If a andlt; 0, then the graph of ax2+ bx + c, has a downward opening.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?

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If a < 0, then the graph of ax²+ bx + c, has a downward opening.

a)
True
b)
False

Correct answer is option 'A'. Can you explain this answer?

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If a < 0, then the graph of ax2+ bx + c, has a downward opening.a)T...

The leading coefficient of the polynomial is less than zero, hence, it has downward opening. For example, the graph of -x² is

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If a < 0, then the graph of ax2+ bx + c, has a downward opening.a)T...

The leading coefficient of the polynomial is less than zero, hence, it has downward opening. For example, the graph of -x² is

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“Why Text Messaging is a Good Thing” by Chelci Spiegel (2013)Many people today think that technology such as text messages and social networking sites are creating distant relationships among people. They say that the relationships are false because face-to-face time is diminishing however, I do not believe this to be the case. These are technologies and technologies are very important tools. That’s just it they’re tools. They can be good or bad depending on how they are used. I believe that text messaging is a benefit to society because it provides fast communication with multiple people unobtrusive conversation and responding time for the receiver.Because text messaging exists we can tell many people something very important very quickly. It is like an SOS message to whomever needs to know. If I have car trouble I can send a text to my father, brother, and friends all at once. Instead of dialing each number separately and maybe or maybe not getting anyone they all get a message then, I receive help more quickly. A more concrete example is from what I was lost in the woods searching for my horse who was also lost late one evening. I sent out one text message to multiple people and by the time I had found my way back to the truck there were seven friends pulled up with trucks mountain bikes and flashlights to help search for the horses all night. That is not evidence of relationships distanced by text messaging but brought together.Because text messaging does not require voice it is far less obtrusive in public places. When I was standing in line at the grocery store one of the ladies were using their phone while waiting for their turn. I heard her entire life story her boy troubles, her work troubles her friend troubles and her money troubles. It was very distracting. With texting people can vent all their frustrations to someone privately. If I am trying to set a date for a barbaque, I can text my neighbor to work out details rather than let the entire store know my weekend plans. Texting is a way to conduct private business in public places.Choose the answer that best corrects the bolded portion of the passage. If the bolded portion is correct as written, choose "NO CHANGE."

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If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.

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In a physics class, students conducted a series of experiments by placing different objects into a beaker of water. They conducted twenty trials for each object. For each trial, they recorded whether or not the object floated.First, they placed a steel paper clip into the water. They observed that the paper clip usually sank; however, they also saw that occasionally, the paper clip stayed afloat if it was placed very gently on top of the water. Next, they repeated the the same procedure using a cork, a toy boat made of aluminum, and a glass marble. They observed that both the cork and the toy boat always stayed afloat in the water, but that the glass marble always sank.Below, three students give their explanations for these observations.Student 1:Objects float when they are less dense than the liquid in which they are immersed. For example, when immiscible liquids of varying densities are mixed together in a container, the most dense liquid will sink to the bottom of the container, while the least dense liquid will rise to the top. This same principle applies to solid objects. Because the cork and the aluminum toy boat always float, cork and the aluminum of the boat must be less dense than water. Because the glass marble always sinks, the glass of the marble must be more dense than water.Objects that are more dense than water can also float due to surface tension. Surface tension occurs because molecules of a liquid are more attracted to each other more than they are to other objects. Molecules on the surface of water are attracted to the molecules around them and below them. This attraction causes a liquids surface to behave if it were covered by a thin film, which resists penetration by other objects. Therefore, small objects such as paper clips can sometimes float on water when the upward force of waters surface tension exceeds the force of gravity pulling such objects down. Because the paper clips often sink and only float sometimes, we can conclude that they are indeed more dense than water, and that their floating is due to surface tension.Student 2:Objects float in two different cases: when they are buoyed by a liquids surface tension or when their average density is less than that of the liquid in which they are immersed. The average density of cork is less than that of water. This is why the cork floats. In contrast, the density of glass is more than that of water. This is why the glass marble sinks.However, the densities of aluminum and of steel are greater than that of water. Thus, density cannot be used to explain why the aluminum toy boat and the paper clip float. Both of these objects float because of surface tension. Because the paper clip does not have much mass, the normal upward force created by waters surface tension can be enough to allow it to float. Other objects with greater mass, like the toy boat, employ a particular shape to magnify the force of surface tension. The curved shape of the boats bottom both stabilizes the boat and increases the amount of the boats surface area that touches the water, maximizing the force due to surface tension that the boat receives.Student 3:In this experiment, the paper clip floats because of surface tension; however, the cork, toy boat, and marble float or sink because of their relationship to a buoyant force. All objects immersed in a liquid experience a buoyant force, which pushes them upward. The strength of this force is equal to the weight of the liquid displaced, or pushed aside, by an object. Every object also experiences a downward force due to gravity, which is measured as the objects weight, and which is directly proportional to the objects mass. When the buoyant force acting on an object is greater than the downward force due to gravity, the object floats. However, when the buoyant force is less than the force due to gravity, the object sinks. Both the cork and the aluminum toy boat are able to displace enough water to create a buoyant force that exceeds the force due to gravity, so they float. However, the glass marble does not displace enough water to create a sufficient buoyant force, so it sinks.Q.Paint is more dense than cooking oil; however, when a drop of paint is dripped into a container of cooking oil, it floats on top of the oil. If Student 1s explanation is correct, which of the following is most likely the reason for this observation?

