Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and AcademiesSargent, Wilson & Hinkle, 1848 - 240 σελίδες |
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Σελίδα 69
... other ? Give an example . 91 . What is a composite quantity ? Give an example . 92. What is the rula for separating a monomial into its prime factors ? RULE . Divide the given quantity by the greatest monomial FACTORING . 69.
... other ? Give an example . 91 . What is a composite quantity ? Give an example . 92. What is the rula for separating a monomial into its prime factors ? RULE . Divide the given quantity by the greatest monomial FACTORING . 69.
Σελίδα 70
... separated into two binomial factors , when the extremes are squares and positive , and the middle term is twice the product of the square roots of the extremes . See Articles 79 and 80 . Thus : a2 + 2ab + b2 = ( a + b ) ( a + b ) . a2 ...
... separated into two binomial factors , when the extremes are squares and positive , and the middle term is twice the product of the square roots of the extremes . See Articles 79 and 80 . Thus : a2 + 2ab + b2 = ( a + b ) ( a + b ) . a2 ...
Σελίδα 71
... separated into factors , according to paragraph 2d , above , thus : a * b * = ( a2 + b2 ) ( a2 — b2 ) = ( a2 + b2 ) ( a + b ) ( ab ) . 5th . When any expression consists of the sum of the odd pow- ers of two quantities , it may be separated ...
... separated into factors , according to paragraph 2d , above , thus : a * b * = ( a2 + b2 ) ( a2 — b2 ) = ( a2 + b2 ) ( a + b ) ( ab ) . 5th . When any expression consists of the sum of the odd pow- ers of two quantities , it may be separated ...
Σελίδα 72
... separating a polynomial into its prime factors , when one of them is a monomial , and the other a polyno- mial ? 94 ... separated into two binomial factors ? What are the factors of x2 - y2 ? Of 9a2-1662 ? What is one of the factors of ...
... separating a polynomial into its prime factors , when one of them is a monomial , and the other a polyno- mial ? 94 ... separated into two binomial factors ? What are the factors of x2 - y2 ? Of 9a2-1662 ? What is one of the factors of ...
Σελίδα 74
... separating each quantity into its prime factors , we have 6ab = 2 × 3ab , 15a2c = 3X5aac . Here we see , that 3 and a are the only factors common to both terms ; hence , both the quantities can be exactly divided , either by 3 or a , or ...
... separating each quantity into its prime factors , we have 6ab = 2 × 3ab , 15a2c = 3X5aac . Here we see , that 3 and a are the only factors common to both terms ; hence , both the quantities can be exactly divided , either by 3 or a , or ...
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added algebraic quantities apples arithmetical progression arithmetical series binomial bushels called cents a piece coefficient common difference complete equation Completing the square denotes Divide the number dividend division dollars entire quantity equal exactly divide exponent expression extract the square find the greatest Find the product Find the square Find the sum find the value following examples fourth fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence last term least common multiple lemon letter minus monomial negative quantities number of terms peaches perfect square polynomial positive quantity pound of coffee preceding prime factors principle proportion pupil quan question quotient ratio Reduce remainder represent the cost represent the number required the numbers required to find result rule second degree solution square root subtracted theorem three numbers tion tities transposing unknown quantity whole number
Δημοφιλή αποσπάσματα
Σελίδα 100 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 22 - Required the distance from A to B, from B to C, and from C to D.
Σελίδα 176 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 136 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 122 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.
Σελίδα 62 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Σελίδα 78 - To find the greatest common divisor of three or more quantities, first find the greatest common divisor of two of them ; then, of that divisor and one of the other quantities, and so on. The last divisor thus found, will be the greatest common divisor sought.
Σελίδα 59 - 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 137 - A farmer has 2 horses, and a saddle worth 25 dollars ; now, if the saddle be put on the first horse, his value will be double that of the second ; but, if the saddle be put on the second horse, his value will be three times that of the first.
Σελίδα 219 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.