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What is the smallest possible value for the product of 2 integers that differ by 7?
  • a)
    8
  • b)
    0
  • c)
    -6
  • d)
    -10
  • e)
    -12
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
What is the smallest possible value for the product of 2 integers that...
Explanation:

Product of Two Integers:
When two integers differ by 7, we can represent them as x and x+7, where x is the smaller integer.

Product Calculation:
The product of these two integers is calculated as:
x * (x + 7)

Finding the Smallest Value:
To find the smallest possible value for the product, we need to determine the smallest value of x.

Calculating the Product:
Let's substitute the smallest value of x into the product formula:
-2 * (-2 + 7) = -2 * 5 = -10

Answer:
Therefore, the smallest possible value for the product of 2 integers that differ by 7 is -10, which corresponds to option 'E'.
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Community Answer
What is the smallest possible value for the product of 2 integers that...
The smallest possible value will occur when it is negative. A negative product will result only when one of the numbers is positive and one is negative. The possible pairs are then -1 and 6, -2 and 5, -3 and 4, -4 and 3, -5 and 2, and -6 and 1. Of these pairs, the smallest product is (-3)(4) = (-4)(3), or -12.
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Directions:Read the passage and choose the best answer to each question.PassagePeople use many different chemicals each day for common household tasks such as cleaning and food preparation.Since the inception of consumer protection laws, chemicals come with toxicity warning labels, directions about proper use, and cautions about the hazards of improper use. Some household chemicals can be quite dangerous, especially when mixed together. One such example is the reaction that occurs when mixing household bleach (NaOCl) with ammonia (NH3). The by-products of the reaction vary depending on the concentrations of the reactants. The following experiments were conducted to determine the levels at which certain by-products resulted from mixing bleach and ammonia.Experiment 1A known by-product of the reaction of bleach and ammonia is chlorine gas (Cl2). Chlorine gas has an intensely disagreeable suffocating odor, and is very poisonous. To determine the quantities of bleach and ammonia that, when mixed together, produce chlorine gas, a varying quantity of bleach was added to eight different ammonia–water solutions and the resulting chlorine gas from each mixture was collected and measured. A solution of 1.0 mole (mol) of NH3 in 1 kg of water was used in each trial. A certain quantity of NaOCl was added to each of the solutions; the amount added was gradually increased for each trial. The amount of chlorine gas produced in each trial was recorded and graphed in Figure 1.Experiment 2Another known by-product of the reaction of bleach and ammonia is nitrogen trichloride (NCl3). Nitrogen trichloride is a yellow, oily, pungent-smelling liquid, often found as a by-product of chemical reactions between nitrogen containing compounds and chlorine. It is highly explosive.To determine the quantities of bleach and ammonia that, when mixed together, produce NCl3, again a varying quantity of bleach was added to eight different ammonia–water solutions and the resulting NCl3 from each mixture was measured. A solution of 1.0 mole (mol) of NH3 in 1 kg of water was used in each trial. A certain quantity of NaOCl was added to each solution; the quantity addedwas gradually increased for each trial. The amount of nitrogen trichloride produced in each trial was recorded in see Table 1.Experiment 3In yet another reaction, bleach and ammonia combined under certain conditions produce a compound known as chloramine. Chloramine (NH2Cl) is a toxic substance commonly used in low concentrations as a disinfectant in municipal water systems as an alternative to chlorination.To determine the mixture of bleach and ammonia at which NH2Cl is produced, a varying amount of ammonia was added to eight different bleach–water solutions and the resulting chlorine gas from each mixture was collected and measured. A solution of 1.0 mole (mol) of NaOCl in 1 kg of water was used in each trial. A certain quantity of NH3 was added to each solution; the quantity of ammonia added was gradually increased for each trial. The amount of chloramine produced in each trial was recorded in Table 2.Q.If a ninth trial were conducted in Experiment 3, adding 1.25 mol of NH3 to the bleach–water solution, the amount of NH2Cl produced would be closest to

The rate of a reversible chemical reaction depends on many factors, including concentrations of the reactants and products, temperature, and presence of enzymes called catalysts. In the forward reaction, two reactants combine to form one product. However, in a reverse reaction, the product is broken down into the two reactants.In order for a forward reaction to occur, the reactants moving around in the test tube must physically interact with each other. The more often reactants interact with each other, the more produce is formed in the same amount of time. The speed at which reactants combine into products (the rate of the reaction) can be calculated by dividing the amount of a chemical produced in a reaction (often measured in moles) by the time it takes to produce that amount.In order to determine the effects of reactant and product concentration, temperature, and presence of catalysts on the rate of a reaction, a scientist studied the following reaction:The scientist varied the conditions of the experiment and measured the rate of the reaction. The results are outlined in Table 1. The units of concentration are moles per liter.Q.What is a possible unit of a rate of reaction?

Adapted from The Varieties of Religious Experience by William James (1902)In the matter of religions, it is particularly easy distinguishing the too orders of question. Every religious phenomenon has its history and its derivation from natural antecedents. What is nowadays called the higher criticism of the Bible are only a study of the Bible from this existential point of view, neglected to much by the earlier church. Under just what biographic conditions did the sacred writers bring forth their various contributions to the holy volume? What had they exactly in their several individual minds, when they delivered their utterances? These are manifestly questions of historical fact, and one does not see how the answer to it can decide offhand the still further question: of what use should such a volume, with its manner of coming into existence so defined, be to us as a guide to life and a revelation? To answer this other question we must have already in our mind some sort of a general theory as to what the peculiarities in a thing should be which give it value for purposes of revelation; and this theory itself would be what I just called a spiritual judgment. Combining it with our existential judgment, we might indeed deduce another spiritual judgment as to the Bibles’ worth. Thus, if our theory of revelation-value were to affirm that any book, to possess it, must have been composed automatically or not by the free caprice of the writer, or that it must exhibit no scientific and historic errors and express no local or personal passions, the Bible would probably fare ill at our hands. But if, on the other hand, our theory should allow that a book may well be a revelation in spite of errors and passions and deliberate human composition, if only it be a true record of the inner experiences of great-souled persons wrestling with the crises of his fate, than the verdict would be much favorable. You see that the existential facts by itself are insufficient for determining the value; and the best adepts of the higher criticism accordingly never confound the existential with the spiritual problem. With the same conclusions of fact before them, some take one view, and some another, of the Bibles value as a revelation, according as their spiritual judgment as to the foundation of values differ.Q. Which is the best form of the underlined selection, "According as their spiritual judgment as to the foundation of values differ"?

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What is the smallest possible value for the product of 2 integers that differ by 7?a)8b)0c)-6d)-10e)-12Correct answer is option 'E'. Can you explain this answer?
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