Example:
This suggests two solutions,
and
.
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
is defined only for
(assuming you're looking for real solutions only). So, we call
an extraneous solution, and the complete solution set (over the real numbers) is
.
Non fiction and formal writing :)
Answer: 7/8
Step-by-step explanation:
Answer:
- reflection over the y-axis;
- dilation with a scale factor of 0.4;
- translation 8 units left and 8 units up
Step-by-step explanation:
<h3>Reflection</h3>
The first transformation changes the sign of the x-coordinate. That means a point that was some number of units (3, for example) <em>right</em> of the y-axis will be transformed to a point 3 untis <em>left</em> of the y-axis. It is reflected across the y-axis.
__
<h3>Dilation</h3>
The second transformation multiplies each coordinate value by 0.4. A point that was some number of units (3, for example) away from the origin, will be transformed to a point 3×0.4 = 1.2 units from the origin. It is dilated by a factor of 0.4.
__
<h3>Translation</h3>
The third transformation subtracts 8 from the x-coordinate and adds 8 to the y-coordinate. The x-coordinate is a measure of the distance to the right of the y-axis, so subtracting 8 from the x-coordinate means the point is 8 fewer units to the right of the y-axis. It is translated left 8 units.
Similarly, the y-coordinate is a measure of the distance up from the x-axis. Adding 8 to the y-coordinate will move the point 8 more units up from the x-axis. It is translated up 8 units.
Answer:
1.5
Step-by-step explanation:
8x3= 24
24/16 = 1.5