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Our education staff publish regular articles, tips and tutorials to help students with their homeworkSun, 22 May 2016 22:08:11 +0000en-UShourly1https://wordpress.org/?v=4.5.2Science Review of Plant Adaptation
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Sun, 22 May 2016 22:08:11 +0000http://schooltutoring.com/help/?p=8954Overview
Some types of plants grow successfully in unusual regions, including aquatic plants, salt-tolerant plants, and desert plants. A few types of plants gather nutrients from trapped insects.

Aquatic Plants

While most plants live on land, some live in water for most of their life cycle. The roots are often submerged in mud, and parts of the plants may have large open spaces that are filled with air, to bring needed oxygen down to the roots. For example, water lilies have spongy tissue in their stems and leaves that bring oxygen down to their roots, and their flowers grow above the water surface. Mangrove trees that grow in shallow water have similar spongy roots, and cypress trees have specialized structures that grow above the water. Plants that grow in wetlands are important to the ecosystem and the overall health of the diverse species that live in the area.

Salt-Tolerant Plants

While most plants cannot live in saline environments, a few types of plants can live in areas of high salt concentrations that would destroy most others. Some of these high concentrations are in salt marshes near seawater. The roots of those plants, such as salt marsh grasses, take in much more salt than is useful. The excess salt is pumped away by cells in the leaves, where it can be washed away by rain, so the proper balance of salt is maintained in the plant itself.

Desert Plants

Desert plants live in areas where there is infrequent rainfall. Large cactus plants have branching roots that cover a large area and grow rapidly to absorb whatever rainfall there is. Thick stems are often covered with a waxy substance and store water between rainfall periods. The stems actually carry out photosynthesis. Small, spiny leaves minimize water loss from evaporation during the hot, dry days.

Carnivorous Plants

Carnivorous plants get nutrients from other sources than the soil. Carnivorous plants such as the Venus flytrap, pitcher plants, and sundew live in soils that are low in nitrogen and calcium, which they digest from the insects they trap. The Venus flytrap has leaves that are hinged in the middle that close suddenly if an insect touches sensitive hairs on them. The trapped insect is digested within those leaves. Similarly, pitcher plants attract insects that fall into curled leaves. At the bottom of the waxy pitcher, trapped insects are digested by enzymes. Sundew trap insects by sticky mucus on their leaves.
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Sun, 22 May 2016 00:07:49 +0000http://schooltutoring.com/help/?p=8950Overview
As a general strategy for factoring polynomials, first check to see if there are any common factors. If there are not, check for the number of terms. If there are two terms, it may be a difference of squares. If there are three terms, it may be a perfect square of a binomial, or it may be possible to factor using a pattern. If there are four terms, it may be possible to factor by grouping.

Difference of Squares

An expression such as x^{2} – 36 follows a common pattern, as both x^{2} and 36 are perfect squares. Recall that they can be factored as (x +6) (x -6), as the middle terms, 6x and -6x, cancel each other out. What about an expression such as 10x^{3} – 40x? First, factor out the common factor 10x(x^{2} – 4) because 10x ·x^{2} is 10x^{3} and 10x·4 is 40x. The expression x^{2} -4 follows the pattern of a difference of squares, as (x+4) (x-4), so the entire factorization of 10x^{3} – 40x is 10x(x +4) (x-4). It is factored completely.

Perfect Square of a Binomial

An expression such as x^{6} + 8x^{3} +16, also follows a common pattern. The first term, x^{6}, can be factored as a perfect square, x^{3}·x^{3}. Similarly, the last term, 16, can be factored as a perfect square, 4·4. The middle term, 8x^{3}, is 4x^{3} + 4x^{3}, so the expression x^{6} + 8x^{3} +16 can be factored as (x^{3} +4) (x^{3} +4). Recall the pattern of the perfect square of a binomial (a^{2} +2ab + b^{2}) equals (a + b) (a +b).

Factor Using a Pattern

Not all trinomials are perfect squares of a binomial. Some trinomials have a leading coefficient of 1, and they will factor as (x + __) (x + ___). Other trinomials have a leading coefficient of (__x + __) (___x + ___). Suppose the expression is 5x^{2} + 15x +10. Each term has a common factor of 5(x^{2} +3x + 2) which can be factored further as 5(x +1) (x +2).

