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 Systems-of-equations/253103: need help with 7x/3 + 5y/4=4 5x/6 - 2y=211 solutions Answer 185329 by jim_thompson5910(28595)   on 2010-01-02 17:01:57 (Show Source): You can put this solution on YOUR website! Start with the first equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. ---------------------------------------------------------------------------- Move onto the second equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. ---------------------------------------------------------------------------- So we now have the system of equations and it turns out that the solution to that system above is the same solution to the original system of equations. Start with the given system of equations: Multiply the both sides of the first equation by 4. Distribute and multiply. Multiply the both sides of the second equation by 5. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Graphs/253101: -5x+6=x+12 Help?1 solutions Answer 185325 by jim_thompson5910(28595)   on 2010-01-02 16:31:39 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 solution is
 Complex_Numbers/253081: How do you simplify: (x+3)/(6) divided by 1+(x/3) *note* / = fractions 1 solutions Answer 185285 by jim_thompson5910(28595)   on 2010-01-02 14:35:41 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply EVERY term by the inner LCD 6 to clear out the inner fractions. Simplify Factor the denominator. Rearrange the terms. Cancel out the common terms. Simplify. So simplifies to In other words,
 Polynomials-and-rational-expressions/253001: Multiply ( x^2 + 4 / x^2 – 4) (x - 2 / x + 2)1 solutions Answer 185282 by jim_thompson5910(28595)   on 2010-01-02 14:27:08 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. FOIL. So simplifies to . In other words, where or
 absolute-value/252999: What is the value of 3|x| - 5|y| if x = –7 and y = –11? (A) –76 (В) -34 (C) –4 (D) 34 (E) 761 solutions Answer 185280 by jim_thompson5910(28595)   on 2010-01-02 14:21:43 (Show Source): You can put this solution on YOUR website! Start with the given expression. Plug in and Take the absolute value of -7 to get 7. Take the absolute value of -11 to get 11. Multiply Subtract So when and
 Numbers_Word_Problems/252970: What is he product of positive integers a and b such that a is greater than b and 1/a+1/b=1/ab=1?1 solutions Answer 185178 by jim_thompson5910(28595)   on 2010-01-01 22:06:11 (Show Source): You can put this solution on YOUR website!Well if 'a' and 'b' are both integers, then ab ('a' times 'b') is also an integer because the product of two integers is always an integer. Because , this means that if we multiply both sides by ab. Since 1 is the only factor of 1, this tells us that 1=1*1 and that a=1 and b=1. So if 'a' and 'b' are both positive integers and , then , , and So either there's a typo somewhere or you copied the problem incorrectly. Please double check the problem.
 Exponents/252911: 2x^2+3xy-4y^2 when x=2 and y=-41 solutions Answer 185035 by jim_thompson5910(28595)   on 2010-01-01 13:16:12 (Show Source): You can put this solution on YOUR website! Start with the given expression. Plug in and Square 2 to get 4 and square -4 to get 16 Multiply Combine like terms. So when and
 Proofs/251007: There is only one premise, and the conclusion has different letters Here it is: A -> B We have to show (A & C) -> B1 solutions Answer 185034 by jim_thompson5910(28595)   on 2010-01-01 13:14:01 (Show Source): You can put this solution on YOUR website!If we use the addition property, we go from A -> B to (A -> B) V ~C (the "V" stands for 'or' and "~" stands for 'not') Rearrange the terms to get ~C V (A -> B) and then use material implication to get C -> (A -> B). From here, use exportation to get (C & A) -> B and then use commutation to get (A & C) -> B. This derivation is pretty straightforward, but the only trick here is the addition of ~C.
 Miscellaneous_Word_Problems/252853: you throw a basketball up in the air. the basketball's height in feet, is given by the function h=-16t^2+30t+4, where t is the time in seconds after the ball leaves your hand.find the greatest height the ball reaches.1 solutions Answer 184954 by jim_thompson5910(28595)   on 2009-12-31 16:23:26 (Show Source): You can put this solution on YOUR website!The max height is at the vertex. In order to find the vertex, we first need to find the t-coordinate of the vertex. To find the t-coordinate of the vertex, use this formula: . Start with the given formula. From , we can see that , , and . Plug in and . Multiply 2 and to get . Reduce. So the t-coordinate of the vertex is . Now that we know the t-coordinate of the vertex, we can use it to find the h-coordinate of the vertex. Start with the given equation. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms. So the h-coordinate of the vertex is . So the vertex is . This means that the max height is which is feet.
 Radicals/252833: find the root -251 solutions Answer 184930 by jim_thompson5910(28595)   on 2009-12-31 14:11:28 (Show Source): You can put this solution on YOUR website! where So
 Linear-equations/252733: find the slope of the line that passes through the given points. Ok are book a little messed up. we are learning about SLopes in Algebra andGeometry A(5,8) B(7,11) E(-1,-2), F(-6,-4) if you could please help me. I need a lot of help. 1 solutions Answer 184795 by jim_thompson5910(28595)   on 2009-12-30 17:34:59 (Show Source): You can put this solution on YOUR website!Let's find the slope of the line through the points A(5,8) and B(7,11) Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get So the slope of the line that goes through the points and is ====================================================================== Now let's find the slope of the line through the points E(-1,-2) and F(-6,-4) Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is
 Distributive-associative-commutative-properties/252728: Simplify the expression by distributing and collecting like terms. 7 – 4(x – 3) – 5x 1 solutions Answer 184790 by jim_thompson5910(28595)   on 2009-12-30 16:44:45 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Multiply Combine like terms. So
Matrices-and-determiminant/252724: how do i use cramer's rule for three equations on this problem
5x-6y=7+7z
6x-4y+10z=-34
2x+4y=29+3z
1 solutions

