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denis23 [38]
3 years ago
6

A dance instructor earns $75 for teaching 3 classes. The instructor receives a 10percent raise Enter how much the instructor ear

ns, in dollars, per class after the raise.
Mathematics
2 answers:
agasfer [191]3 years ago
7 0

<u><em>Answer:</em></u> $27.50

<u><em>Step-by-step explanation:</em></u>

First, we find what 10% of $75.00. Easiest way to do that is to move the decimal over one place to the left:

75.00 ⇒ 7.500 ⇒ 7.50

So the instructor would get a 7.50 raise added to her pay:

75.00 + 7.50 = 82.50

Finally, we divide 82.50 by 3 for each dance class:

82.50 ÷ 3 = 27.50

And there is your answer! The instructor would get $27.50 per class after their raise.

Hope this helps!

Diano4ka-milaya [45]3 years ago
5 0

Answer:$27.50

Step-by-step explanation:

3 classes=$75.00 10/100×75/1=$7.5 total for class is 75.00+7.5=82.5 per class=82.5÷3=27.5

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Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.
Jobisdone [24]
This question is in reverse (in two ways): 

<span>1. The definition of an additive inverse of a number is precisely that which, when added to the number, will give a sum of zero. </span>

<span>The real problem, in certain fields, is usually to show that for all numbers in that field, there exists an additive inverse. </span>

<span>Therefore, if you tell me that you have a number, and its additive inverse, and you plan to add them together, then I can tell you in advance that the sum MUST be zero. </span>

<span>2. In your question, you use the word "difference", which does not work (unless the number is zero - 0 is an integer AND a rational number, and its additive inverse is -0 which is the same as 0 - the difference would be 0 - -0 = 0). </span>

<span>For example, given the number 3, and its additive inverse -3, if you add them, you get zero: </span>
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<span>However, their "difference" will be 6 (or -6, depending which way you do the difference): </span>

<span>3 - (-3) = 6 </span>
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<span>(because -3 is a number in the integers, then it has an additive inverse, also in the integers, of +3). </span>

<span>--- </span>

<span>A rational number is simply a number that can be expressed as the "ratio" of two integers. For example, the number 4/7 is the ratio of "four to seven". </span>

<span>It can be written as an endless decimal expansion </span>
<span>0.571428571428571428....(forever), but that does not change its nature, because it CAN be written as a ratio, it is "rational". </span>

<span>Integers are rational numbers as well (because you can always write 3/1, the ratio of 3 to 1, to express the integer we call "3") </span>

<span>The additive inverse of a rational number, written as a ratio, is found by simply flipping the sign of the numerator (top) </span>

<span>The additive inverse of 4/7 is -4/7 </span>

<span>and if you ADD those two numbers together, you get zero (as per the definition of "additive inverse") </span>

<span>(4/7) + (-4/7) = 0/7 = 0 </span>

<span>If you need to "prove" it, you begin by the existence of additive inverses in the integers. </span>
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<span>Next, show that this (in the integers) can be applied to the rationals in this manner: </span>

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<span>(4 + -4)/7 = ? </span>
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<span>(0)/7 = 0/7 = 0 </span>

<span>Since this is true for ALL integers, then it must also be true for ALL rational numbers.</span>
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