Elementary Algebra |
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Page 9
... divide all algebraical quantities into positive quantities and negative quantities , according as they are expressed with the sign + or the sign ; and this is quite irrespective of any actual process of addition and subtraction . This ...
... divide all algebraical quantities into positive quantities and negative quantities , according as they are expressed with the sign + or the sign ; and this is quite irrespective of any actual process of addition and subtraction . This ...
Page 34
... divide one simple expression by another , divide the coefficient of the dividend by that of the divisor , and subtract the index of any letter in the divisor from the index of that letter in the dividend . Example 4. 84a5x3 ÷ 12a4x ...
... divide one simple expression by another , divide the coefficient of the dividend by that of the divisor , and subtract the index of any letter in the divisor from the index of that letter in the dividend . Example 4. 84a5x3 ÷ 12a4x ...
Page 35
... divide a compound expression by a single factor , divide each term separately by that factor . This follows at once from Art . 34 . Examples . ( 1 ) ( 9x - 12y + 3z ) ÷ -- 3 = -3x + 4y - z . ( 2 ) ( 36a3b2 - 24a2b5 – 20a4b2 ) ÷ -4a2b ...
... divide a compound expression by a single factor , divide each term separately by that factor . This follows at once from Art . 34 . Examples . ( 1 ) ( 9x - 12y + 3z ) ÷ -- 3 = -3x + 4y - z . ( 2 ) ( 36a3b2 - 24a2b5 – 20a4b2 ) ÷ -4a2b ...
Page 36
... Divide 1 . 3x3 by x2 . 2. 27x4 by -9x3 . 3 . 356 by 7x3 . 4 . abx2 by -αx . 5. x3y by xy . 6 . a4x3 by - a2x3 . 7 ... divide one compound expression by another . RULE . 1. Arrange divisor and dividend in ascending or descending powers of ...
... Divide 1 . 3x3 by x2 . 2. 27x4 by -9x3 . 3 . 356 by 7x3 . 4 . abx2 by -αx . 5. x3y by xy . 6 . a4x3 by - a2x3 . 7 ... divide one compound expression by another . RULE . 1. Arrange divisor and dividend in ascending or descending powers of ...
Page 37
... Divide 24x2 – 65xy + 21y2 by 8x - 3y . 1 8x - 3y ) 24x65xy + 21y2 ( 3x − 7y 24x2 - 9xy -56xy + 21y2 -56xy + 21y2 Divide EXAMPLES VI . b . 1. x2 + 3x + 2 by x + 1 . 3. 2-11a + 30 by a - 5 . 5. 3x2 + 10x + 3 by x + 3 . 7 , 5x2 + 11x + 2 ...
... Divide 24x2 – 65xy + 21y2 by 8x - 3y . 1 8x - 3y ) 24x65xy + 21y2 ( 3x − 7y 24x2 - 9xy -56xy + 21y2 -56xy + 21y2 Divide EXAMPLES VI . b . 1. x2 + 3x + 2 by x + 1 . 3. 2-11a + 30 by a - 5 . 5. 3x2 + 10x + 3 by x + 3 . 7 , 5x2 + 11x + 2 ...
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Common terms and phrases
a+3b a+b+c a₁ a²+b² arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Popular passages
Page 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Page 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Page 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Page 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Page 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Page 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....