If the roots of the quadratic equation ax^2 + bx + c = 0 are real and equal, what is the relationship between the discriminant and the coefficients?

The discriminant b^2 - 4ac is equal to zero.

The discriminant b^2 - 4ac is greater than zero.

The discriminant b^2 - 4ac is negative.

The discriminant equals the product of the coefficients.

What can be said about the sum and product of the roots of the quadratic equation 3x^2 - 5x + 2 = 0 ?

The sum of the roots is \frac{5}{3} and the product of the roots is \frac{2}{3} .

The sum of the roots is 5 and the product of the roots is 2 .

The sum of the roots is -\frac{5}{3} and the product of the roots is \frac{2}{3} .

The sum of the roots is \frac{2}{3} and the product of the roots is \frac{5}{3} .

For which values of the discriminant b^2 - 4ac does the quadratic equation ax^2 + bx + c = 0 have two distinct real roots?

The discriminant is greater than zero.

The discriminant is less than zero.

The discriminant is equal to 4ac .

The discriminant is equal to zero.

Given the quadratic equation 2x^2 - 4x + 3 = 0 , what is the nature of its roots?

The roots are complex and conjugate.

The roots are real and distinct.

For the quadratic equation x^2 - 6x + 9 = 0 , what is the sum and product of its roots?

The sum of the roots is 6 and the product of the roots is 9 .

The sum of the roots is zero and the product of the roots is 9 .

The sum of the roots is 9 and the product of the roots is 6 .

The sum of the roots is -6 and the product of the roots is -9 .

What is the nature of the roots of the quadratic equation 5x^2 + 2x + 1 = 0 ?

The roots are complex and conjugate.

The roots are real and distinct.

For the quadratic equation x^2 - 10x + 25 = 0 , what is the nature of its roots and the sum of the roots?

The roots are real and equal, and their sum is 10 .

The roots are complex, and their sum is -10 .

The roots are real and distinct, and their sum is 10 .

The roots are real and equal, and their sum is -10 .

Nature of the roots and sum& product of the roots of quadratic equations

All living things are made up of one or more cells. A cell is the smallest unit that can carry on all of the processes of life. Beginning in the 17th century, curious naturalists were able to use microscopes to study objects too small to be seen with the unaided eye. Their studies led them to propose the cellular basis of life. Hooke In 1665, English scientist Robert Hooke studied nature by using an early light microscope, such as the one in Figure 4-1a. A light micro- scope is an instrument that uses optical lenses to magnify objects by bending light rays. Hooke looked at a thin slice of cork from the bark of a cork oak tree. “I could exceedingly plainly perceive it to be all perforated and porous,” Hooke wrote. He described “a great many little boxes” that reminded him of the cubicles or “cells” where monks live. When Hooke focused his microscope on the cells of tree stems, roots, and ferns, he found that each had similar little boxes. The drawings that Hooke made of the cells he saw are shown in Figure 4-1b. The “little boxes” that Hooke observed were the remains of dead plant cells, such as the cork cells shown in Figure 4-1c. SECTION 1 OBJECTIVES ● Name the scientists who first observed living and nonliving cells. ● Summarize the research that led to the development of the cell theory. ● State the three principles of the cell theory. ● Explain why the cell is considered to be the basic unit of life. VOCABULARY cell cell theory Robert Hooke used an early microscope (a) to see cells in thin slices of cork. His drawings of what he saw (b) indicate that he had clearly observed the remains of cork cells (300) (c). FIGURE 4-1 (a) (b) (c) Copyright © by Holt, Rinehart and Winston. All rights reserved. 70 CHAPTER 4 Leeuwenhoek The first person to observe living cells was a Dutch trader named Anton van Leeuwenhoek. Leeuwenhoek made microscopes that were simple and tiny, but he ground lenses so precisely that the magnification was 10 times that of Hooke’s instruments. In 1673, Leeuwenhoek, shown in Figure 4-2a, was able to observe a previ- ously unseen world of microorganisms. He observed cells with green stripes from an alga of the genus Spirogyra, as shown in Figure 4-2b, and bell-shaped cells on stalks of a protist of the genus Vorticella, as shown in Figure 4-2c. Leeuwenhoek called these organisms animalcules. We now call them protists. THE CELL THEORY Although Hooke and Leeuwenhoek were the first to report observ- ing cells, the importance of this observation was not realized until about 150 years later. At this time, biologists began to organize information about cells into a unified understanding. In 1838, the German botanist Matthias Schleiden concluded that all plants were composed of cells. The next year, the German zoologist Theodor Schwann concluded the same thing for animals. And finally, in his study of human diseases, the German physician Rudolf Virchow (1821–1902) noted that all cells come from other cells. These three observations were combined to form a basic theory about the cel- lular nature of life. The cell theory has three essential parts, which are summarized in Table 4-1. Anton van Leeuwenhoek (1632–1723) is shown here with one of his hand-held lenses (a). Leeuwenhoek observed an alga of the genus Spirogyra (b) and a protist of the genus Vorticella (c). FIGURE 4-2 TABLE 4-1 The Cell Theory All living organisms are composed of one or more cells. Cells are the basic units of structure and function in an organism. Cells come only from the reproduction of existing cells. (a) (b) (c) www.scilinks.org Topic: Cell Theory Keyword: HM60241 mb06se_csfs01.qxd 5/18/07 10:54 AM Page 70

