ANSWER
EXPLANATION
We want to write
as a single logarithm.
Use the power rule to rewrite the middle term:
Use the product rule to obtain:
Apply the quotient rule:
Really, everytime I actually need help with a question,
1 answer:
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Answer:
4
Step-by-step explanation:
use the Pythagoras' theorem
formula for an ABC triangle( right angled)
AB is height
BC is hypotenuse
CA is length
=
+
in your case
AB is 7
BC is 8
CA is unknown so we write x
=
+
64=49+
64-49=
15=
=x
3.87=x
4=x
Answer:
7) K'(1, 1), N'(4, 0), Q'(4, 4)
9) F'(4, 2), W'(4, 5), K'(3, 2)
Step-by-step explanation:
When you are not sure about reflections and rotations, it can be useful to actually draw a graph. The line of reflection is the perpendicular bisector of the segment connecting a point with its image. That is, the image is the same distance from the line on the other side. A point that is <em>on</em> the line of reflection is "invariant," it doesn't move.
__
7) Reflecting across the x-axis changes the sign of the y-coordinate. That is all. Any point on the x-axis (y=0) is unchanged. The transformation is ...
(x, y) ⇒ (x, -y)
__
9) Reflecting across a vertical line changes the x-coordinate. The new value of x will be ...
x' = 6 - x
The "6" is double the x-coordinate of the vertical line. The transformation is ...
(x, y) ⇒ (6-x, y)
_____
<em>Derivation of the formula for reflection on x=3</em>
In general if M is the midpoint of a point (A) and its reflection (A'), then we have ...
M = (A +A')/2
2M = A + A'
2M -A = A'
When a point is reflected across a vertical line, all of the y-coordinate values remain unchanged. So, for A=(x, y) and M=(3, y), we have ...
A' = 2(3, y) -(x, y) = (6-x, 2y-y)
A' = (6 -x, y)
So, the reflection transformation across the line x = 3 is ...
(x, y) ⇒ (6-x, y)
