We have been given a parent function 
and we need to transform this function into 
.
We will be required to use three transformations to obtain the required function from .
First transformation would be to shift the graph to the right by 4 units. Upon using this transformation, the function will change to 
.
Second transformation would be to compress the graph vertically by half. Upon using the second transformation, the new function becomes 
.
Third transformation would be to shift the graph upwards by 5 units. Upon using this last transformation, we get the new function as .
4 1/3 = 13/3 = 1/3 x 13/1 = 4 1/3
Answer:
The reason why points and lines my be co-planer even when the plane containing them is not drawn is because the by their definition two lines or a line and a point or three points which are fixed in space always have have a direction of view from which they appear as a single line, or for the three points, appear to be on a single line.
This can be demonstrated by the shape of a cross which is always planner
Examples include
1) Straight lines drawn across both side of the pages of an open book to meet at the center pf the book can always be made planner by the orientation#
2) This can be also demonstrated by the plane of the two lines in the shape of a cross which is always planner regardless of the orientation of the cross
3) The dimension that can be defined by three points alone is that of a planner (2-dimensional) triangle shape
Step-by-step explanation:
Given:
Current population = x
The population of a city is expected to decrease by 6% next year.
To find:
The expression that represents the expected population next year.
Solution:
We have,
Current population = x
Decrease rate = 6%.
Expected population next year = Current population - 6% of Current population
=
=
=
Therefore, the expression for the expected population next year is 0.94x.
Answer:
x = 80
Step-by-step explanation:
Thank you for the clear diagram. We don't always get them.
Argument
There are two kinds of angles associated with a triangle
- Interior angles
- Exterior angles
You have both kinds in this question. The interior angles are the ones that make up the triangle itself. The ones you are concerned about are x and 38°.
The other kind is formed by extending one of the sides. In this question, the value of the exterior angle is 118°.
Rule
The two interior angles NOT connected to the given exterior angle are equal (when added) to the exterior angle.
In plain English what that means is
x + 38 = 118
Solution
x + 38 = 118 Subtract 38 from both sides.
x + 38 - 38 = 118 - 38
x = 80
So x = 80
