Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y <
4x − 2 y is greater than or equal to negative 5 over 2 times x minus 2 Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points) Part B: Is the point (−2, −2) included in the solution area for the system? Justify your answer mathematically. (4 points)
1 answer:
Part A:
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).
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Hey there!
When finding the difference of expressions like these, there's a few things you should keep in mind.
1. When finding the difference of two polynomials, multiply the polynomial that implied to be "negative" by –1 to expand the problem and make it easier to solve.
2. You combine terms based on their unknown terms, like x, y, x², ab, etc. You cannot combine the terms x and x², but you can combine the terms 6b and 8b by adding them.
3. You can rearrange your terms however you see fit. If a polynomial is implied as "positive", you can multiply that entire polynomial by +1 to get rid of the parentheses.
With all that in mind, you can go ahead and solve for your difference, like so:
will be your difference.
Hope this helped you out! :-)
When finding the difference of expressions like these, there's a few things you should keep in mind.
1. When finding the difference of two polynomials, multiply the polynomial that implied to be "negative" by –1 to expand the problem and make it easier to solve.
2. You combine terms based on their unknown terms, like x, y, x², ab, etc. You cannot combine the terms x and x², but you can combine the terms 6b and 8b by adding them.
3. You can rearrange your terms however you see fit. If a polynomial is implied as "positive", you can multiply that entire polynomial by +1 to get rid of the parentheses.
With all that in mind, you can go ahead and solve for your difference, like so:
Hope this helped you out! :-)
Answer:
Gradient = -5
Step-by-step explanation:
The gradient of a line is the slope of the line.
The standard form of the line equation is y = mx + b
where m is the slope ( or gradient) b is the y - intercept.
Given :
2y = -10x + 1