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.
9514 1404 393
Answer:
?° = 153°
Step-by-step explanation:
The measure of an arc is the same as the measure of the central angle it subtends. The arc is marked 153°. The central angle (?°) has that same measure.
?° = 153°
Answer:
1 golf ball : $2.50
Step-by-step explanation:
- You can first divide 6 and 15 by 3, and get 2 and 5.
- Then, you divide 5 by 2, which is 2.5
- Therefore, the unit rate is 1 golf ball : $2.50
Answer:
Vertical and Supplementary
Step-by-step explanation:
Vertical:
each of the pairs of opposite angles made by two intersecting lines.
Supplementary:
Two Angles are Supplementary when they add up to 180 degrees. These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. But the angles don't have to be together.
The area of the top of a desk which is shown and the dimensions of the top is 5 feet and 2 feet, is 10 squared feet.
<h3>What is the area of a rectangle?</h3>
Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
Here, (a)is the length of rectangle and (b) is the width of the rectangle
A drawing of the top of a desk is shown.
The image of drawing ins not given in the problem. Here, the length of the desk is 5 feet and the width of the desk is 2 feet according to the data.
Put the values in the above written formula as,
Thus, the area of the top of a desk which is shown and the dimensions of the top is 5 feet and 2 feet, is 10 squared feet.
Learn more about the area of rectangle here;
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