Answer:
-21=24
Step-by-step explanation:
Subtract 24 from 3
-21=8+2^2
Raise 4 to the power of 2
-21=8+16
Add 8 and 16
-21=24
Answer:
63
Step-by-step explanation:
Set up the proportion
(6x+3)/17 = (8x - 1)/21 Cross Multiply
21 * (6x + 3) = 17 (8x - 1) Remove the brackets
126x + 63 = 136x - 17 Subtract 126x from both sides
63 = 136x - 126x - 17 Combine
63 = 10x - 17 Add 17 to both sides
63 + 17 = 10x Combine the left
80 = 10 x Divide by 10
80/10 = x
x = 8
Now you want 8x - 1
8*8 - 1 = 63
The denominator of the second fraction is the difference of squares, so can be factored using the formula for that.
(n^2 -4) = (n -2)(n +2)
Now, you will note that the second fraction has a numerator that is equal to one of the factors in the denominator. In other words, the whole fraction can be simplified to ...
(n +2)/((n +2)(n -2)) = 1/(n -2) . . . . with the restriction n≠-2
This reduced form of the fraction has the same denominator as the first fraction, so you can say that the lowest common denominator is that: (n -2).
_____
If there is some reason you don't want to reduce the second fraction, the lowest common denominator will be (n -2)(n +2).
The <u>correct answer</u> is:
B) A 90° counterclockwise rotation about the origin, followed by a reflection across the x-axis, followed by a translation 8 units right and 1 unit up.
Explanation:
The coordinates of the <u>points of the pre-image</u> are:
(3, 1)
(3, 4)
(5, 7)
(6, 5)
(6, 2)
The coordinates of the <u>points of the image</u> are:
(7,-2)
(4,-2)
(1,-4)
(3,-5)
(6,-5)
A 90° counterclockwise rotation about the origin negates the y-coordinate and switches it and the x-coordinate. Algebraically,
(x,y)→(-y,x).
When this is applied to our points, we get:
(3, 1)→(-1, 3)
(3, 4)→(-4, 3)
(5, 7)→(-7, 5)
(6, 5)→(-5, 6)
(6, 2)→(-2, 6)
A reflection across the x-axis negates the y-coordinate. Algebraically,
(x, y)→(x, -y).
Applying this to our new points, we have:
(-1, 3)→(-1, -3)
(-4, 3)→(-4, -3)
(-7, 5)→(-7, -5)
(-5, 6)→(-5, -6)
(-2, 6)→(-2, -6)
A translation 8 units right and 1 unit up adds 8 to the x-coordinate and 1 to the y-coordinate. Algebraically,
(x, y)→(x+8, y+1).
Applying this to our new points, we have:
(-1, -3)→(-1+8,-3+1) = (7, -2)
(-4, -3)→(-4+8,-3+1) = (4, -2)
(-7, -5)→(-7+8,-5+1) = (1, -4)
(-5, -6)→(-5+8,-6+1) = (3, -5)
(-2, -6)→(-2+8,-6+1) = (6, -5)
These match the coordinates of the image, so this is the correct series of transformations.
Answer:
Step-by-step explanation:
The formula of a volume of a pyramid:
<em>B</em><em> - area of a base</em>
<em>H</em><em> - height</em>
We have
Substitute:
