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Functions/214736: I have to find the composition of functions! Can't figure this one out either! g(x)=3/(x-1) f(x)=(x-1)/(x-3) find (fog)(x) Again, thanks!!!!! 1 solutions Answer 162174 by jim_thompson5910(28598)   on 2009-09-18 18:07:38 (Show Source): You can put this solution on YOUR website! Remember that is another way of saying . Start with the given function. Plug in Note: this involves replacing 'x' on the left side with and replacing each 'x' on the right side with . Multiply EVERY term by the inner LCD to clear out the inner fractions. Simplify Distribute Combine like terms. So

Linear_Equations_And_Systems_Word_Problems/214725: This question is from textbook Practicing to Take the GRE General Test I am having problems with this word problem: A group can charter a particular aircraft at a total fixed cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12. What is the cost per person if 40 people charter the aircraft? I have defined the cost if 40 people charter as x and the cost if 36 people charter as y. The only equation I can come up with so far is 36y=40(x+12), but I know I need some other equation if I want to solve for either variable. The back of the book states the answer as 108, but I cannot figure out how to get there. Thanks in advance for your help! 1 solutions Answer 162168 by jim_thompson5910(28598)   on 2009-09-18 17:38:19 (Show Source): You can put this solution on YOUR website! Let x=cost per person (for 40 people) in dollars y=total cost in dollars If 40 people attend, then the cost per person 'x' is simply the total cost 'y' divided by the number of people going (40). In other words, (eg: if the total cost is $80, then the cost per person is dollars). This is your first equation. Now if 36 people attend instead of 40, the cost per person will increase by $12. So this means that the new cost per person is if 36 people go. This is equal to (since the total cost is now divided among 36 people). So . This is the second equation. Start with the second equation. Plug in Multiply EVERY term by the LCD to clear out the fractions. Multiply and simplify. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. Since 'y' is the total cost, this means that the total cost is $4,320 Move back to the first equation. Plug in Divide Since 'x' is the cost per person when 40 people were going, this means that the cost per person for 40 people is $108.

Linear-systems/214712: use the intercepts to graph the equation 4x-2y=8 please help me solve and graph 1 solutions Answer 162150 by jim_thompson5910(28598)   on 2009-09-18 16:38:34 (Show Source): You can put this solution on YOUR website! x-intercept To find the x-intercept, plug in and solve for x Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Divide both sides by to isolate . Reduce. So the x-intercept is . ------------------------------------------ y-intercept To find the y-intercept, plug in and solve for y Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Divide both sides by to isolate . Reduce. So the y-intercept is . Now plot the points and draw a straight line through them to graph the equation Graph of

Inequalities/214692: Solve the inequality, and express the solutions in terms of intervals whenever possible: 3x - 2 > 18 1 solutions Answer 162126 by jim_thompson5910(28598)   on 2009-09-18 14:00:27 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add 2 to both sides. Add Divide both sides by 3 to isolate 'x' So the solution is which in interval notation is

Graphs/214690: Give the center and radius of the circle: x^2+y^2-10x+6y+25 I first completed the square: (x^2-10x+25)+(y^2+6y+9)=-25 (x-5)^2+(y-3)^2=-25+25+9 (x-5)+(x-3)=9 (-5,-3) with a radius of 9 but I am not sure if I did that right?!?! 1 solutions Answer 162125 by jim_thompson5910(28598)   on 2009-09-18 13:55:32 (Show Source): You can put this solution on YOUR website! The last equation should be , since factors to . We can take this equation and then rewrite as and to to get Recall that the general equation of a circle is where (h,k) is the center and 'r' is the radius. Looking at (which is in the circle form described above), we see that , and (I'm just matching the two forms). So the center is (5,-3) and the radius is 3 units. So you just had some minor errors (such as the sign differences and forgetting to take the square root of 9)

Exponents/214688: write each expression using positive exponets. 7^-2 1 solutions Answer 162124 by jim_thompson5910(28598)   on 2009-09-18 13:51:27 (Show Source): You can put this solution on YOUR website! Recall that . In other words, if you have a negative exponent, you can rewrite the expression with a positive exponent by flipping the fraction. In this problem, or simply

Expressions-with-variables/214209: Write an algebraic expression for, "four times the sum of 2a and (b) increased by twice the sum of 6a and 2b." Then simplify, indicating the properties used. 1 solutions Answer 162123 by jim_thompson5910(28598)   on 2009-09-18 13:34:10 (Show Source): You can put this solution on YOUR website! "four times the sum of 2a and (b)" translates to "twice the sum of 6a and 2b" means that and altogether, "four times the sum of 2a and (b) increased by twice the sum of 6a and 2b." tells us Start with the given expression Distribute Combine like terms. So

