Step-by-step explanation:
the general slope intercept form is
y = ax + b
a is the slope (and always the factor of x). it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.
b is the y-intercept, the y value of the point, where the line crosses the y-axis (in other words : the y value when x = 0).
so, look at the chart. where do we see points with integer coordinates (these are the easiest to read correctly and work with) ?
I see for example (0, -6) and (4, -7).
to go from the first to the second point :
x changes by +4 units (from 0 to 4).
y changes by -1 unit (from -6 to -7).
the slope a is therefore -1/4.
and the first point i picked gives us also automatically the y-intercept (-6).
so, the line equation is
y = (-1/4)x - 6
Answer:
20
Step-by-step explanation:
The correct transformation is a rotation of 180° around the origin followed by a translation of 3 units up and 1 unit to the left.
<h3>
Which transformation is used to get A'B'C'?</h3>
To analyze this we can only follow one of the vertices of the triangle.
Let's follow A.
A starts at (3, 4). If we apply a rotation of 180° about the origin, we end up in the third quadrant in the coordinates:
(-3, -4)
Now if you look at A', you can see that the coordinates are:
A' = (-4, -1)
To go from (-3, -4) to (-4, -1), we move one unit to the left and 3 units up.
Then the complete transformation is:
A rotation of 180° around the origin, followed by a translation of 3 units up and 1 unit to the left.
If you want to learn more about transformations:
brainly.com/question/4289712
#SPJ1
Answer:
See the argument below
Step-by-step explanation:
I will give the argument in symbolic form, using rules of inference.
First, let's conclude c.
(1)⇒a by simplification of conjunction
a⇒¬(¬a) by double negation
¬(¬a)∧(2)⇒¬(¬c) by Modus tollens
¬(¬c)⇒c by double negation
Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.
An alternative approach to De Morgan's law is the following:
By contradiction proof, assume h is true.
h⇒d∨h by addition
(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.
