The vertices of triangle WXY have coordinates W(3, 2), X(5, 5), and Y(7, 3). Triangle WXY was transformed to produce triangle WꞌXꞌYꞌ, with coordinates Wꞌ(−2, −1) and Yꞌ(2, 0).What are the coordinates of vertex Xꞌ?

Answers

Answer 1

Answer: We will do the analysis for each of the 3 vertices:
1st vertex:
W': We observe W'(x', y') and W(x, y)
x' = -2
x = 3
so, x plus some value will give the value of x'. We form the equation the following way:
x + Cx = x' (Cx will be the value used to MOVE the x to x' value)
When trying to solve the equation, we put values inside the equation:
3 + Cx = -2
The x coordinate is MOVED by some value Cx to become the x' coordinate (That is how we transform the triangle; by transforming each of its vertices by the same values for x and y coordinates, both respectfully).
Solving the equation, we get:
Cx = -2 - 3
Cx = -5.
The conclusion is: x coordinate is MOVED to the LEFT (because of the minus) by 5 units on axis.
Lets see for which amount y coordinate for this vertex is MOVED:
y'=-1
y=2
We obtain the equation again:
Add to y coordinate value some constant (Cy), to obtain the value of new (transformed coordinate) y'.
y+Cy=y'
2+Cy=-1
Cy=-1-2
Cy=-3
The conclusion is that y coordinate for this vertex is MOVED down on Y axis by 3 units on axis.
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We now observe in same manner the second vertex Y', and we expect to obtain the same constants as we obtained for the previous vertex, because that is the rule for the transformation being done, each vertex should MOVE by same amount of units on X and Y axis respectfully.
Hence, we now observe Y'(x', y') and Y(x, y):
x'=2
x=7
x+Cx=x' (some constant value added to x will produce the new value of x')
7+Cx=2
Cx=2-7
Cx=-5
So, the x coordinate value is MOVED to the left (meaning of minus) by 5 units, and the value of x' coordinate is obtained (transformation).
Next, we have for Y axis coordinates:
y'=0
y=3
y+Cy=y'
3+Cy=0
Cy=0-3
Cy=-3
So the conclusion is that y coordinate value is MOVED down by 3 units on Y axis, and in such way we obtained y' via transformation.
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We do the same approach for the third vertex X':
X'(x',y') and X(x,y)
We have to find coordinates for vertex X'(x',y')
We have coordinates to use, for X(x,y)=X(5,5).
x'=?
y'=?
x=5
y=5
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1) x+Cx=x'
5+(-5)=x' (because for previous two vertices we obtained that the constant Cx is for both vertices -5, Cx=-5)
hence, x'=5-5
x'=0
2) y+Cy=y'
5+(-3)=y' (because for previous two vertices we obtained that the constant Cy is for both vertices -3, Cy=-3)
y'=5-3
y'=2
Hence, the third TRANSFORMED vertex X' is with coordinates X'(0,2).
I attached a .png image here, so you could see the transformed triangle in a coordinate system.

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Write (picture included) as a complex number in standard form.

Answers

Answer:

-9/4 -4i

Step-by-step explanation:

-3i + 3/4 + 2i -(3+ 3i)

The first step is to simplify the terms

-3i + 3/4 + 2i -(3+ 3i)

Now we distribute the negative sign

-3i + 3/4 + 2i -3- 3i

Now combine like terms

3/4 -3 -3i+2i -3i

-2 1/4 -4i

Change the mixed number to an improper fraction.

-(4*2+1)/4 -4i

-9/4 -4i

A submarine is cruising at 25m below sea level. It descends 15m. What is the new depth?

Answers

Answer:

40m below sea level

Step-by-step explanation:

25m+15=40

Answer:

40 m below sea level

im assuming 25m+15m because the submarines decending

Which equations have the same solution as p−3=5?Hint: There are 3 equations

3p=30
3 p is equal to 30

p+2=10
p plus 2 is equal to 10

p8=1
p over 8 is equal to 1

p+7=16
p plus 7 is equal to 16

4p=32

Answers

Answer:

p + 2 = 10

$(p)/(8) =1$

4p = 32

Step-by-step explanation:

p - 3 = 5

p - 3 + 3 = 5 + 3

p = 8

3p = 30

3p ÷ 3 = 30 ÷ 3

p = 10

10 ≠ 8

p + 2 = 10

p + 2 - 2 = 10 - 2

p = 8

8 = 8

$(p)/(8) =1$

$8((p)/(8)) =8(1)$

8 = 8

p = 8

p + 7 = 16

p + 7 - 7 = 16 - 7

p = 9

9 ≠ 8

4p = 32

4p ÷ 4 = 32 ÷ 4

p = 8

8 = 8

A server gets an average of $4.50 in tips for each table he serves. In the morning, the server had 12 tables and in the afternoon the server had 13 tables Find his tips

Answers

Answer:

$112.50

Step-by-step explanation:

so the first thing you would do is add 12 to 13 to get

12 + 13 = 25

then multiply 25 by 4.50 to get

25 x 4.50 = 112.50

so the average number of tips the server has received is $112.50

Patty is 50 mi. due north of Todd. Emma is due east of Todd. The angle between the direction of the shortest distance from Emma and Patty and due east is 40°. To the nearest mile, how far is Emma from each person?

Answers

For this it would be helpful if you draw a diagram of the situation. You will see that a right triangle can be formed from the problem. We use trigonometric functions to solve. We do as follows:

sin 40 = 50/y
tan 40 = 50/x

Solving we obtain,
x = 60 mi
y = 78 mi

Hope this answers the question. Have a nice day.

Answer:

Hence, the distance between Todd and Emma is:41.955 mi.

and the distance between Patty and Emma is:32.14 mi.

Step-by-step explanation:

We will see that we will get a right angled triangle based on our information(The graph is attached to the answer)

Now let x denotes the distance between Emma and Todd.

and y denotes the distance between Emma and Patty.

Now as the triangle is right angled so we can use the trignometric identities to find the distance.

$\tan40\degree=(50)/(x)$