Southeast Asia, vast region of Asia situated east of the Indian subcontinent and south of China. It consists of two dissimilar portions: a continental projection (commonly called mainland Southeast Asia) and a string of archipelagoes to the south and east of the mainland (insular Southeast Asia). Extending some 700 miles (1,100 km) southward from the mainland into insular Southeast Asia is the Malay Peninsula; this peninsula structurally is part of the mainland, but it also shares many ecological and cultural affinities with the surrounding islands and thus functions as a bridge between the two regions. Mainland Southeast Asia is divided into the countries of Cambodia, Laos, Myanmar (Burma), Thailand, Vietnam, and the small city-state of Singapore at the southern tip of the Malay Peninsula; Cambodia, Laos, and Vietnam, which occupy the eastern portion of the mainland, often are collectively called the Indochinese Peninsula. Malaysia is both mainland and insular, with a western portion on the Malay Peninsula and an eastern part on the island of Borneo. Except for the small sultanate of Brunei (also on Borneo), the remainder of insular Southeast Asia consists of the archipelagic nations of Indonesia and the Philippines. Southeast Asia stretches some 4,000 miles at its greatest extent (roughly from northwest to southeast) and encompasses some 5,000,000 square miles (13,000,000 square km) of land and sea, of which about 1,736,000 square miles is land. Mount Hkakabo in northern Myanmar on the border with China, at 19,295 feet (5,881 meters), is the highest peak of mainland Southeast Asia. Although the modern nations of the region are sometimes thought of as being small, they are—with the exceptions of Singapore and Brunei—comparatively large. Indonesia, for example, is more than 3,000 miles from west to east (exceeding the west-east extent of the continental United States) and more than 1,000 miles from north to south; the area of Laos is only slightly smaller than that of the United Kingdom; and Myanmar is considerably larger than France. All of Southeast Asia falls within the tropical and subtropical climatic zones, and much of it receives considerable annual precipitation. It is subject to an extensive and regular monsoonal weather system (i.e., one in which the prevailing winds reverse direction every six months) that produces marked wet and dry periods in most of the region. Southeast Asia’s landscape is characterized by three intermingled physical elements: mountain ranges, plains and plateaus, and water in the form of both shallow seas and extensive drainage systems. Of these, the rivers probably have been of the greatest historical and cultural significance, for waterways have decisively shaped forms of settlement and agriculture, determined fundamental political and economic patterns, and helped define the nature of Southeast Asians’ worldview and distinctive cultural syncretism. It also has been of great importance that Southeast Asia, which is the most easily accessible tropical region in the world, lies strategically astride the sea passage between East Asia and the Middle Eastern–Mediterranean world. Within this broad outline, Southeast Asia is perhaps the most diverse region on Earth. The number of large and small ecological niches is more than matched by a staggering variety of economic, social, and cultural niches Southeast Asians have developed for themselves; hundreds of ethnic groups and languages have been identified. Under these circumstances, it often is difficult to keep in mind the region’s underlying unity, and it is understandable that Southeast Asia should so often be treated as a miscellaneous collection of cultures that simply do not quite fit anywhere else. Roofs of the Forbidden City, Beijing, China Britannica Quiz All About Asia Yet from ancient times Southeast Asia has been considered by its neighbors to be a region in its own right and not merely an extension of their own lands. The Chinese called it Nanyang and the Japanese Nan’yō, both names meaning “South Seas,” and South Asians used such terms as Suvarnabhūmi (Sanskrit: “Land of Gold”) to describe the area. Modern scholarship increasingly has yielded evidence of broad commonalities uniting the peoples of the region across time. Studies in historical linguistics, for example, have suggested that the vast majority of Southeast Asian languages—even many of those previously considered to have separate origins—either sprang from common roots or have been long and inseparably intertwined. Despite inevitable variation among societies, common views of gender, family structure, and social hierarchy and mobility may be discerned throughout mainland and insular Southeast Asia, and a broadly common commercial and cultural inheritance has continued to affect the entire region for several millennia. These and other commonalities have yet to produce a conscious or precise Southeast Asian identity, but they have given substance to the idea of Southeast Asia as a definable world region and have provided a framework for the comparative study of its components.

