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zlopas [31]
3 years ago
12

Which expression is equivalent to |a|≤3 ?

Mathematics
2 answers:
weqwewe [10]3 years ago
8 0
<h3>Answer: Choice 2.   a \ge -3 \ \text{ and } \ a \le 3</h3>

=====================================================

Explanation:

The rule is that if |a| \le k for some positive number k, then it can be written as the compound inequality -k \le a \le k. This is a shorthand way of writing the two inequalities a \ge -k \ \text{ and } \ a \le k combined together.

note: -k \le a is the same as a \ge -k

From here, we replace k with 3

Therefore, |a| \le 3 turns into -3 \le a \le 3 which breaks down further to a \ge -3 \ \text{ and } \ a \le 3

The keyword "and" is important as we can't pick one or the other. We must pick both a \ge -3 and also a \le 3

Nonamiya [84]3 years ago
4 0

Answer:

Choice 2.  

Step-by-step explanation:

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2 years ago
Find an equation of the line. Write the equation using function notation.
Gemiola [76]

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

y = -4x+9

Step-by-step explanation:

Given equation of line is:

4y=x-8

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2

Let m1 be the slope of given line

Then

m_1 = \frac{1}{4}\\

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4

The slope intercept form of line is given by:

y = m_2x+b

Putting the value of slope

y = -4x+b

to find the value of b, putting (3,-3) in equation

-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9

Putting the value of b in the equation

y = -4x+9

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

y = -4x+9

Keywords: Equation of line, slope

Learn more about equation of line at:

  • brainly.com/question/4837736
  • brainly.com/question/4805611

#LearnwithBrainly

4 0
3 years ago
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