Answer 184789 by jim_thompson5910(28595)   on 2009-12-30 16:39:56 (Show Source):
You can put this solution on YOUR website!
The first goal is to get all of the variable terms to the left side for each equation.

Subtract 7z from both sides.

---------------------

Move onto the third equation.

Subtract 3z from both sides.

-----------------------

So we now have the system

Now let's use Cramer's Rule to solve this system

 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are , , and and they are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant. To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other two solutions. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is --------------------------------------------------------- Let's reset again by letting which is the coefficient matrix. Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix Now compute the determinant of to get . To find the third solution, divide the determinant of by the determinant of to get: So the third solution is ==================================================================================== Final Answer: So the three solutions are , , and giving the ordered triple (2, 4, -3) Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant.

If you need more help or practice with Cramer's Rule, check out this solver.

 Quadratic_Equations/252647: p(d)= 1+d/33, gives the pressure in the atmosphere(atm) at a depth(d) in the sea Note p(0)=1 atm, p(33)=2 find the pressure at 100 feet.1 solutions Answer 184678 by jim_thompson5910(28595)   on 2009-12-29 22:47:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in Combine like terms. Divide So the pressure at 100 ft is about 4.03 atm.
 Linear-equations/252646: 11+6x=2x-131 solutions Answer 184677 by jim_thompson5910(28595)   on 2009-12-29 22:45:24 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 solution is
 Square-cubic-other-roots/252641: Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?1 solutions Answer 184673 by jim_thompson5910(28595)   on 2009-12-29 21:55:35 (Show Source): You can put this solution on YOUR website!Simply add the two fractions and to get: So she'll need cups of sugar. Now the question is: which fraction is larger, or ? To answer this question, first assume that they are equal: Cross multiply Multiply Now change the equal sign '=' to a less than sign '<' (since 600 is less than 624). Because the left side is less than the right, this means that the left side of is smaller than the right. So change the '=' to a '<' to get Since is smaller than , this means that she has less sugar than what she needs. So she does NOT have enough sugar. -------------------------------------------------------------------- How much does she need then? Well let's figure that out. To find that out, just subtract the amount she has () from the amount she needs () to get: So she needs of a cup of sugar.
 Equations/252640: slope 9 and y intercept (0,8) y=1 solutions Answer 184672 by jim_thompson5910(28595)   on 2009-12-29 21:43:16 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add 8 to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
 Equations/252629: 1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 162, how long is each side?1 solutions Answer 184650 by jim_thompson5910(28595)   on 2009-12-29 20:29:24 (Show Source): You can put this solution on YOUR website!Let x = length of first side. Since "The sides of the quadrilateral are consecutive numbers", this means that the side lengths are: x, x+1, x+2, and x+3. Also, because the perimeter is 162, we know that (just add up the four sides and set the sum equal to 162). Start with the given equation. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is giving the four sides to be: x = 39 x+1 = 40 x+2 = 41 x+3 = 42
 Equations/252631: the hypotenuse of a right triangle is 20 inches. one of the legs has a meadure of 16 inches. what is the measure of the other leg? the answer i got was not an option1 solutions Answer 184648 by jim_thompson5910(28595)   on 2009-12-29 20:26:55 (Show Source): You can put this solution on YOUR website! We basically have this triangle set up: To find the unknown length, we need to use the Pythagorean Theorem. Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Subtract from both sides. Combine like terms. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Simplify the square root. ================================================================ Answer: So the solution is which means that the measure of the remaining leg is 12 inches.
 Linear-equations/252628: Find an equation of the line passing through the point (5,4) and parallel to the line whose equation is 2x + y = 3.1 solutions Answer 184647 by jim_thompson5910(28595)   on 2009-12-29 20:09:47 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. We can see that the equation has a slope and a y-intercept . Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is . Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Distribute Multiply Add 4 to both sides. Combine like terms. So the equation of the line parallel to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the parallel line (green) through the point .
