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Bingel [31]
3 years ago
7

An airport offers 2 shuttles that run on different schedules. If both shuttles leave the airport at 4.00 pm at what time will th

ey leave the airport together
Mathematics
1 answer:
Ksivusya [100]3 years ago
8 0

Answer:

4:18 pm

Step-by-step explanation:

An airport offers 2 shuttles that run on different schedules.If both shuttles leave the airport at 4:00 p.m.,at what time will they next leave theairport together.

Shuttle A leaves every 6 minutes

Shuttle B leaves every 9 minutes

Solution

To solve for when next both shuttles will leave the airport together, find the least common multiples of 6 minutes and 9 minutes

Shuttle A (every 6 minutes) = 6, 12, 18, 24

Shuttle B (every 9 minutes) = 9, 18, 27, 36

The least common multiples of 6 minutes and 9 minutes is 18 minutes

4:00 pm + 18 minutes

= 4:18 pm

The next time both shuttles will leave theairport together is 4:18 pm of the same day

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Answer:

D. 5/6

Step-by-step explanation:

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2 years ago
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 32. Is Theod
ICE Princess25 [194]

Answer:

Yes, the triangles are simirar with a scale factor of 3/2.

Step-by-step explanation:

We find the scale factor by dividing corresponding sides:

12/8=3/2

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3 years ago
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>
<span>3 + (-3) = 0 </span>

<span>However, their "difference" will be 6 (or -6, depending which way you do the difference): </span>

<span>3 - (-3) = 6 </span>
<span>-3 - 3 = -6 </span>

<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>
<span>ALL integers each have an additive inverse. </span>
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<span>Next, show that this (in the integers) can be applied to the rationals in this manner: </span>

<span>(4/7) + (-4/7) = ? </span>
<span>common denominator, therefore you can factor out the denominator: </span>

<span>(4 + -4)/7 = ? </span>
<span>Inside the bracket is the sum of an integer with its additive inverse, therefore the sum is zero </span>
<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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Answer:

Step-by-step explanation:

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Which is also a point on the diameter

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a = 0

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2 years ago
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