Factor Four Terms by Grouping

Some expressions with four terms can be factored by grouping, just as trinomials can. For example, 6x^{3} -9x^{2} + 4x -6 can be factored by factoring each group. 6x^{3} -9x^{2 }can be factored as 3x^{2} (2x -3), and 4x -6 can be factored as 2(2x -3). The two groups can be combined as (2x -3) (3x^{2} +2).
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Sun, 15 May 2016 21:52:17 +0000http://schooltutoring.com/help/?p=8946Overview
Not all polynomial expressions are of the form x^{2} +ax +b, where the leading coefficient is equal to 1. Some polynomial expressions have a coefficient that is not equal to 1, and it must be factored also. However, the FOIL method can still be used, with one extra step to find the first product.

Factoring Trinomials

Suppose a polynomial expression is in the form of ax^{2} +bx +c, where a (the leading coefficient) is not equal to 1. That means that in order to factor the expression as (___x + ___) (___x +_____) the numbers in the first blanks will equal the coefficient a, the outside product and inside product can be added to equal the coefficient b, and the last blanks will have the product c.

The First and Last Products

After checking to see if there aren’t any factors common to all terms, find the common factors for the leading coefficient a. Suppose the polynomial expression to factor is 6x^{2} +7x +2. The first term is 6x^{2}, so in order to factor it, find the factors of 6x^{2}. One pair is x, 6x, and another pair is 2x, 3x. Next find the factors of the last term 2. Because the number 2 is positive, the factors will either be both positive, 1 and 2, or both negative, -1 and -2.

The Middle Products

Using the possible factors for the first and last terms, try all the possible combinations: (x +1) (6x +2); (x +2) (6x +1); (3x +1) (2x +2); and (2x +1) (3x +2). Since the first and last terms have already been factored, it is a matter of finding the correct combination of middle products. For the first combination (x +1) (6x +2) the outer product is 2x and the inner product is 6x, equaling 8x. For the second combination, (x +2) (6x +1), the outer product is x and the inner product is 12x, equaling 13x. The third combination, (3x +1) (2x +2), the outer product is 6x and the inner product is 2x, equaling 8x again. The fourth combination, (2x +1) (3x +2), the outer product is 4x and the inner product is 3x, equaling 7x, the correct factorization.

Factoring Common Products

Sometimes, all terms in a polynomial have a common factor which must be factored out before the rest of the polynomial can be factored. Suppose the polynomial is 8m^{2} +8m -6. Each term has a common factor 2(4m^{2} +4m -3). Next, see if (4m^{2} +4m -3) can be factored further. The factorizations of 4m^{2} are 1m, 4m; 2m, 2m; and the factorizations of -3 are -1, 3; and 1, -3, since the factors of a negative number do not have the same sign. Again, it is a matter of finding the possible combinations and trying out the products (m-1) (4m +3); (4m-1) (m +3); (m+1) (4m -3); (4m +1) (m-3); (2m -1) (2m + 3); and (2m +1) (2m-3). The first combination, (m-1) (4m +3) equals 4m^{2} –m -3. The second, (4m-1) (m +3), equals 4m^{2}-11m -3. The third (2m +1) (2m -3) equals 4m^{2} -4m -3. The fourth, (2m-1) (2m +3), equals 4m^{2} +4m -3. The correct factorization of 8m^{2} +8m -6 is 2(2m-1) (2m+3).
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Sun, 08 May 2016 01:12:09 +0000http://schooltutoring.com/help/?p=8941Overview
Commas, colons, and semicolons are used within sentences as punctuation to separate clauses from one another. They are not interchangeable, but may be related.

Commas in Series

Commas are used to separate words in a series, such as peas, beans, potatoes, and corn. The series may be in single words or in separate short phrases, such as in the sentence “He came, he saw, and he conquered. When etc. ends a series, it should be preceded by a comma. The abbreviation etc. stands for et cetera, Latin for and the rest. The moving sale included tables, chairs, bookcases, etc., set up in the parking lot. Commas are also used between cities and states. They moved to Spokane, Washington. They are used after a specific date such as May 7, 2016.

Commas Separating Clauses

Use a comma after a word or phrase that is used as an interjection, as a parenthetical expression, or as a transition. Well, we decided to go on Saturday. For example, commas are used after expressions such as of course, nevertheless, and similarly, when they are at the beginning of a sentence. Commas are also used when a phrase is a dependent clause or in apposition. Jill, the last person I expected to see, came on the train. Besides having to buy a car, he needed a place to live.