 Probability-and-statistics/252627: Can I please get some assistance with the formula for e. 2. U.S. Population by Region. The U.S. population by region (in millions) for selected years is given in the table. Find the probability that a U.S. resident selected at random satisfies the following: e.) What are the odds that a randomly selected U.S. resident in 2000 was not from the South? REGION 1995 1997 2000 Northwest 51.4 51.6 53.6 Midwest 61.8 62.5 64.4 South 91.8 94.2 100.2 West 57.7 59.4 63.2 TOTAL 262.7 267.7 281.4 Answer: 302 to 167 1 solutions Answer 184646 by jim_thompson5910(28595)   on 2009-12-29 20:06:39 (Show Source): You can put this solution on YOUR website!Note: Because we're only concerned with the year 2000, we'll only draw values from the last column. To find the probability that you select a resident at random that is NOT in the south, simply note that probability that you select an individual that does live in the south is... P(Resident from the South) = Number of Residents Who Live in the South/Total US Residents = 100.2/281.4 = 0.35608 So the probability of choosing someone from the south is about 0.35608 (about a 35.6% chance). Since we want everything but residents from the South, just subtract this probability from 1 (ie 100%) to get: 1-0.35608 = 0.64392 So the probability of selecting a resident that is NOT from the South in the year 2000 is 0.64392 (which is about a 64.4% chance) Another way to do this is to add up all of the data values in the 2000 column that are NOT the south and divide them by the total 281.4
 absolute-value/252622: Solve the inequality and graph the solution set: |3k + 8| > -9 1 solutions Answer 184642 by jim_thompson5910(28595)   on 2009-12-29 19:15:10 (Show Source): You can put this solution on YOUR website!Because the absolute value of any number is ALWAYS positive, this means that for any value of 'k'. So is ALWAYS true for any value of 'k'. So there are an infinite number of solutions. To graph the solution set, just shade the entire number line.
 absolute-value/252621: Find the absolute value: |3x+4|+11 = 4 1 solutions Answer 184640 by jim_thompson5910(28595)   on 2009-12-29 19:12:49 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 11 from both sides. Since the expression is NEVER true (note: remember, the absolute value of any number is always positive), there are no solutions to Also, notice if we graph and (just set each side equal to y and graph), we get: Graph of (red) and (green) and we can see that the two graphs never intersect. So there are no solutions.
 Linear-systems/252604: There are 35 tickets to be sold for the dance. The number of tickets sold to seniors must be four times the number of tickets sold to juniors. please give me 2 linear equations and a solution. A diamond today costs 10$more than twice what it cost last year. The sum of the cost (last year and this year) is 2500$. What is the cost of last years diamond? i need 2 linear equations and a solution for this question also. THANK U SO MUCH! 1 solutions Answer 184609 by jim_thompson5910(28595)   on 2009-12-29 16:24:26 (Show Source): You can put this solution on YOUR website!# 1 Let s = # of senior tickets and j = # of junior tickets Since there are 35 tickets in total, and we're assuming that only junior and senior tickets are sold, this means that . In other words, adding up the two totals will give you the grand total of 35. Also, because "The number of tickets sold to seniors must be four times the number of tickets sold to juniors", we know that . In English, the number of senior tickets 's' is 4 times the number of junior tickets 'j'. Start with the first equation. Plug in Combine like terms on the left side. Divide both sides by to isolate . Reduce. So there are 7 junior tickets. Go back to the second equation Plug in Multiply So there are 28 senior tickets. As a check, take note that 28 is indeed 4 times 7 AND 28+7=35. So we've met our conditions. ====================================================================== # 2 Let t = cost of diamond today and y = cost of diamond last year Since "A diamond today costs 10$more than twice what it cost last year", we can say that (ie double the cost from last year 'y' and add 10 to get the new cost today 't'). Also, because "The sum of the cost (last year and this year) is 2500$", we know that (just add up the two individual costs to get the grand total of $2500) Start with the second equation. Plug in Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the cost of the diamond last year was$830. If you want to keep going then... Go back to the first equation Plug in Multiply Add So the cost of the diamond today is \$1670.