A Prairie Guard Dog I am on a journey. My trip is to a prairie. It is in the outdoor world called nature. Many animals live in a prairie habitat. This place has what prairie dogs need to survive. A prairie has a lot of grasses but few trees. Without places to hide, a prairie can be dangerous for some animals. Good Morning! It is early in the morning. First, I see a prairie dog. I name him Pete. He peeks his head out of his burrow underground. He looks around. Then Pete calls loudly to his family, "Yip!" He lets them know it is safe to come out. Soon four prairie dogs come out. Pete is the guard and he is restless. He cannot rest because he is always looking around for danger. This allows the other prairie dogs to safely munch on grasses and seeds. They can also groom each other or work on their burrow. A Scare Oh no! Pete spies a large badger! When he sees it, he gives a loud bark, "Yap! Yap!" His family recognizes the warning. Some hide in tall grasses, and some jump into the burrow. The badger runs at Pete, but the watchful guard is able to escape into the burrow. I am glad he is able to get away from danger. After a few minutes, Pete peeks his head out again and he is back on the job. Break Time The sun gets higher, and it is hot now. The prairie dogs slip into their deep burrow where it is cooler. Even Pete goes in. Tunnels, like hallways, lead to different areas. There is a sleeping room. There is a room used like a bathroom. The prairie dogs cover up roots and seeds in one room. Later, they eat the buried food there. Second Shift I keep watching the burrow. Finally, the sun begins to set and a different prairie dog peeks its head out. I name him Gary. Pete must be off duty. "Yip," Gary calls. The other prairie dogs come back out. The prairie dogs eat and play until the moon is high in the sky. Then they go to sleep in their burrows. I wonder if Pete will be back on duty. I will see in the morning.

Hello friends, welcome to a new Happy Learning video. Have you ever wondered how plants feed? To answer this question, we need to understand... photosynthesis. Photosynthesis is a process in which plants make their own food to be able to grow and develop. In order to perform photosynthesis, they need various elements: sunlight, carbon dioxide obtained from air, and water, and chlorophyll, which is a green substance that all plants have and is fundamental for performing photosynthesis since it could not happen without it. By the way, chlorophyll is what gives all plants their green color. But how does photosynthesis take place? Look at this plant. As you can see, its roots are anchored to the ground. And through them, the plant absorbs water and minerals in the soil. Water with minerals are transported up the stem, reaching the leaves. The leaves are full of tiny pores called stomata which absorb carbon dioxide that the air in the surrounding contains. All this containing water, minerals and carbon dioxide is called raw sap. Now it's chlorophyll's turn. The chlorophyll in the leaves has all the necessary ingredients for photosynthesis to take place. And when it receives sunlight, the process begins by transforming the raw sap into elaborated sap, which also circulates around the plant and works as food. All plants feed from elaborated sap, and they store it in their roots like a carrot, or in their fruit, like an apple or a pear. Now we know how photosynthesis takes place, but why is it so important? Without plants, there would be no life on Earth. We wouldn't have oxygen to breathe or food to feed on. You already know that herbivores eat plants, and carnivores eat herbivores. Plants are fundamental for the food chain. And they are also fundamental for our respiration. Actually, when humans breathe, we turn oxygen into carbon dioxide. Quite the opposite of when plants perform photosynthesis. A curious fact you need to know is that at night, because plants don't have sunlight to photosynthesize, they breathe like humans do. They take in oxygen and release carbon dioxide. Remember that. And one last thing so you understand the importance of photosynthesis. When plants absorb dirty and contaminated gases, they transform them into pure air, into oxygen, and this way they clean the atmosphere and all nature. Plants are the best solution to fight against contamination, don't you think? Goodbye friends and don't forget to subscribe to Happy Learning TV.

Tornadoes Introduction. What can lift roofs from buildings and sweep houses into the air? Tornadoes can! Tornadoes come in many sizes. Some tornadoes are only a few feet (1 meter) across. Others are more than a mile (1.6 km) wide. Some tornadoes touch down for a short time. Others travel for hundreds of miles. How Tornadoes Form. Why do tornadoes happen? Scientists are not sure. Tornadoes come from giant thunderstorms called supercells. A supercell happens when warm, moist air rises to mix with cold, dry air. The mixing of cold and warm air causes the air to spin. The spinning wind turns into a cloud in a funnel shape. As the cloud turns, the wind becomes stronger. When the funnel cloud touches the ground, it is a tornado. Measuring Tornadoes. Scientists have a way to measure the strength of tornadoes. They look at the harm caused by a tornado. They use the amount of harm to estimate the wind speed. They use a special scale called the EF Scale. The EF Scale measures the strength of the tornado. Where Tornadoes Form. Tornadoes may be hard to measure, but scientists have a good idea where they'll strike. It's true that a tornado can hit anywhere in the world at any time. Most tornadoes happen in the central part of the United States. This area is called Tornado Alley. More than one thousand tornadoes strike Tornado Alley each year. Tornado Safety. There is no way to be sure that a tornado will strike. The National Weather Service (NWS) tries to help people stay safe during tornadoes. If they put out a tornado watch, a tornado might strike. If they put out a tornado warning, a tornado has been spotted. If there is a tornado warning. it's important to get to a safe place. Go indoors. The safest place is a basement. If you can't get to a basement, go into а closet or bathroom. The spinning air in a tornado makes things fly around. This can be dangerous. It's always important to protect your head. You should get close to the ground. Go under a desk or table. You can even lie down in a bathtub. It is not safe to stay in a mobile home in a tornado. If you are in a tall building, go to the stairs. If you are in a car, wear your seatbelt and lean forward. If you are outside, lie down on the ground. Conclusion. Tornadoes are amazing and scary examples of the power of nature. People still have many questions about tornadoes. What causes a tornado? What is it really like inside a tornado? Maybe we will find out one day.

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