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In a physics class, students conducted a series of experiments by placing different objects into a beaker of water. They conducted twenty trials for each object. For each trial, they recorded whether or not the object floated.First, they placed a steel paper clip into the water. They observed that the paper clip usually sank; however, they also saw that occasionally, the paper clip stayed afloat if it was placed very gently on top of the water. Next, they repeated the the same procedure using a cork, a toy boat made of aluminum, and a glass marble. They observed that both the cork and the toy boat always stayed afloat in the water, but that the glass marble always sank.Below, three students give their explanations for these observations.Student 1:Objects float when they are less dense than the liquid in which they are immersed. For example, when immiscible liquids of varying densities are mixed together in a container, the most dense liquid will sink to the bottom of the container, while the least dense liquid will rise to the top. This same principle applies to solid objects. Because the cork and the aluminum toy boat always float, cork and the aluminum of the boat must be less dense than water. Because the glass marble always sinks, the glass of the marble must be more dense than water.Objects that are more dense than water can also float due to surface tension. Surface tension occurs because molecules of a liquid are more attracted to each other more than they are to other objects. Molecules on the surface of water are attracted to the molecules around them and below them. This attraction causes a liquids surface to behave if it were covered by a thin film, which resists penetration by other objects. Therefore, small objects such as paper clips can sometimes float on water when the upward force of waters surface tension exceeds the force of gravity pulling such objects down. Because the paper clips often sink and only float sometimes, we can conclude that they are indeed more dense than water, and that their floating is due to surface tension.Student 2:Objects float in two different cases: when they are buoyed by a liquids surface tension or when their average density is less than that of the liquid in which they are immersed. The average density of cork is less than that of water. This is why the cork floats. In contrast, the density of glass is more than that of water. This is why the glass marble sinks.However, the densities of aluminum and of steel are greater than that of water. Thus, density cannot be used to explain why the aluminum toy boat and the paper clip float. Both of these objects float because of surface tension. Because the paper clip does not have much mass, the normal upward force created by waters surface tension can be enough to allow it to float. Other objects with greater mass, like the toy boat, employ a particular shape to magnify the force of surface tension. The curved shape of the boats bottom both stabilizes the boat and increases the amount of the boats surface area that touches the water, maximizing the force due to surface tension that the boat receives.Student 3:In this experiment, the paper clip floats because of surface tension; however, the cork, toy boat, and marble float or sink because of their relationship to a buoyant force. All objects immersed in a liquid experience a buoyant force, which pushes them upward. The strength of this force is equal to the weight of the liquid displaced, or pushed aside, by an object. Every object also experiences a downward force due to gravity, which is measured as the objects weight, and which is directly proportional to the objects mass. When the buoyant force acting on an object is greater than the downward force due to gravity, the object floats. However, when the buoyant force is less than the force due to gravity, the object sinks. Both the cork and the aluminum toy boat are able to displace enough water to create a buoyant force that exceeds the force due to gravity, so they float. However, the glass marble does not displace enough water to create a sufficient buoyant force, so it sinks.Q. The density of fresh, newly cut wood is less than water, and fresh wood always floats; however, over time, floating pieces of wood may sink. Which of the following explanations would Student 1 most likely give for this observation?

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The graph of the quadratic polynomial -x2+ x + 90 will open upwards.

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If a < 0, then the graph of ax2+ bx + c, has a downward opening.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?

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