Answer:
(x, y) ⇒ (-x, y)
Step-by-step explanation:
When you're looking for a rule that transforms one figure to the other, the first step is to look at the figures. You want to identify their orientation (order of vertices) and the relative locations of corresponding vertices.
Here, vertices VWX are in <em>clockwise</em> order. The corresponding vertices V'W'X' are in <em>counterclockwise</em> order. For that to happen, there must be a reflection involved.
The y-axis goes through the midpoints of VV', WW' and XX'. This means the y-axis is the line of reflection. The coordinates of V'W'X' have the same y-values as their originals, but their x-values have changed sign.
The algebraic rule for these two figures is ...
(x, y) ⇒ (-x, y) . . . . . . reflection over y-axis; sign of x changes
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<em>Additional comment</em>
No rotation is involved here.
The rule (x, y) ⇒ (x, y+10) means the y-coordinate has had 10 added to it. That causes a translation upward by 10 units. This <em>is</em> the algebraic rule.
Answer: 4 (OPTION 2)
Step-by-step explanation:
1. To solve this problem you must apply the Intersecting secants theorem, as you can see below:

Where:


2. Then you must susbstitute values and solve for x, as following:

Therefore the answer is the second option.
Answer:
(a) 
(b) 
(c) Jim initially had 48; Kirk initially had 12
Step-by-step explanation:
Given


Solving (a): An equation for the amount they originally had.
From the question, we understand that j is 4 times as many as k.
Mathematically, this is:


Solving (b): Equation after Kirk wins
Initially Kirk had k.
To get the new expression, we add 18 to k.
This gives: 18 + k
In the same vein, Jim's number of chirps will reduce by 18.
Initially, Jim had j chirps (or 4k chirps)
To get the new expression, we subtract 18 from j.
This gives: j - 18
So, the equation is:

Solving (c): Number of chirps they started with.
In (b), we have:

Substitute 4k for j

Collect Like Terms


Divide both sides by 3

Substitute 12 for k in 


Step-by-step explanation:
volume = [(15×11)+(½×15×8)] x 12
= (165+60) x 12
= 225×12
= 2,700 cm³