Linear-equations/214676: media services charges $20 for a phone and $30/month for its economy plan. What is the total cost of C (t) of operating a media service phone for t months? C(t)= what is the total cost for 7 months of service? C(t)= 1 solutions Answer 162122 by jim_thompson5910(28598)   on 2009-09-18 13:27:08 (Show Source): You can put this solution on YOUR website! Any linear function can be written in the form where 'm' is the slope and represents the change of the function and 'b' is the initial value of the function. In our case, the change is $30 (since the total cost goes up $30 a month) while the initial fee is $20. So this means and giving us the function If you're unsure of the answer, simply plug in values of 't' Examples: When , the number of months is zero. So this represents the start of the plan. Plug this into C(t) to get . So no matter what, you're going to pay $20 up front (which is exactly what the problem states). Now one month later, the value of 't' is now . If you simply add $30 to the down payment of $20, you get $50. In other words, you've paid $50 for the first month. If we plug in t=1, we get which is exactly what we just got. So you may be asking why we're going through all the trouble of using functions when we could just add. Using functions will save us time for larger values of 't'. For instance, let's say you want to know what the total cost will be 20 months from now. Are you going to add 20 sets of $30 to 20 to find the answer? You could, but why do that when you can simply use the function. Also, you can also answer other questions that the previous technique would have a hard time doing so. --------------------------------------------------------------------- To find the cost of 7 months of service, just plug in t=7: Start with the given function. Plug in Multiply Add So 7 months of service will cost $230

Probability-and-statistics/214683: if a jar contains 23 red marbles and 4 green marbles, the probability that a marble selectted from the jar at random will be green is? If the above green is not replaced, what is the probability that the next pulled marbles is red? if you reached into the jar 4 times, what is the probability that you would never choose a green marble (after each pullout you do not replace the chosen marble? 1 solutions Answer 162121 by jim_thompson5910(28598)   on 2009-09-18 13:18:02 (Show Source): You can put this solution on YOUR website! a) Total number of marbles = 23 + 4 = 27 marbles P(Green Marble) = (# of green marbles)/(# of marbles total) = 4/27 = 0.148 So the probability is 4/27 which is about a 14.8% chance ------------------------------------ b) Since the selected marble from part a) is not replaced, the total number of marbles is now 27-1=26 P(Red Marble) = (# of red marbles)/(# of marbles total) = 23/26 = 0.885 So the probability is 23/27 which is about a 88.5% chance ------------------------------------ c) To find the probability of NOT choosing green after four selections, you simply calculate the probability of choosing red 4 times in a row (without replacement). This works because there are only two choices in marble selection. So the basic outline is P(4 red) = P(red)*P(red with 1 less from total)*P(red with 2 less from total)*P(red with 3 less from total) I'll let you take it from here. Let me know if you still need help.

Probability-and-statistics/214681: if a jar contains 23 red marbles and 4 green marbles, the probability that a marble selected from the jar at random will be green is? 1 solutions Answer 162119 by jim_thompson5910(28598)   on 2009-09-18 13:10:46 (Show Source): You can put this solution on YOUR website! Total number of marbles = 23 + 4 = 27 marbles P(Green Marble) = (# of green marbles)/(# of marbles total) = 4/27 = 0.148 So the probability is 4/27 which is about a 14.8% chance

Polynomials-and-rational-expressions/214677: please help me solve this questionfind all numbers for which the rational expression is undefined 8/w-1 1 solutions Answer 162118 by jim_thompson5910(28598)   on 2009-09-18 13:08:31 (Show Source): You can put this solution on YOUR website! Is the expression or is it ??? is undefined when the denominator is zero. So set the denominator equal to zero and solve for 'w' to get ----> So is undefined when -------------------------------- is undefined when the denominator is zero. So set the denominator equal to zero to get So is undefined when

Equations/214537: Please help me solve the following question 5/2t - t = 3 + 3/2t 1 solutions Answer 162043 by jim_thompson5910(28598)   on 2009-09-17 19:55:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Subtract from both sides. Combine like terms on the left side. Simplify. Since this equation is NEVER true for any 't' value, this means that there are no solutions.

Polynomials-and-rational-expressions/214534: This question is from textbook blitzer college algebra essential factor x^2+2x-3 1 solutions Answer 162042 by jim_thompson5910(28598)   on 2009-09-17 19:45:25 (Show Source): You can put this solution on YOUR website! Jump to Answer Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,3 -1,-3 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*(-3) = -3 (-1)*(3) = -3 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 -3 1+(-3)=-2 -1 3 -1+3=2 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term =============================================================== Answer: So factors to . In other words, . Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical). Jump to Top

Equations/214498: What is the charge of an ion with 38 electrons, 38 neutrons, and 35 protons? 1 solutions Answer 162021 by jim_thompson5910(28598)   on 2009-09-17 18:58:11 (Show Source): You can put this solution on YOUR website! This is more a chemistry question, but I happen to know a little bit about it. Remember that an ion is simply "an atom or molecule where the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge." (from Wikipedia). Recall that the charge of an electron is -1 while the charge of a single proton is +1. If there are more protons than electrons, then the atom/molecule is positively charged which makes it a cation. If there are more electrons than protons, then the atom/molecule is negatively charged which makes it an anion. To find the net charge, simply subtract the number of electrons from the number of protons to get: 35-38 = -3 Note: this is the same as saying: 38(1)+35(-1) = -3 So the net charge of this ion is -3 which means that it's negatively charged and that it's an anion.

