The coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.
<h3>What is a transformation?</h3>
A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
<h3>The types of transformation.</h3>
In Geometry, there are different types of transformation and these include the following:
Based on the information provided, triangle UVW would be rotated counterclockwise through an angle of 270 degree at origin to produce triangle U'V'W', we have:
![\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D)
Therefore, the image of triangle UVW would be given by this matrix:
![\left[\begin{array}{ccc}-3&8&6\\8&4&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%268%266%5C%5C8%264%26-8%5Cend%7Barray%7D%5Cright%5D)
Image = ![\left[\begin{array}{ccc}8&4&-8\\3&-8&-6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%264%26-8%5C%5C3%26-8%26-6%5Cend%7Barray%7D%5Cright%5D)
Based on the image above, we can logically deduce that the coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.
Read more on transformations here: brainly.com/question/12518192
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5x + -4y = 13
Solving
-5x + -4y = 13
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4y' to each side of the equation.
-5x + -4y + 4y = 13 + 4y
Combine like terms: -4y + 4y = 0
-5x + 0 = 13 + 4y
-5x = 13 + 4y
Divide each side by '-5'.
x = -2.6 + -0.8y
Simplifying
x = -2.6 + -0.8y
Simplifying
3x + -4y + -11 = 0
Reorder the terms:
-11 + 3x + -4y = 0
Solving
-11 + 3x + -4y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '11' to each side of the equation.
-11 + 3x + 11 + -4y = 0 + 11
Reorder the terms:
-11 + 11 + 3x + -4y = 0 + 11
Combine like terms: -11 + 11 = 0
0 + 3x + -4y = 0 + 11
3x + -4y = 0 + 11Combine like terms: 0 + 11 = 11
3x + -4y = 11
Add '4y' to each side of the equation.
3x + -4y + 4y = 11 + 4y
Combine like terms: -4y + 4y = 0
3x + 0 = 11 + 4y
3x = 11 + 4y
Divide each side by '3'.
x = 3.666666667 + 1.333333333y
Simplifying
x = 3.666666667 + 1.333333333y
For this case we have the following conversions:
1 yard = 3 feet
The estimate distance Is:
400yd = 1200feet
200yd=600 feet
Ten, the estimate Is:
1200 + 600 = 1800 feet
The real distance Is:
The total distance in yards is given by:
440 + 220 = 660 yd
Then, let's transform this distance to feet, with the given conversion:
660 * 3 = 1980 feet
The distance traveled is reasonable for a person
Comparing the estimate and the actual answer, the distance malcom Ran Is reasonable.
Answer:
Malcolm ran 1980 feet.
The distance is reasonable.
Answer:
3:8 3 sodas for 8 drinks
Step-by-step explanation:
6/16
3/8
Answer:
$4
Step-by-step explanation:
The two purchases can be written in terms of the cost of an adult ticket (a) and the cost of a student ticket (s):
7a +16s = 120 . . . . . . . . price for the first purchase
13a +9s = 140 . . . . . . . . price for the second purchase
Using Cramer's rule, the value of s can be found as ...
s = (120·13 -140·7)/(16·13 -9·7) = 580/145 = 4
The cost of a student ticket is $4.
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<em>Comment on Cramer's Rule</em>
Cramer's rule is particularly useful for systems that don't have "nice" numbers that would make substitution or elimination easy methods to use. If you locate the numbers in the equation, you can see the X-patterns that are used to compute the numerator and denominator differences.
The value of a is (16·140 -9·120)/(same denominator) = 1160/145 = 8. I wanted to show you these numbers so you could see the numerator X-pattern for the first variable.
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Of course, graphical methods can be quick and easy, too.