Colons

A colon is often used to explain or introduce a list, especially if that list is formal or long. The requirements for the program included: a term of at least six months, residence in the area, and work for a nonprofit agency. Similarly, a colon is used in a book or periodical title that contains a title and a subtitle. The book is called Audrey Hepburn: A Life in Pictures. Colons are used between hours and minutes. The train arrived at 8:15.

Semicolons

Semicolons are often used in a series to clarify a list of items when individual items also have punctuation. For example, the letter was sent to Mary Wright in Portland, Oregon; Will Rosenthal in Portland, Maine; John Pearson in Des Moines, Washington; and Laura North-Williams in Des Moines, Iowa.

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Wed, 04 May 2016 04:06:50 +0000http://schooltutoring.com/help/?p=8937Overview
Complete sentences have end punctuation depending on their meaning. Most sentences have periods, but some have question marks, and others have exclamation points.

Types of Sentences

Generally, there are four types of sentences: declarative, interrogative, imperative, and exclamatory. Declarative sentences make a point or present facts or opinions. Interrogative sentences ask direct questions. Imperative sentences give orders or make requests. Exclamatory sentences create emphasis or present strong emotion. The type of punctuation used depends upon the type of sentence and what is being conveyed.

The Period

The period is the most common end mark. It is used at the end of a declarative sentence, and does not convey strong emotion. If a question is indirect, a period is also used. The sentence “She asked why the door was left open” would end with a period if it stood alone. Periods are also used after abbreviations that stand for single words, such as the months, days of the week, or words such as Inc., Co., or Ltd. A period is used as a decimal point before a decimal, as in 3.1416 or .005. However, when an abbreviation with a period ends a sentence, only one period is necessary to end the sentence. The library is open from 7 A.M. to 11 P.M. Send the letter to Horizon Air, Inc.

The Question Mark

Most interrogative sentences end with question marks, if the question is direct. Why was the door left open? Where did you leave the book? Who is going on the bus? What is the meaning of this? When are you going on vacation? How will you know? Also, if a direct question is in a quotation, the question mark is within the quotation marks. For example, Steve asked, “Has anyone seen the movie?”

The Exclamation Point

Imperative sentences that give strong orders or exclamatory sentences that present strong emotion end with exclamation points. Leave the room! Keep off the grass! Danger! Poison! Oh, no, you don’t! Evacuate the building! Exclamation points are best used sparingly for emphasis.

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Science Review of Seeds
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Sun, 01 May 2016 17:03:07 +0000http://schooltutoring.com/help/?p=8933Overview
In many types of seeds, the hard casing of the seed is surrounded by flesh called a fruit. Many fruits are attractive to animals, providing food, so the seeds are dispersed that way. Others are dispersed by wind and water. Some seeds are dormant until the conditions are right for plants to grow, while others sprout rapidly. Seeds then germinate and grow into plants.

Fruits

The developing seed of a flowering plant (angiosperm) is contained within a tough seed coat. The seed coat contains the embryo and its food supply. The ovary wall thickens to form a fruit that encloses the hard seeds. Some fruits are fleshy and sweet, such as grapes, berries, and cherries, while others are tough, such as bean pods. Since a fruit is any seed enclosed within an embryo wall, vegetables such as corn, beans, and tomatoes are also fruits, even though they do not taste sweet.

Seed Dispersal

The fruit does not nourish the seedling as it grows, as the food supply is within the seed itself. Some fruits attract birds and mammals as food sources. The seeds pass through the digestive tract and are dispersed that way. Other seeds, such as those of ash and maple trees, are encased in structures that float on the air. The aerodynamic wings that surround a maple seed are actually a fruit. Coconuts are light enough to float on water for long enough to be carried to distant islands.

Seed Dormancy

Some seeds, such as beans, sprout very quickly if they have enough water and warmth. Other types of seeds enter a period of dormancy, where the embryo within them is still alive but will not sprout until the conditions are right. They will not grow until the soil temperature and moisture is right to support the developing seedlings. For example, many plants that grow in temperate regions do not sprout until the spring.

Seed Germination

During germination, the early growth stage of a plant, seeds absorb water. The tough seed coat swells and cracks open beneath the soil. The root grows from the seed and eventually the growing plant breaks through the surface of the soil.

