A square has 4 equal sides which make up the perimeter.
Therefore the length of one side = (16x + 32y) / 4 = 4x + 8y Answer
Answer:
The given algebraic representation (x,y) → (-x, y) represents the reflection of a point (x, y) across the y-axis.
Step-by-step explanation:
We know that when a point P(x, y) is reflected across the y-axis, the x-coordinate changes/reverses its sign, but the y-coordinate stays the same.
Thus, the rule of reflection of a point P(x, y) across y-xis is:
P(x, y) → P'(-x, y)
For example, if a point A(1, 2) is reflected across the y-axis, the coordinates of the image A' of the point A(1, 2) will be:
A(1, 2) → A'(-1, y)
In our case, we are given the algebraic representation
(x,y) → (-x, y)
Here:
- The x-coordinate changes/reverses its sign
- The y-coordinate stays the same.
Thus, the given algebraic representation (x,y) → (-x, y) represents the reflection of a point (x, y) across the y-axis.
Ok so to solve this problem we're going to need to find out how much money they made (their revenue) and the subtract the cost of paying the employees.
So, let's start by finding their revenue
Step 1: Multiply the cost of each beverage by the number sold
Coffees: 20 x 2.85 = 57
Lattes: 17 x 4.80 = 81.6
Step 2: add up the money made from the coffees and the money made from the lattes to get the total revenue
57 + 81.6 = 138.6
So the shop made $138.60 on Tuesday. Let's set that aside while we find out how much the shop's costs were.
Step 3: Find the price of paying two employees for 6 hours
2 x 6 x 14.5 = 174
So the shop had to pay the employees $174.00 for working there.
Step 4: Find the overall profit/loss by subtracting the cost from the revenue
138.6 - 174 = -35.4
So the shop had a loss of $35.40 on Tuesday.
Hope that helps! Feel free to leave a comment or send me a message if I can clarify anything :)
You can do this without drawing even. Let's say the coordinates are
A, B and C, respectively, and we're looking for D.
If the other vertex is opposite A(2,1), it will be at B+C-A = (8, 11)
If the other vertex is opposite B, it will be at A+C-B = (4, -1)
If the other vertex is opposite C, it will be at A+B-C = (0, 3)
Explanation: think of one of the vertexes as a corner of the parallelogram and you want to travel to the opposite corner. That means you must add both vectors that represent the sides. So from A to D, you'd have to add (B-A) and (C-A). That gives us A+(B-A)+(C-A) simplifies to B+C-A.
<h2><u>Answer (d</u>) :</h2>
These triangles are congruent under the SAS congruence criterion. We can prove it using the following steps :
Given :
In triangle 1 and 2 :
- A side in triangle 1 and a side in triangle 2 are equal.
- Another side in triangle 1 and triangle 2 is equal.
- The angle between the equivalent sides is also equal.
Since the SAS congruence criterion says that two triangles are congruent if two of their sides and one included angle is equal and since these 2 triangles fulfill all of those rules, we can conclude that these triangles are congruent under the SAS congruence criterion.
