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:
a homogeneous mixture of two or more substances in relative amounts that can be varied continuously up to what is called the limit of solubility
Domain is all the possible inputs of an equation. In this example, the only concern is the x + 5 because the denominator cannot equal 0 because we can't divided by 0. So we set x + 5 equal to zero and solve for x.
x + 5 = 0
x = -5
The restriction is that x cannot equal -5.
Answer:
≈ 23.4
Step-by-step explanation:
A = bh
270 = 15b
b = 18
Now you know the two legs, use the Pythagorean Theorem to find the value of the hypotenuse: a² + b² = c²
15² + 18² = c²
225 + 324 = c²
c² = 549
c = √549
When adding two digit numbers u will be looking at the ones and deciding if they can regroup them for a ten. You might want to equate regrouping with trading a term that you will understand immediately you will begin to add 2 digit numbers by using ten and ones blocks. And the answer is (107)