Answer:
Step-by-step explanation:
Given
Required
Get equivalent expression using completing the square
<em>Follow these steps:</em>
<em />
Add to both sides of the equation
Expand the right-hand side
Factorize:
9514 1404 393
Answer:
-3 ≤ x ≤ 19/3
Step-by-step explanation:
This inequality can be resolved to a compound inequality:
-7 ≤ (3x -5)/2 ≤ 7
Multiply all parts by 2.
-14 ≤ 3x -5 ≤ 14
Add 5 to all parts.
-9 ≤ 3x ≤ 19
Divide all parts by 3.
-3 ≤ x ≤ 19/3
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<em>Additional comment</em>
If you subtract 7 from both sides of the given inequality, it becomes ...
|(3x -5)/2| -7 ≤ 0
Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.
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For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...
|f(x)| < (some number) . . . . or ≤
If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:
|f(x)| > g(x) ⇒ f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0
Any solutions to these inequalities must respect their domains.
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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