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Triangles/275264: can a triangle possibly have the sides of 1,3, and 5 1 solutions Answer 200767 by jim_thompson5910(28715)   on 2010-02-28 16:20:36 (Show Source): You can put this solution on YOUR website! No it cannot. Notice how 1+3=4 which is 1 unit short of the third length of 5.

Quadratic_Equations/275262: Can someone help with the following problem with finding the zeroes? f(x) = 5x^2 - 2x - 1 1 solutions Answer 200764 by jim_thompson5910(28715)   on 2010-02-28 16:19:55 (Show Source): You can put this solution on YOUR website! The zeros are the x values that make . In other words, they are the x values that satisfy the equation Start with the given equation. 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 . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce. So the solutions are or

Quadratic_Equations/275252: Can someone explain how to solve the following problem with finding zeroes? f(x) = x^2+6x+5 1 solutions Answer 200759 by jim_thompson5910(28715)   on 2010-02-28 16:11:19 (Show Source): You can put this solution on YOUR website! The zeros are the x values that satisfy the equation Start with the given equation. 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 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 zeros are or

Quadratic_Equations/275246: Can someone please help with the following: x^2 - 8x + 5 = 0 1 solutions Answer 200756 by jim_thompson5910(28715)   on 2010-02-28 16:07:54 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) Break up the fraction. Reduce. or Break up the expression. So the solutions are or

Linear-equations/275250: Find the slope and the y intercept of the graph of 3x+7=-4 1 solutions Answer 200755 by jim_thompson5910(28715)   on 2010-02-28 16:07:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point

Quadratic_Equations/275248: Can someone explain how to solve the following problem? 2x^2 + 1 = 5x 1 solutions Answer 200752 by jim_thompson5910(28715)   on 2010-02-28 16:05:40 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 5x 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 Subtract from to get Multiply and to get . or Break up the expression. So the solutions are or

Graphs/275243: How do I graph 4x-y=3 on a coordinate plane? 1 solutions Answer 200746 by jim_thompson5910(28715)   on 2010-02-28 15:54:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 4 and the run is 1. This means that to go from point to point, we can go up 4 and over 1 So starting at , go up 4 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Polynomials-and-rational-expressions/275230: 4(3d-5)=2(5d+1) Please solve for d I know the answer is 11 and I started my work by doing 4(3d-5)-2(5d+1)=0 But I'm not sure if that is right. Please help me. 1 solutions Answer 200743 by jim_thompson5910(28715)   on 2010-02-28 15:45:20 (Show Source): You can put this solution on YOUR website! For more help with solving linear equations, check out this linear equation solver. Solved by pluggable solver: Linear Equation Solver Start with the given equation. Distribute. Add to 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

Equations/275207: 3/7(5x+2)-16=8 1 solutions Answer 200734 by jim_thompson5910(28715)   on 2010-02-28 15:10:10 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Linear Equation Solver Start with the given equation. Distribute. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Human-and-algebraic-language/275215: Studying probabilities ... Three cards are drawn in succession and without replacement from a standard deck of 52 cards. What is the probability that they are all face cards ( jack, queen, king)? The textbook says the answer is 11/1105, but for the life of me I can't get it to come out. Can you help me please? Thanks in advance! 1 solutions Answer 200732 by jim_thompson5910(28715)   on 2010-02-28 15:00:33 (Show Source): You can put this solution on YOUR website! P(3 Face Cards) = P(Face Card AND Face Card AND Face Card) Remember that the keyword "and" tells us to multiply. Since there are 4 suits and 3 face cards, there are 12 face cards. Because we're not replacing the cards, the number to choose from will go down. So on the first draw we have 12 face cards to choose from (out of 52). On the second draw, we have 11 face cards to pick from (out of 51). Finally, on the third draw, we now have 10 face cards to choose from (out of 50). So P(Face Card AND Face Card AND Face Card) = P(Face Card)*P(Face Card)*P(Face Card) P(Face Card AND Face Card AND Face Card) = (# of face cards/# total)*(# of face cards/# total)*(# of face cards/# total) P(Face Card AND Face Card AND Face Card) = (12/52)*(11/51)*(10/50) P(Face Card AND Face Card AND Face Card) = 11/1105 So this means that P(3 Face Cards) = 11/1105

Linear-systems/274981: What is the slope-intercept equation for the line below? (4,1) (0,-4) 1 solutions Answer 200683 by jim_thompson5910(28715)   on 2010-02-28 00:47:52 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and 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 Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 1 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and