Rational-functions/214421: Evaluate the following piecewise defined function at f(0), f(2), and f(3) f(x)= 5 if x<2 2x-3 if x>=2 1 solutions Answer 161959 by jim_thompson5910(28598)   on 2009-09-17 13:47:58 (Show Source): You can put this solution on YOUR website! Take note that x=0 satisfies the inequality . So to find , plug x=0 into the first function . The values x=2 and x=3 are both greater than or equal to 2. So they satisfy . This means to find f(2) and f(3), just plug in x=2 and x=3 respectively into .

absolute-value/214420: |-2| 1 solutions Answer 161957 by jim_thompson5910(28598)   on 2009-09-17 13:33:20 (Show Source): You can put this solution on YOUR website! Remember, the absolute value of ANY number is ALWAYS positive.

Polynomials-and-rational-expressions/214414: how to factor 16x^4-1 1 solutions Answer 161954 by jim_thompson5910(28598)   on 2009-09-17 13:21:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as Take note that we have a difference of squares in which and . We can factor this difference of squares using the formula Start with the difference of squares formula Plug in and So factors to We can keep going and factor further. Rewrite as . Rewrite as Notice that we again have a difference of squares in which and . We can factor this difference of squares using the formula Start with the difference of squares formula Plug in and So factors to --------------------------------------------- Answer: Putting all of this together tells us that completely factors to

Equations/214415: 6x+7=25 solve for x 1 solutions Answer 161952 by jim_thompson5910(28598)   on 2009-09-17 13:15:52 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 7 from both sides. Combine like terms. Divide both sides by 6 to isolate 'x' Reduce So the solution is

Divisibility_and_Prime_Numbers/214411: This question is from textbook algebra 1 an integrated approach if a is an integer, which of the following is always an odd integer? (a)4a+2 (b)10a (c)8a+1 (d).83 please help!!!!!! 1 solutions Answer 161951 by jim_thompson5910(28598)   on 2009-09-17 13:09:51 (Show Source): You can put this solution on YOUR website! Recall that if 'k' is an integer, then is ALWAYS odd. Why? The number is ALWAYS even (because all even integers are a multiple of 2). If you add 1 to an even integer, you will get an odd integer. So this shows us that is ALWAYS odd where 'k' is an integer. So the goal is to try to transform each choice into either the form (even form) or (odd form). a) Start with the given expression Factor out the GCF 2 Replace 'a+1' with 'k' (which is an integer) So is ALWAYS even (try plugging in some integers for 'a' to test this). ----------------------------- b) We can rewrite as which can come to (where . So is ALWAYS even. ----------------------------- c) We can rewrite as and then let . Now replace '4a' with 'k' to get . So (where ) This shows us that is ALWAYS odd. ----------------------------- d) The value 0.83 is neither even nor odd. Why is this? A number can only be even or odd when it is a whole number or integer. Since 0.83 is NOT a whole number, it is neither even nor odd. So to recap, the only odd integer of the group is

Polynomials-and-rational-expressions/214181: Need help in this problem? Is (-2,-2) a solution of the system x-3y=4 3x+y=-8 1 solutions Answer 161766 by jim_thompson5910(28598)   on 2009-09-16 15:36:06 (Show Source): You can put this solution on YOUR website! Simply plug in x=-2 and y=-2 into both equations and simplify. If you get two identities, then (-2,-2) is the solution. If one is not (or both aren't) an identity, then (-2,-2) is NOT the solution. Note: an identity is an equation that is ALWAYS true. A simple identity is 0=0.

