Answer:
B.
Step-by-step explanation:
So we know right off the bat the angles ABE and CBD are congruent because of vertical angles.
Now we can look at the sides.
The ratio for 27:18 = 3:2
The ratio for 36:24 = 3:2
They check out.
That means that the answer is B. SAS
The distance between P and Q is 10 units. hope this helps have a nice day
Any
![x](https://tex.z-dn.net/?f=x)
in this set will be real numbers that are both less than
![-3](https://tex.z-dn.net/?f=-3)
and greater than
![5](https://tex.z-dn.net/?f=5)
. But that's not possible, so this set is empty.
Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,
![\int\limits^1_0 {(pi)y^{2} } \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%20%7B%28pi%29y%5E%7B2%7D%20%7D%20%5C%2C%20dx)
which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,
![\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_0%20%7Bpi%20-%20pix%5E%7B2%7D%20%7D%20%5C%2C%20dy%20%3D%20%5Cint%5Climits%5E2_0%20%7B1%20-%20y%5E%7B2%7D%2F4%20%7D%20%5C%2C%20dy)
If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.
Answer:
x = 7 x = -6
Step-by-step explanation:
x^2−x−42=0
Factor
What two numbers multiply to -42 and add to -1
-7*6 = -42
-7+6 = -1
(x-7) (x+6) =0
Using the zero product property
x-7 =0 x+6 =0
x = 7 x = -6