Solve 3x > 174, and use the interactive number line tool to graph the solution. What is true about the graph? Check all that
1 answer:
You might be interested in
Answer:
Condition 1: y>0
Condition 2: x+y>-2
Step-by-step explanation:
We are told that we have a set of points in the Cartesian system (i.e. x-y coordinate), so we can define our point as:
We are given two conditions and we want to create a system of inequalities. Now, generally speaking, inequalities are expressions relating mathematical expressions through 'comparison' (i.e. less than, greater than, or less/greater and equal to) usually recognized by ,
,
and
, respectively.
So in our case let set up our inequalities.
Condition 1: the y-coordinate is positive
This can be mathematically translated as
(i.e. is greater than 0, therefore positive)
Condition 2: the sum of the coordinates is more than -2
This can be mathematically translated as
(i.e. the summation of the two coordinates is greater than -2 but not equal to).
The system of inequalities described by the two conditions is:
Two lines are perpendicular between each other if their slopes fulfills the following property
where m1 and m2 represents the slopes of line 1 an 2, respectively.
To find the slope of a line we can write it in the form slope-intercept form
Our original line is
Then its slope is
Now we have to find the slope of the second line. Using the first property,
Then the second line has to have a slope of 8.
The options given to us are:
Then we have to determine which of these options have a slope of 8. To do that we write them in the slope-intercept form:
Once we have the options in the right form, we note that the only one of them that has a slope of 8 is the last one.
Then the line perpendicular to the original one is