8581735
Description
Flashcards by Lance Erickson, updated more than 1 year ago
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Created by Lance Erickson
over 7 years ago
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| Question | Answer |
| For Final only: what is the dimensions of the matrix? | 3 x 4 |
| how would you solve this system? | best to clear fractions! multiply first equation by 15 to get 5x + 3y = 15 and the second by 8 to get 4x + y = -4. |
| For Final only: use backward substitution to solve the system | 2z = -8 so z = -4. substitute this into z on 2nd equation to solve for y. y = -13/2. use these to now solve for x in first equation |
| write as a single log | log (5^7p^4) |
| solve for x. | ex to log log3 (5) = x+ 2. now subtract 2. use change of base if you need decimal answer. |
| write as a single log. | ln (10 sqrt(5p) e^2 ) |
| what is the domain of this function? | x/4 - 5 > 0 next, multiply by 4 x-20 > 0 so x > 20 |
| solve. | "cancel e" (using inverses) to get 2 + 3 log x = 8 clean up: logx = 2 so 10^2 = x x=100 |
| solve for x. | main idea: change log to exp 2^1 = (3x - 1)^1/3 cube both sides 8= 3x - 1 x = 3 |
| solve | clean up (divide by 2), then notice bases are the same so you can cancel to get x^2+ 2 = 1 get x alone or use formula: x^2 = -1 so x = + - i |
| solve for x. | Bring logs together first! log4 ( (2x-1)(x+1) ) = .5 log to exp 4^.5 = (2x-1)(x+1) 2=(2x-1)(x+1) FOIL then =0 and formula |
| solve for x. | cancel 5 using inverses cube both sides x-1 = 64 x = 65 |
| solve for x | cancel logs (using inverses) to get x = x^2 - 2. finish with quad. formula |
| solve for x | you want to cancel x but first bring logs on left side together. log (x ( x+3) ) = log 10 x(x + 3) = 10 x^2 + 3x = 10 get "= 0" then formula |
| A fundraiser sold children and adult tickets. The former were $5 and the latter $7 each. If they raised $660 by selling 100 tickets, how many of each ticket were sold? write a system of equation. | c+a = 100 5c+7a =660 |
| For Final only: Write a system of equations | 3x+ 4y = 6 -3x + 2y = 12 |
| For Final only: what is the dimensions | 2 x 3 |
| For Final only: write a matrix equation to solve this and then solve. | AX= B where A is left and B = right. x = A-1 B answer by calculator: y = 3 and x = -2 |
| Solving a system you find the following: x = 0 what does this tell you? | the solution is consistent and by graphing method the graphs will meet |
| Solving a system you find the following: 4 = 0 what does this tell you? | solution set is inconsistent and graphs will not meet |
| Solving a system you find the following: 0 = 0 what does this tell you? | solution is consistent but coincidental. |
| simplify | All you are doing is simplifying each log: 5 - 5 + 3 = 3 |
| what is the domain? | 2x + 6 > 0 so x . -3 |
| expand | 3log5 (25) + 3 log5 (x) - 1/2 log5 (y) |
| expand | 3 ln(2) + 3 ln (e) - 6 ln (p) |
| Find the inverse of f(x) = 3(x-1) ^2+7 | switch x and y and solve for y: = [(x-7)/3]^1/2 |
| Find the inverse of f(x) = 3ln(x-1) +7 | switch x and y and solve for y: = e ^ [(x-7)/3] |
| Find the inverse of f(x) = 4^(3x-1) -2 | switch x and y and solve for y: |
| Find the domain for each: y = 3log(5-2x) + 34 y = 3log[2x(x-3)(x+1)] + 34 | Set up with ( ) > 0 then use number line: x < 2.5 (-1,0) U (3, inf.) |
| given part of the graph of the exponential graph of f(x) and f(1) = 4 then find f(x) | Take 2 points and substitute into y = c a^x and solve. answer y = 8 x .5 ^x use the points (1,4) and (3,1) from the graph |
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