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Sat, 30 Apr 2016 19:47:24 +0000http://schooltutoring.com/help/?p=8928Overview
Bubbles are usually formed when a globule of gas is suspended in a liquid. Some common examples include the bubbles of carbon dioxide found in carbonated drinks, water vapor in boiling water, and soap bubbles.

Carbonated Water

Bubbles form when very small air pockets are trapped in liquids. For example, supersaturated carbon dioxide is introduced under pressure into either plain water or water with flavors added to form carbonated soft drinks. It is weakly acidic. Although carbonation is a natural part of the fermentation process in making sparkling wines, champagne, and beer, artificial carbonated water was not produced until the mid-1700s. By the 1800s, flavorings were added.

Boiling

When a liquid, such as water, is heated to its boiling point, small bubbles of water vapor begin to form and then break at its surface. At first, bubbles of water vapor form slowly, then increase rapidly, as more water is heated. At the boiling point of a liquid, its vapor pressure is equal to the pressure of the gas above it.

Soap Bubbles

Soap bubbles consist of a very thin film of soapy water that surround a sphere of air. The soap itself reduces the surface tension of the water, so that the soap bubbles can form. When plain water flows out of a tap, bubbles form, but the surface tension of the plain water is high enough that those bubbles burst immediately. Soap bubbles are iridescent because light reflects off the surface of the thin film itself, as the bubble itself is clear. Although soap bubbles will pop if their surface ruptures, they can last longer if glycerin is added to the bubble solution.

Foam

Foams contain series of multiple gas bubbles connected by thin surface layers, such as foams of soap bubbles or foaming liquid. The bubbles contained in the foam are not all the same size and clump together. The foaming effect can also occur if there are impurities in the liquid, such as if milk is added to boiling water. Fire retardants are usually foams.
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Sun, 24 Apr 2016 05:03:51 +0000http://schooltutoring.com/help/?p=8924Overview
Factoring polynomial expressions is similar to factoring special polynomials. The difference is that both elements do not have to be perfect squares. It is the reverse of multiplying two binomials by using FOIL.

Factoring Trinomials

Trinomials of the form x^{2} +bx +c, when c>0 have certain aspects in common. The coefficient of the squared term is 1, so the only form to factor is the variable itself, in this case x times x. The constant c is a positive value. If the constant c is a positive number, but not a perfect square, it may have a variety of factors.

Using FOIL in Reverse

In order to multiply two binomials, FOIL is used, for the first term, the outer terms, the inner terms, and the last terms. It is also useful when factoring trinomials, only it is used to unravel the trinomial. In these examples, the first term, x^{2}, can be factored as x ·x. The factorization will have the form of (x + ___) (x + ____), so that first term is already known in these examples.

The Constant Term

The constant term c has a fixed numeric value, so that the last terms in each binomial will be factors of c. Suppose the binomial is x^{2} +7x +12. The constant 12 has a number of factors, as 12 ·1 is 12, 6·2 is 12, and 3·4 is also 12. The constant 12 also has negative factors, as -12·-1 is 12, ·-6·-2 is 12, and -3·-4 is also 12.

The Middle Terms

Since there are usually a number of factors for the constant, there has to be a way to narrow them down and choose the correct one. Recall that the inner terms and the outer terms are added, while the last terms are multiplied. In order for a pair of factors to work, they must be added so that their sum is the coefficient of the middle term of the trinomial. In this example, the coefficient of the middle term is 7. The first pair of factors, 12 +1, equals 13; the second pair, 6 +2, equals 8; and the third pair, 3 +4, equals 7. By substitution, x^{2} +7x + 12 factors as (x +3) (x +4).

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Sat, 23 Apr 2016 23:30:14 +0000http://schooltutoring.com/help/?p=8920Overview
Factoring polynomials in general is the reverse process of multiplying them, and then finding common factors. However, some polynomials follow special patterns, such as the difference of two squares and trinomial squares, leading to shortcut methods of factoring.