Polynomials-and-rational-expressions/214178: How is this algebra problem done? factor p^2+12p+36 1 solutions Answer 161764 by jim_thompson5910(28598)   on 2009-09-16 15:33:54 (Show Source): You can put this solution on YOUR website! Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,2,3,4,6,9,12,18,36 -1,-2,-3,-4,-6,-9,-12,-18,-36 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*36 2*18 3*12 4*9 6*6 (-1)*(-36) (-2)*(-18) (-3)*(-12) (-4)*(-9) (-6)*(-6) Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 36 1+36=37 2 18 2+18=20 3 12 3+12=15 4 9 4+9=13 6 6 6+6=12 -1 -36 -1+(-36)=-37 -2 -18 -2+(-18)=-20 -3 -12 -3+(-12)=-15 -4 -9 -4+(-9)=-13 -6 -6 -6+(-6)=-12 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term Condense --------------------------------------------- Answer: So factors to . Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Polynomials-and-rational-expressions/214177: How do I solve this algebra problem? solve x(x-8)= -15 1 solutions Answer 161763 by jim_thompson5910(28598)   on 2009-09-16 15:32:48 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Add 15 to both sides. Notice we have a quadratic in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the answers are or

Exponential-and-logarithmic-functions/214160: I should write this problem in exponential for and simplify.... I know how that works (usually) I just dont get how to do it with this problem; cubed root of "a" times the fith root of "a"..... 3_________________________5 v---- < (the v--- is the sqrt.) times v--- (just ignore the _____) __a_________________________a Hope my "doodling" helped a bit..... 1 solutions Answer 161750 by jim_thompson5910(28598)   on 2009-09-16 15:12:08 (Show Source): You can put this solution on YOUR website! Start with the given expression Convert to exponential notation. Use the identity to multiply Add the fractions. Convert back to radical notation. So

Vectors/214134: Use pythagorean therom to find the distance between (5,3) and(-2,-3). Can you give me a step by step of this promblem 1 solutions Answer 161735 by jim_thompson5910(28598)   on 2009-09-16 13:53:38 (Show Source): You can put this solution on YOUR website! Start with the distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . So our answer is Which approximates to So the distance between the two points is approximately 9.22 units.

Percentage-and-ratio-word-problems/214133: Two numbers are in the ratio 3: 8. Their sum is 44. What is the difference between the two numbers? 1 solutions Answer 161733 by jim_thompson5910(28598)   on 2009-09-16 13:48:28 (Show Source): You can put this solution on YOUR website! Since "Two numbers are in the ratio 3: 8", this means . Also, because "Their sum is 44", we know that . So simply solve this system of equations to find 'x' and 'y'. Let me know if this is enough to get you started.

Distributive-associative-commutative-properties/214131: what is (3a+b)(2a-5b) 1 solutions Answer 161731 by jim_thompson5910(28598)   on 2009-09-16 13:42:10 (Show Source): You can put this solution on YOUR website! Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. Now collect every term to make a single expression. Now combine like terms. So FOILs to . In other words, .

Quadratic_Equations/214129: 1 solutions Answer 161729 by jim_thompson5910(28598)   on 2009-09-16 13:40:29 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice we have a quadratic in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the answers are or

Graphs/214116: How do you graph the relatin (0,0), (2,4), (-4,0), and find the domain and range.It asks you to determine whether the relation is a function or not. I am totally lost. Please help! Thank you! This is not from a book. It was a worksheet given to me. 1 solutions Answer 161726 by jim_thompson5910(28598)   on 2009-09-16 13:17:46 (Show Source): You can put this solution on YOUR website! Simply plot the points given. The domain is the set of all x values while the range is the set of all y values of the given points. So we get: Domain: {0, 2, -4} Range: {0, 4} Take note that each value of 'x' only maps to one 'y' value. So this means that the relation is a function.

Equations/214126: My daughter is in 5th grade and learning "Hands on Equations" using manipulatives. I was never very good with algebra so I can't remember any of it and am no help to her. Are you familiar with this technique? Can you show me how to solve x + 2 + 2x = x + 10? This is not from a textbook...just an example for me. Thanks! 1 solutions Answer 161725 by jim_thompson5910(28598)   on 2009-09-16 13:13:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is

Radicals/214122: Please help me with find factoring. Thank you Mutiply and simplify by factoring. Sqrt(45)*Sqrt(250) Sqrt(45)*(250)=11250 Sqrt(11250)= factoring will be? 1 solutions Answer 161724 by jim_thompson5910(28598)   on 2009-09-16 13:12:15 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor each radicand into a product in which one factor is a perfect square (the largest perfect square factor) Break up the roots. Take the square root of the perfect squares 9 and 25 to get 3 and 5. Recombine the roots. Multiply Factor 50 into 25*2 (take note how 25 is the largest perfect square that goes into 50) Break up the root. Take the square root of 25 to get 5. Multiply So

Exponential-and-logarithmic-functions/214121: 1. Simplify and write the expression below using positive exponents only. (2u-3v2)-2 1 solutions Answer 161723 by jim_thompson5910(28598)   on 2009-09-16 13:06:04 (Show Source): You can put this solution on YOUR website! Recall that and . In other words, to rewrite an expression with positive exponents, just flip the base. So in this case . So So Now flip the fraction to make the outer exponent positive: Now simplify to get: ====================================================== Answer: So