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Systems-of-equations/253103: need help with 7x/3 + 5y/4=4 5x/6 - 2y=21 1 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

Quadratic_Equations/253100: The square of a negative integer minus itself is 110. Find the integer. 1 solutions Answer 185324 by jim_thompson5910(28595)   on 2010-01-02 16:31:00 (Show Source): You can put this solution on YOUR website! Since "The square of a negative integer minus itself is 110", this means that Start with the given equation. Subtract 110 from both sides. Notice that the quadratic is 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 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 possible solutions are or But since we're told that the integer is negative, this means that the only 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) 76 1 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=-4 1 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) -> B 1 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 -25 1 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

Linear-equations/252731: ok well we are doing this in geometry but its a review from algebra P(2,5); 4x-y=8 We have to write and equation of the line that passes through the point p and is perpendicular to the line with the given equation p(1,4); y=2x+4 P(5,3); y=5x+2 If you could please help because i am not following very well in my class 1 solutions Answer 184794 by jim_thompson5910(28595)   on 2009-12-30 17:32:47 (Show Source): You can put this solution on YOUR website! # 1 Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular 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 5 to both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation of the line perpendicular to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point . ================================================================== # 2 We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular 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. note: If you need help with fractions, check out this solver. So the equation of the line perpendicular to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point . ================================================================== # 3 We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular 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 3 to both sides. Combine like terms. So the equation of the line perpendicular to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point .

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. Start with the first 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-13 1 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 option 1 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.

Trigonometry-basics/252614: Can you help me solve this questions, please? The original ferris wheel, designed by George Ferris, was 250 feet in diameter. Making 1 revolution for every 40 seconds, h(t)=125sin(0.157t -pi/2) +125 represents the height h (feet) of a seat on the wheel at any time t (seconds). The ride begins when t = 0. During the first 30 seconds of the ride, at what time is a rider on the ferris wheel exactly 125 feet above the ground? and also, help me with: approximate the solution to 2cosx+x=0 to the nearest hundredth. Hints: it should be in radian mode and there are no () around the x+x Thanks so much!! 1 solutions Answer 184639 by jim_thompson5910(28595)   on 2009-12-29 19:07:33 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in Subtract 125 from both sides. Combine like terms. Divide both sides by 125. Reduce. Rearrange the equation Take the arcsine of both sides. or Evaluate the arcsine of 0 to get or . Don't forget to add in integer multiples of ---------------------------Side Note---------------------- Take note how if , then we just get 0 or . If , then we get or . If we continue this, we can see that we'll hit all of the integer multiples of . Because of this we can condense the right side to just . -------------------------------------------------------- Condense the right side (see side note above). Add to both sides. Combine like terms. Multiply both sides by to isolate 't'. Multiply. Now let's plug in some values of 'n'. If n=0, then If n=1, then . However, since we're only worried about the first 30 seconds, this means that which would exclude the 't' value when . Any other value of 'n' will generate a 't' value outside the interval ===================================== Answer: So the only solution is (which is approximate) which means that at about 10.00507 seconds, the rider will be 125 feet above the ground during the first 30 seconds. =========================================================================== # 2 Since the variable we want to solve for in is buried in a trig function and is outside the trig function, there is no way to solve for it exactly. So we have to use a graphing calculator to approximate the roots of . Graphing the given expression, we get Graph of Now use the graphing calculator's root/zero function to find the approximate root of which rounds to to the nearest hundredth. So the answer is

Graphs/252617: using the graph, determine the value of y when x=4 |||||||||||| | | / | | | / | |||||||/|||| X | |/ | | / | |||||||||||| y 1 solutions Answer 184638 by jim_thompson5910(28595)   on 2009-12-29 18:44:56 (Show Source): You can put this solution on YOUR website! It's hard to determine which points that line goes through. Do you have a better picture? Or can you tell me which points the graph goes through?

Numbers_Word_Problems/252619: I am checking my sons math. Find four consecutive even integers such that 6 time the sum of the first and second is 8 more than 10 times the fourth. Rob Dewey...Mitchell's Dad. 1 solutions Answer 184637 by jim_thompson5910(28595)   on 2009-12-29 18:43:55 (Show Source): You can put this solution on YOUR website! Consecutive even integers follow the form: x, x+2, x+4, x+6, etc... So because "6 time the sum of the first and second is 8 more than 10 times the fourth", this translates to Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right 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 solution is which means that the four consecutive even integers are x = 28 x+2 = 30 x+4 = 32 x+6 = 34

Trigonometry-basics/252605: The height of the ocean at the dock is modeled by the function, h= 3sin(pi*t/4) +5 where h is measured in feet and t is the time in hours. If t=0 refers to 12:00 a.m., what is the height of the ocean at 10:00 a.m.? find the exact value of the vertical asymptotes for 0<=x<=pi for the function y=cot(3x) if sin(x)= -3/5 with x in the quadrant 4, find the sec(x) Thanks so much!! 1 solutions Answer 184615 by jim_thompson5910(28595)   on 2009-12-29 16:47:52 (Show Source): You can put this solution on YOUR website! I'll do the first two to get you going. # 1 Since "t=0 refers to 12:00 a.m", this means that refers to 10:00 a.m. (just add 10 hours to 0) Start with the given equation. Plug in Reduce. Rearrange the terms Subtract from the argument (this is valid because you'll end up on a coterminal angle). Combine like terms. Use the unit circle to evaluate the sine of to get 1. Multiply Add So the height of the ocean at 10:00 a.m. is 8 feet. ================================================================= # 2 Remember that and . So this means that or in short, To find the vertical asymptotes of , we'll set the denominator equal to zero and solve for 'x' (since division by zero is undefined). Set the denominator equal to zero. Take the arcsine of both sides. or Evaluate the arcsine of 0 to get or . Don't forget to add on multiples of to each solution. or Divide both sides by 3 to isolate 'x' in each case. As a shortcut, you can condense the solution to where 'n' is an integer. So if , where 'n' is an integer, then . But since , this means that we're only going to look at the solutions (for n=0), (where n=1), (when n=2), and (when x=3). Note: any other solution is outside the interval . So the four vertical asymptotes of are , , , and

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.

Linear-systems/252597: Solve the following system of equations algebraically: 3x+2y=4 4x+3y=7 1 solutions Answer 184601 by jim_thompson5910(28595)   on 2009-12-29 15:58:03 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 3. Distribute and multiply. Multiply the both sides of the second equation by -2. 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. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to 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)