Signed-numbers/275051: How do solve the missing numbers of signed numbers in equations? Example: a) -19+x=2 b)x-13-12=10 1 solutions Answer 200681 by jim_thompson5910(28715)   on 2010-02-28 00:45:50 (Show Source): You can put this solution on YOUR website! a) For more help with solving linear equations, check out this linear equation solver. Solved by pluggable solver: Linear Equation Solver Start with the given equation. Add to both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is ================================================ b) Solved by pluggable solver: Linear Equation Solver Start with the given equation. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is

Functions/275011: Write a linear function g given that g(0)=5 and g(10)=9. Answers are multiple choice a. g(x)=5/2x-5 b. g(x)=5/2x+5 c. g(x)=2/5x-5 d. g(x)=2/5x+5 I dont understand how to figure out how to get the answer. Thanks for your help 1 solutions Answer 200680 by jim_thompson5910(28715)   on 2010-02-28 00:42:03 (Show Source): You can put this solution on YOUR website! Since g(0)=5 and g(10)=9, we know that the line goes through the points (0,5) and (10,9) So let's find the equation of the line that goes through the points and First let's find the slope of the line through the points and 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 Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 5 to both sides. Combine like terms. So the equation that goes through the points and is Now simply replace the 'y' with g(x) to get the function So the function is making the answer d)

Linear-equations/275021: write an equation of the line containing the given point perpendicular to the given line. Express your answer in the form y=mx+b. (3,6);6x+y=8 1 solutions Answer 200679 by jim_thompson5910(28715)   on 2010-02-28 00:38:23 (Show Source): You can put this solution on YOUR website! First solve for y to get Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula: where is the perpendicular slope So plug in the given slope to find the perpendicular slope When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second Multiply the fractions. So the perpendicular slope is So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (3,6), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Make into equivalent fractions with equal denominators Combine the fractions Reduce any fractions So the equation of the line that is perpendicular to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

Equations/275045: 4x+3+2x=6x+2-x So far this is what I have. 4x+2x+3=6x-x+2 Rewrite for like terms 6x+3=5x+2 That is where I get lost, can you help me? 1 solutions Answer 200678 by jim_thompson5910(28715)   on 2010-02-28 00:33:22 (Show Source): You can put this solution on YOUR website! For more help with solving linear equations, check out this linear equation solver. Solved by pluggable solver: Linear Equation Solver Start with the given equation. 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. ---------------------------------------------------------------------- Answer: So the solution is

Linear-systems/275008: Using the addition method 7x-4y=14 -7x+6y=11 1 solutions Answer 200663 by jim_thompson5910(28715)   on 2010-02-27 21:00:35 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: 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 . ------------------------------------------------------------------ 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 . So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent.

Polynomials-and-rational-expressions/274999: (x+3)(x+5) 1 solutions Answer 200659 by jim_thompson5910(28715)   on 2010-02-27 20:28:52 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: FOIL (ie Expand) Two Binomials 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 --------------------- Answer: So FOILs and simplifies to In other words,

Expressions-with-variables/274982: 7x-10=12 I'm having trouble with this one, please help if you can. Thank you 1 solutions Answer 200657 by jim_thompson5910(28715)   on 2010-02-27 20:09:35 (Show Source): You can put this solution on YOUR website! For more help with solving linear equations, check out this linear equation solver. Solved by pluggable solver: Linear Equation Solver Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is

Expressions-with-variables/274951: A, B and C are whole and positive numbers. A+B+C=38 and A*B*C=630. What are the numbers? How do I find that out with three variables and only two equations? Thanks so much! Guðrún 1 solutions Answer 200625 by jim_thompson5910(28715)   on 2010-02-27 17:19:24 (Show Source): You can put this solution on YOUR website! Because we're only looking for positive integer solutions, this set of solutions will be finite even though we're missing a third equation. To find these solutions, simply list all of the factors of 630 and see which set of 3 factors add up to 38. For example, 630=2*5*63 which means that 2+5+63=70. It turns out that there are only 6 sets of solutions and they are A = 2, B = 15, C = 21 A = 2, B = 21, C = 15 A = 15, B = 2, C = 21 A = 15, B = 21, C = 2 A = 21, B = 2, C = 15 A = 21, B = 15, C = 2 For example, when A = 2, B = 15, C = 21, then 2*15*21=630 and 2+15+21=38 Basically, there are 3 unique numbers here (they're just being rearranged) and the numbers are 2, 15, and 21.

Equations/274952: 4y+2=y+5 1 solutions Answer 200623 by jim_thompson5910(28715)   on 2010-02-27 17:08:50 (Show Source): You can put this solution on YOUR website! For more help with solving linear equations, check out this linear equation solver. Solved by pluggable solver: Linear Equation Solver 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

Trigonometry-basics/274890: Find all numbers "t" such that ( 7/25, t )is a point on the unit circle. 1 solutions Answer 200612 by jim_thompson5910(28715)   on 2010-02-27 16:44:00 (Show Source): You can put this solution on YOUR website! Hint: Solve the equation to find the solutions.

