Elementary AlgebraMacmillan Company, 1905 |
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Página 25
... preceding example , what number may be added to obtain the same result ? 4. The sum total of the units +1 , +1 , +1 , +1 , +1 , −1 , -1 , and -1 , is 2. What is the value of the sum if two nega- tive units are taken away ? If three ...
... preceding example , what number may be added to obtain the same result ? 4. The sum total of the units +1 , +1 , +1 , +1 , +1 , −1 , -1 , and -1 , is 2. What is the value of the sum if two nega- tive units are taken away ? If three ...
Página 26
... preceding examples could be obtained by the following Principle . To subtract , change the sign of the subtrahend and add . The numerical results of Exs . 1-3 of course do not prove this principle , but it may be deduced as follows : to ...
... preceding examples could be obtained by the following Principle . To subtract , change the sign of the subtrahend and add . The numerical results of Exs . 1-3 of course do not prove this principle , but it may be deduced as follows : to ...
Página 36
... preceding definition , however , becomes meaningless if the multiplier is a fractional or negative number . To take a number 2 or -7 times is just as meaningless as to go to bed 2 times or to fire a gun -7 times . A more useful ...
... preceding definition , however , becomes meaningless if the multiplier is a fractional or negative number . To take a number 2 or -7 times is just as meaningless as to go to bed 2 times or to fire a gun -7 times . A more useful ...
Página 37
... preceding illustrations lead to the Law of Signs : The product of two numbers with like signs is positive ; the product of two numbers with unlike signs is negative . To obtain the absolute value of a product we multiply the absolute ...
... preceding illustrations lead to the Law of Signs : The product of two numbers with like signs is positive ; the product of two numbers with unlike signs is negative . To obtain the absolute value of a product we multiply the absolute ...
Página 47
... preceding type of examples deserve special mention : I. ( a + b ) 2 = a2 + 2ab + b2 . II . ( a - b ) 2 = a2 — 2 ab + b2 . - III . ( a + b ) ( a - b ) — a2 — b2 . = Expressed in general language : I. The square of the sum of two numbers ...
... preceding type of examples deserve special mention : I. ( a + b ) 2 = a2 + 2ab + b2 . II . ( a - b ) 2 = a2 — 2 ab + b2 . - III . ( a + b ) ( a - b ) — a2 — b2 . = Expressed in general language : I. The square of the sum of two numbers ...
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Términos y frases comunes
a+b)² a²b a²b² a³b a³b³ ab² ab³ algebraic angle arithmetic arithmetic means ax² binomial binomial theorem Check Clearing of fractions coefficient consecutive numbers contains denominator diagram difference digits divided division examples exceeds EXERCISE Extract the square factors Find the H. C. F. Find the number Find the sum Find the value following equations following expressions function given graph graphically Hence inches method miles per hour monomial multiplied negative obtain polynomials problem proportional quadratic equation quadratic surd quotient radical ratio reduced remainder sides Simplify simultaneous equations Solve the equation Solve the following square root Substituting subtract surds symbols term Transposing triangle unknown number unknown quantities Va² x²y x²y² x²y³ xy² yards zero
Pasajes populares
Página 164 - The sum of the three angles of any triangle is equal to 180°.
Página 47 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Página 135 - A fraction may be reduced by division to an integral or mixed expression, if the degree of the numerator is equal to, or greater than, that of the denominator.
Página 170 - If the product of two numbers is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Página 104 - A trinomial belongs to this type, ie it is a perfect square, when two of its terms are perfect squares, and the remaining term is equal to twice the product of the square roots of these terms.
Página 299 - Or ж2 + 2x-24 = 0. 325. If both members of an equation are divided by an expression involving the unknown quantity, the resulting equation contains fewer roots than the original one. In order to obtain all roots of the original equation, such a common divisor must be made equal to zero, and the equation thus formed be solved. Eg let it be required to solve If we divide both members by x — 3, we obtain ж + 3 = 5 or x = 2.
Página 105 - We have seen that the product of the sum and the difference of two numbers is equal to the difference of the squares of these numbers. Conversely, the difference of the squares of any two numbers is equal to the product of the sum and the difference of these numbers.
Página 77 - Uniting, - 2 x = - 30. Dividing, x — 15. Check. In 15 years A will be 30 ; 5 years ago he was 10 ; but 30 = 3 x 10. Ex. 3. To a quantity of water contained in a vessel., 56 gallons were added, and there was then in the vessel 8 times as much as at first. How many gallons did the vessel contain at first ? Let x = the number of gallons contained in the vessel at first. The verbal statement expressed in letters gives x + 66 = 8 x.
Página 55 - To divide a polynomial by a monomial, divide each term of the dividend by the divisor and add the partial quotients.
Página 162 - The sum of two numbers is 123, and if the greater is divided by the smaller, the quotient is 2 and the remainder is 3. Find the numbers.