Ok, so here your being asked to solve 6x2<span> + 5x = -7
The procedure that I did was using this formula it led me to get the following:
</span>Using the formula:
x = -(-5) ± √(-5)² - 4(6)(-6)/ 2(6)
x = 5 ± √ 25 + 144 / 12
x = 5 ± √ 169 / 12
x = 5 ± 13/12
x1 = 5 + 13/12
x1 = 18/12
x1 = 3/2
x2 = 5 - 13/12
x2 = -8/12
<span>
x2 = - 2/3
Hope this helped :)</span>
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>
<span>For example, the additive inverse of 4 is -4 </span>
<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>
Answer:
Question A:
1. 1/2 = 0.5 (Terminating)
2. 5/6 = 0.833333.. (Repeating)
3. 21/3 = 1.6666666.. (Repeating)
Question B:
1. 0.6 = 3/5
2. 1.25 = 5/4 = 1 1/4
3. 0.125 = 1/8
Step-by-step explanation:
A. Write the fraction or mixed number as a terminating or repeating decimal.
In order to convert a fraction into decimal, the numerator has to be divided by denominator.
1. 1/2
The answer is: 0.5 which is a terminating decimal.
2. 5/6
The answer is: 0.833333.. which is a repeating decimal.
3. 2 1/3 (assuming the question is this)
The answer is 1.6666666.. which is a repeating decimal.
B. Write the terminating decimal as fraction or mixed number i
n simplest form.
1. 0.6
2. 1.25
3. 0.125
Hence,
Question A:
1. 1/2 = 0.5 (Terminating)
2. 5/6 = 0.833333.. (Repeating)
3. 21/3 = 1.6666666.. (Repeating)
Question B:
1. 0.6 = 3/5
2. 1.25 = 5/4 = 1 1/4
3. 0.125 = 1/8
