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3 years ago

Write an absolute value to describe: 6 is at most 3 units from x

Mathematics

1 answer:

shepuryov [24]3 years ago

7 0

Answer:

|6-x| ≤ 3

Step-by-step explanation:

The distance from 6 to x can be written as 6-x or as x-6. We generally want the positive distance, so we can use the absolute value function to turn either one of these forms to a positive value:

|6-x| or |x-6| . . . . . . each is fully equivalent to the other

This distance is at most 3, so we can write ...

|6 -x| ≤ 3

_____

<em>Comment on the form of the answer</em>

The expression could also be written as |x-6| ≤ 3. We chose the one we did because the wording regards the distance of 6 from x. Usually the "from" value is considered the reference that is subtracted from anything we want to compare to that reference. This is a matter of convention and personal preference, not a requirement for the solution to the problem.

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Solve each question mentally <br> -3x = 21

Snowcat [4.5K]

X = -7

3 • 7 = 21

-3 • (-7) = 21

If you multiply two negative numbers you’ll end up with a positive. Thus, - 3 (-7) = 21.

6 0

3 years ago

One solution of the quadratic equation X2 – 19x + 48 = 0 is 3. What is the other solution?

Liula [17]

Answer:

Step-by-step explanation:

The equation is X2 – 19x + 48 = 0

Using the quadratic formula

X= - b +- √ ( b^2 - 4ac)/ 2a

Where a= 1 b= -19 c= 48

Substitute into the formula we have

CHECK THE ATTACHMENT

HENCE, the solution are 3 and 16

7 0

3 years ago

Two angles are complementary three times the measure of one of the angles is 10° more than the measure of the other angle. find

Mumz [18]

Answer:

The difference is 40,

Step-by-step explanation:

Complementary angles , x+y =90

so we know angle 1, we call it 3x and angle 2 we call it y= 3x+10

so 3x +10= 90-x

4x=100

x=25

angle 1= 3(25) - 10

y= 65

65-25= 40

8 0

3 years ago

Read 2 more answers

The lengths of nails produced in a factory are normally distributed with a mean of 4.84 centimeters and a standard deviation of

Helga [31]

Answer:

Top 3%: 4.934 cm

Bottom 3%: 4.746 cm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 4.84, \sigma = 0.05$