Recognizing the Difference of Two Squares

In order for a polynomial to be the difference of two squares, there must be two terms in the polynomial (a binomial), both terms in the binomial must be perfect squares, and there must be a minus sign between them. For example, the binomial x^{2} -16 has two terms in the binomial, there is a minus sign between them, and both x^{2} and 16 are perfect squares, as the square root of x^{2} is x, and the square root of 16 is 4. Suppose the polynomial were x^{4} +81. Although it is a binomial, and both x^{4} and 81 are perfect squares, there is a plus sign between them, so it doesn’t satisfy all the conditions. Suppose the polynomial was 4x^{2} – 10. The monomial 4x^{2} is a perfect square (2x), the expression is a binomial, and there is a minus sign between them. However, 10 is not a perfect square, so it is not the difference of two squares. Suppose the expression is -9x^{2} +25. It can be turned around, using the commutative property, so that the expression becomes 25-9x^{2}. It is a binomial, the minus sign is between the two terms, and both 25 and 9x^{2} are perfect squares, as the square root of 25 is 5 and the square root of 9x^{2} is 3x.

Factoring the Difference of Two Squares

Recall from the discussion of special products of polynomials that the product of (x +y) (x-y) equals x^{2} – y^{2} because xy and –xy cancel each other out. Therefore, a binomial such as x^{2} –y^{2} can be factored so that it follows the pattern (x +y) (x-y). For example, the binomial 16x^{2} – 81 follows the pattern of the difference of two squares, and can be factored as (4x +9)(4x-9) because the square root of 16x^{2} is 4x and the square root of 81 is 9.

Recognizing Trinomial Squares

Trinomial squares also follow special conditions. Recall from the discussion of special products of polynomials that (x +y) ^{2} is always a trinomial in the form of x^{2} +2xy +y^{2}. Similarly, (x-y) ^{2} is always a trinomial in the form x^{2} -2xy + y^{2}. Therefore, a trinomial is a trinomial square if two of the terms are perfect squares, there are no minus signs before either of them, and the other term is twice the product of the first two. For example, x^{2} +6x +9 fits the pattern because both x^{2 }and 9 are perfect squares. The square root of x^{2} is x, the square root of 9 is 3, and 3x + 3x is 6x.

Factoring Trinomial Squares

After recognizing a trinomial square, it is a short step to factoring it. For example, since both x^{2} and 9 are perfect squares, the square root of x^{2} is x and the square root of 9 is 3. To check, multiply (x + 3) (x + 3) using FOIL, for x^{2} + 3x +3x = 9, or x^{2} + 6x +9.

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Sun, 17 Apr 2016 22:00:41 +0000http://schooltutoring.com/help/?p=8915Overview
Capitalization of particular words in English sentences follows a few basic rules. However, it is easy to overlook capitalization when proofreading, since most of the time capitalization errors will not be caught by the spell-checker in the computer program.

First Word of a Sentence

The first word of a sentence is always capitalized. Therefore, the first word of the next sentence is capitalized. This is true even if the sentence is not complete, although the writer usually will make that sentence complete, or combine the phrase with another sentence during the editing phase of the document. Also, capitalize the first word of a complete sentence within quotation marks. Do not capitalize words when the quotation is indirect or continues within the same sentence.

Proper Nouns

Proper nouns, such as names of people and places, are capitalized, such as Mary, John, Montana (the state), Canada (the country), Antarctica (the continent), Mars (the planet), Betelgeuse (the star), and so on. If more than one proper name is used, capitalize the words within the name, such as Mary Jones, Golden Gate Bridge, New Horizons, San Francisco, and New York City. Adjectives derived from proper nouns, such as Russian dressing, the English language, and the Martian landscape, should also be capitalized. However, notice that the second word in the phrase is not capitalized as that word is not part of the name. There are many salad dressings, many languages, and many landscapes, for example. Whether the word the is capitalized depends upon whether or not it is part of the proper noun, such as The Dalles, The Bellingham Herald, or The Hague. If it is not part of the proper noun, it is left without capitals.

Titles of Books

Principal words within titles are capitalized, such as the first word, nouns, pronouns, adjectives, adverbs, and verbs. Titles include titles of books, pictures, plays, movies, TV shows, musical compositions, and other documents. For example, one of my favorite children’s books is A Wrinkle inTime by Madeleine L’Engle. The movie Gone with the Wind is a classic. We watched Game of Thrones on TV.

Common Errors

When addressing a family member, the word is capitalized. Mother, may I go out for a swim? However, when referring to a family member, the word is not capitalized. My mother always attended my concerts. Similarly, I went to visit Aunt Lucille in Alaska, with her name specified. However, I went to visit my aunt in Alaska, as her name isn’t specified.

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