Essentials of Algebra for Secondary Schools

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D.C. Heath & Company, 1904 - 367 σελίδες

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Σελίδα 280 - In any proportion,, the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 132 - At what time between 3 and 4 o'clock are the hands of a watch opposite to each other ? Let x = the number of minute-spaces passed over by the minutehand from 3 o'clock to the required time. Then, since the hour-hand is 15 minute-spaces in advance of the minute-hand at 3 o'clock, x — 15 — 30, or x — 45, will represent the number of minute-spaces passed over by the hour-hand.
Σελίδα 41 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Σελίδα 132 - How far can he ride in a coach which travels 41 miles an hour, so as to return in time, walking back at the rate of 3| miles an hour ? 44.
Σελίδα 22 - From §§36 and 37, we have the following rule: To subtract one number from another, change the sign of the subtrahend, and add the result to the minuend.
Σελίδα 281 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 59 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (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 two, plus the square of the second.
Σελίδα 280 - In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth.
Σελίδα 161 - A certain sum of money at simple interest amounts in m years to a dollars, and in n years to b dollars. Required the sum and the rate of interest. 47. A...
Σελίδα 140 - If necessary, multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities in the resulting equations of equal absolute value.

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