A Short Course in Higher Algebra: For Academies, High Schools, and CollegesLeach, Shewell, and Sanborn, 1889 - 426 σελίδες |
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Αποτελέσματα 1 - 5 από τα 82.
Σελίδα 11
... Whence , Therefore , and 3. The sum of the ages 13 years younger than B. Let Then By the conditions , Or , Whence , And , Therefore , 6x = : 66 . x = 11 , the number of dollars A has , 2 x 22 , the number of dollars B has , 33 , the ...
... Whence , Therefore , and 3. The sum of the ages 13 years younger than B. Let Then By the conditions , Or , Whence , And , Therefore , 6x = : 66 . x = 11 , the number of dollars A has , 2 x 22 , the number of dollars B has , 33 , the ...
Σελίδα 54
... whence , 9y2-12xy + 4x2 = ( 3 y − 2 x ) ( 3 y − 2 x ) = ( 3y - 2x ) 2 ; which is another form of the answer . EXAMPLES . Factor the following : 3. x2 + 2xy + y2 . 4. 4 + 4m + m2 . 5. x2 14x + 49 . --- 6. a2 - 10a + 25 . 7. y2 + 2y + 1 ...
... whence , 9y2-12xy + 4x2 = ( 3 y − 2 x ) ( 3 y − 2 x ) = ( 3y - 2x ) 2 ; which is another form of the answer . EXAMPLES . Factor the following : 3. x2 + 2xy + y2 . 4. 4 + 4m + m2 . 5. x2 14x + 49 . --- 6. a2 - 10a + 25 . 7. y2 + 2y + 1 ...
Σελίδα 78
... whence , Fx MabF2 ( 2 ) From ( 1 ) and ( 2 ) we have A × B = Fx M ( Art . 42 , 7 ) . That is , the product of any two quantities is equal to the product of their highest common factor and lowest common multiple . Hence , to find the ...
... whence , Fx MabF2 ( 2 ) From ( 1 ) and ( 2 ) we have A × B = Fx M ( Art . 42 , 7 ) . That is , the product of any two quantities is equal to the product of their highest common factor and lowest common multiple . Hence , to find the ...
Σελίδα 81
... ас b be any fraction . Dividing its numerator by c , we have To prove that α ac divided by c . is b b = ac a By Art . 145 , ( 1 ) , сх b b a ac Whence it follows that ÷ C . b b II . Let be any fraction . by c , FRACTIONS . 81.
... ас b be any fraction . Dividing its numerator by c , we have To prove that α ac divided by c . is b b = ac a By Art . 145 , ( 1 ) , сх b b a ac Whence it follows that ÷ C . b b II . Let be any fraction . by c , FRACTIONS . 81.
Σελίδα 82
... Whence it follows that bc = - 147. If the numerator and denominator of a fraction be both multiplied , or both divided , by the same quantity , the value of the fraction is not altered . For , by Arts . 145 and 146 , multiplying the ...
... Whence it follows that bc = - 147. If the numerator and denominator of a fraction be both multiplied , or both divided , by the same quantity , the value of the fraction is not altered . For , by Arts . 145 and 146 , multiplying the ...
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Άλλες εκδόσεις - Προβολή όλων
A Short Course in Higher Algebra: For Academies, High Schools, and Colleges Webster Wells Προβολή αποσπασμάτων - 1889 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ab² annuity arithmetical means arithmetical progression Binomial Theorem cent compound interest Clearing of fractions coefficient cologarithms common logarithm continued fraction convergent cube root decimal point denominator denote derive the formula digits divided divisor eighth term equal EXAMPLES Expand exponent expression Extracting the square find the logarithm find the number Find the value following equations following rule geometrical means geometrical progression given equation Given log harmonical means Hence increased integral interest being compounded last term mantissa Multiplying Note number corresponding number of combinations number of permutations number of terms obtain partial fractions present value quadratic quadratic equation quantities taken quotient radical sign remainder Required the number result second member second term Solve the equation Solve the following square root Subtracting unknown quantity Whence
Δημοφιλή αποσπάσματα
Σελίδα 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Σελίδα 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Σελίδα 269 - 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 129 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Σελίδα 267 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Σελίδα 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Σελίδα 227 - A courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.
Σελίδα 44 - 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 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.
Σελίδα 136 - Find the value of one of the unknown quantities, in terms of the other and known quantities...