
In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.
Here's a list of partial sums
- 1+1/2 = 1.5
- 1+1/2+1/4 = 1.75
- 1+1/2+1/4+1/8 = 1.875
- 1+1/2+1/4+1/8+1/16 = 1.9375
- 1+1/2+1/4+1/8+1/16+1/32 = 1.96875
- 1+1/2+1/4+1/8+1/16+1/32+1/64 = 1.984375
- 1+1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 1.9921875
- 1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 = 1.99609375
We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.
Answer: 8
Step-by-step explanation: 10-2=8
Answer:
4/7 or 4 up, 7 to the right.
Step-by-step explanation:
We have to isolate y, so if we subtract 4x from both sides we get:
-7y = -4x + 5
Then we divide by -7
y = 4/7x + 5/7
The slope is 4/7 or 4 up, 7 to the right.
