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aleksandr82 [10.1K]
2 years ago
13

The weight of each fountain pen manufactured in a factory must be 10g with a tolerance of 2g. Pens that are not within the toler

ated weight must be thrown away. Write an inequality that can be used to assess which pens are tolerable (w is the weight of the pen)?
Mathematics
1 answer:
FromTheMoon [43]2 years ago
5 0

According to the information given, the absolute value inequality that can be used to assess which pens are tolerable is:

|w - 10| \leq 2

The <em>absolute value</em> function measures the <u>distance of a point to the origin</u>, and is defined by:

  • |x| = x, x \geq 0
  • |x| = -x, x < 0

The weight must be of 10g, with a tolerance of 2g, which means that the <u>absolute value of the difference between the weight w and 10g must be of at most 2g</u>, hence the inequality is:

|w - 10| \leq 2

To learn more about absolute value inequalities, you can take a look at brainly.com/question/24005819

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KATRIN_1 [288]
X² <span>+ 11x + 7

because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:

(-b </span>± √((b)² - 4ac))/(2a)

in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))

not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
(-11 ± √(121 - 28))/2
(-11 ± √93)/2

and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:

(x - (-11 - √93)/2) and (x + (-11 - √93)/2)

they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:

(x + (11 + √93)/2) (x - (11 - √93)/2)

and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
7 0
3 years ago
Can someone check my answer &amp; explain?
Novay_Z [31]

Answer:

The answer should be 3 cubic cm

Step-by-step explanation:

First you have to get the area of the right triangle base 1/2 bh. That would be 2x3/2=3

To find volume, you plug the area in the volume formula

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v=1/3 (3)(3)

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4 0
3 years ago
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By using pythagoras theorem where
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So, hypotenuse = 13
8 0
3 years ago
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Harlamova29_29 [7]

Answer:4x+30

Step-by-step explanation:

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So then 10+20+4x

Which is 4x+30

4 0
3 years ago
Read 2 more answers
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Natasha2012 [34]
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3 years ago
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