Explanation:
When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.
The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.
When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.
Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:
- x > ... or x ≥ ... ⇒ shading is to the right of the boundary
- y > ... or y ≥ ... ⇒ shading is above the boundary
Otherwise, the shaded solution space will be below or to the left of the boundary line.
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Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.
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The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.
Answer:
y =3x - 5
Step-by-step explanation:
Well one of the way to do this question is the formula given below your question, but for me, i rather do it this way
OK they gave u y=3x - 12
And they say another line is parallel, once u see the word parallel means they have the same angle, same slope, same gradient ( sorry if I give u the wrong terms, since I learn mine in Malay)
So first u got to understand the slope-intercept form
y = mx + c
y is your y coordinate
x is your x coordinate
m is your gradient ( as in how much the line slants)
c is the y - intercept, as in, if u draw a graph, the y-coordinate where your line touches the y-axis (the vertical line)
So since the say the both lines are parallel, so both of their "m" is the same that is 3. Why? Cuz just compare
y = mx + c
y = 3x - 12
Therefore the m is 3
Therefore u alredy got your first value, so put it in your slope intercept form
y = mx + c
y = 3x + c
Now how to find c? Very easy, just put in the value of y and x from the coordinate ( that the line youre finding is on) they gave u, just put the value in
They gave u
(1, - 2)
So when x = 1, y = - 2
Therefore put it in
y = 3x + c
-2 = 3 (1) + c
c = - 5
Since now u have your m and c value, your slope intercept form is done, just put it in
y = mx + c
y = 3x + (-5)
y = 3x -5
Step-by-step explanation:
Simple
We will subtract
21 - 16 = 5
So 5 more students can join the class
Ok, so IDK if I'm about to do this problem right, but here we go;
so first, lets change these all to decimals (I more of a decimal gal)
3 1/2 = 3.5
3 2/3 = 3.6666 (repeating)
3 3/5 = 3.6
3 3/8 = 3.375
So now, just order them from greatest to least.
3.66666, 3.6, 3.5, 3.375.
Now, change them back to fractions.
3 2/3, 3 3/5, 3 1/2, 3 3/8
So, if I'm correct, the answer is 3 2/3%, 3 3/5%, 3 1/2%, 3 3/8%
Hopefully I solved your problem!