Problems-with-consecutive-odd-even-integers/274832: If a, b, c, and d are consecutive integers such that a < b < c < d, then in terms of a, the sum a + b + d = a a+4 b 2a+3 c 3a+3 d 3a+4 1 solutions Answer 200609 by jim_thompson5910(28715)   on 2010-02-27 16:39:57 (Show Source): You can put this solution on YOUR website! If a, b, c, and d are consecutive integers with a < b < c < d, then b=a+1, c=a+2, and d=a+3 So which makes the answer d)

Graphs/274939: graph the line y = 3/4x + 1 1 solutions Answer 200599 by jim_thompson5910(28715)   on 2010-02-27 16:06:27 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 4. This means that to go from point to point, we can go up 3 and over 4 So starting at , go up 3 units and to the right 4 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Graphs/274934: find the x-intercept and y-intercept of the line given by the equation. 9x + 3y = -13 1 solutions Answer 200598 by jim_thompson5910(28715)   on 2010-02-27 16:05:48 (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. Multiply. Divide both sides by to isolate . 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. Divide both sides by to isolate . So the y-intercept is .

Length-and-distance/274921: An equation of a line through (-6, 6) which is parallel to the line y = 4x +4 has slope: and y intercept at: 1 solutions Answer 200588 by jim_thompson5910(28715)   on 2010-02-27 15:45:49 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (-6,6), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Combine like terms So the equation of the line that is parallel to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

Length-and-distance/274923: The equation of the line that goes through the point ( 6 ,2 ) and is parallel to the line 2 x + 5 y = 4 can be written in the form y = mx+b where m is:_ and where b is:_ 1 solutions Answer 200581 by jim_thompson5910(28715)   on 2010-02-27 15:37:04 (Show Source): You can put this solution on YOUR website! First solve for y to get Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (6,2), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Make into equivalent fractions with equal denominators Combine the fractions Reduce any fractions So the equation of the line that is parallel to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

Square-cubic-other-roots/274775: simplify by factoring 4√486 is 1 solutions Answer 200504 by jim_thompson5910(28715)   on 2010-02-27 00:26:34 (Show Source): You can put this solution on YOUR website! First, let's simplify The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number. So let's list the factors of 486 Factors: 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486 Notice how 81 is the largest perfect square, so lets factor 486 into 81*6 Factor 486 into 81*6 Break up the square roots using the identity Take the square root of the perfect square 81 to get 9 So the expression simplifies to In other words, ---------------------------------------- So this means that ================================================================= Answer: So

Graphs/274761: how those these graphing look like y>x-2 1 solutions Answer 200503 by jim_thompson5910(28715)   on 2010-02-27 00:23:29 (Show Source): You can put this solution on YOUR website! In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

Exponential-and-logarithmic-functions/274779: Can someone please explain why logbx/ logby does not equal logbx - logby? 1 solutions Answer 200502 by jim_thompson5910(28715)   on 2010-02-27 00:20:19 (Show Source): You can put this solution on YOUR website! To prove something false, we usually resort to a counterexample. A counterexample is an explicit example in which proves a theorem or equation false (usually by a contradiction of some sort). So let's say that and . This would then mean that Now plug and into to get So in short, and when and . Clearly which means that when and . --------------------------------------------------------------- Here's another way of looking at it. By the change of base formula, By another identity, So let's assume that . If this is the case, then Equate the bases and arguments to get and . The second equation simplifies to . Solve for b to get . Now if , this means that which is impossible (you can't divide by zero).

Points-lines-and-rays/274776: I am having a hard time with my Geomarty homework I would really like if i were to get some kind of help. The question on the homework says... 1.Draw the following triangle A(-3,2) B(9,2) C(3,-6) 1 solutions Answer 200500 by jim_thompson5910(28715)   on 2010-02-27 00:01:21 (Show Source): You can put this solution on YOUR website! Plot the 1st point A(-3,2) Plot the 2nd point B(9,2) Plot the 3rd point C(3,-6) Now connect the points to plot the triangle:

Points-lines-and-rays/274778: Whats the distance between (4,4) and (7,8) 1 solutions Answer 200499 by jim_thompson5910(28715)   on 2010-02-26 23:51:12 (Show Source): You can put this solution on YOUR website! Note: is the first point . So this means that and . Also, is the second point . So this means that and . 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 . Take the square root of to get . So our answer is So the distance between the two points is 5 units.