Answer:
x-1 = 0 or x-7 =0
x=1 or x=7
Step-by-step explanation:
(x-1) (x-7) =0
Using the zero product property
x-1 = 0 or x-7 =0
x-1+1 =0 +1 or x-7+7 =0+7
x=1 or x=7
Answer:
$1440
Step-by-step explanation:
$72/hour
For 20 hours, she receives
20 hours × $72/hour = $1440
Here, 3m is a scalar that we use to multiply each element of the matrix.
We have
![3m \left[\begin{array}{cc}-5m&2m\\6m&6n\end{array}\right]](https://tex.z-dn.net/?f=%20%203m%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-5m%262m%5C%5C6m%266n%5Cend%7Barray%7D%5Cright%5D%20)
.
We get
![\left[\begin{array}{cc}(3m)(-5m)&(3m)(2m)\\(3m)(6m)&(3m)(6n)\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283m%29%28-5m%29%26%283m%29%282m%29%5C%5C%283m%29%286m%29%26%283m%29%286n%29%5Cend%7Barray%7D%5Cright%5D%20)
which simplifies to
![\left[\begin{array}{cc}-15m^2&6m^2\\18m^2&18mn\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-15m%5E2%266m%5E2%5C%5C18m%5E2%2618mn%5Cend%7Barray%7D%5Cright%5D%20)
In a rigid transformation, the shape of the image remains the same as the preimage
The correct options are;
Rotation; a → b
Translation: a → d
Reflection over a horizontal line: c → e
Reflection over a vertical line: g → f
Rotation then reflection: a → h
Rotation then translation: e → j
The reasons why the above selections are correct are as follows;
- Rotation; Figure <em>a</em> is rotated about a common center to figure <em>b</em> to move from <em>a</em> to <em>b</em>
- Translation: Figure <em>a</em> can be translated towards the left and then upwards to reach figure <em>b</em>
- Reflection over a horizontal line: A reflection over a horizontal line is similar to a reflection across the x-axis, therefore an example of a reflection over horizontal line is c → e
- Reflection over a vertical line: A reflection over a vertical line will turn a left pointing triangle to a right pointing triangle as shown in g → e
- Rotation then reflection: The preimage is first rotated about an axis before it is then reflected as seen in the clockwise rotation figure <em>a</em> about its axis, followed by a reflection across a vertical axis to figure <em>h</em>
- Rotation then translation: The rotation and translation composite transformation can be seen in figure <em>e </em>which is rotated to point left, and then translated into the position of figure <em>j</em>
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Learn more about rigid transformations here:
brainly.com/question/14301866
Answer:
the answer will be 4/3 in slope form
Step-by-step explanation:
the answer will be 4/3 in slope form
