Answer:
y = -1/2x-8
Step-by-step explanation:
If the lines are parallel, they have the same slope.
y = -1/2x +3 is in the form y=mx+b where m is the slope and b is the y intercept
-1/2 is the slope so the new line will have a slope of -1/2
(0,-8) is the y intercept since x=0
We can write the equation since we know the slope (-1/2) and the y intercept (-8)
y = -1/2x-8
<h3>
Answer: D) 1/3</h3>
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Explanation:
Start at (2,-3). Move up 3 and over to the right 6 spots to move to (8,0) which is where point F is located.
We can write the slope as rise/run = 3/6
Go back to (2,-3). Move up 1 and to the right 2 spots to arrive at F ' (4,-2)
Let's now compare the upward movements:
- Initially we moved up 3 units when trying to get to point F
- Now we're only moving up 1 unit when getting to F'
The starting point each time is (2,-3) which is the center of dilation. The jump from 3 to 1 is "times 1/3" and that's our scale factor. Every linear distance in the image is 1/3 times as long compared to the preimage.
We can also get the same scale factor when comparing the horizontal movements as well. The jump from 6 to 2 is also "times 1/3".
Answer:
x = e^12/100
Step-by-step explanation:
Solve for x over the real numbers:
10 ln(100 x) - 3 = 117
Add 3 to both sides:
10 ln(100 x) = 120
Divide both sides by 10:
ln(100 x) = 12
Cancel logarithms by taking exp of both sides:
100 x = e^12
Divide both sides by 100:
Answer: x = e^12/100
Answer:
NOTES
Step-by-step explanation:
Answer:
The area is changing at 15.75 square feet per second.
Step-by-step explanation:
The triangle between the wall, the ground, and the ladder has the following dimensions:
H: is the length of the ladder (hypotenuse) = 10 ft
B: is the distance between the wall and the ladder (base) = 6 ft
L: the length of the wall (height of the triangle) =?
dB/dt = is the variation of the base of the triangle = 9 ft/s
First, we need to find the other side of the triangle:
Now, the area (A) of the triangle is:
Hence, the rate of change of the area is given by:
Therefore, the area is changing at 15.75 square feet per second.
I hope it helps you!