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Recent problems solved by 'MathLover1'

MathLover1 answered: 6623 problems
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Graphs/656155: 3y - 12x = 18 1 solutions Answer 409364 by MathLover1(6625)   on 2012-09-24 10:55:37 (Show Source): You can put this solution on YOUR website! ...first simplify, both sides divide by ..to find zeros, set and solve for and set and solve for

Quadratic_Equations/656156: Zero`s of 6x*6x-5x+7 & 6x*6x+5x-7 1 solutions Answer 409362 by MathLover1(6625)   on 2012-09-24 10:31:02 (Show Source): You can put this solution on YOUR website! Zero`s of ..use quadratic formula solutions: and & ..use quadratic formula solutions: and

Complex_Numbers/656149: x^2+8x+20=0 1 solutions Answer 409359 by MathLover1(6625)   on 2012-09-24 10:11:59 (Show Source): You can put this solution on YOUR website! ...use quadratic formula to solve for ...note that , and solutions: or

Linear-equations/656140: solving by elimination 5x-7y=-49 3x+9y=-3 1 solutions Answer 409358 by MathLover1(6625)   on 2012-09-24 10:02:31 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero. So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 5 and 3 to some equal number, we could try to get them to the LCM. Since the LCM of 5 and 3 is 15, we need to multiply both sides of the top equation by 3 and multiply both sides of the bottom equation by -5 like this: Multiply the top equation (both sides) by 3 Multiply the bottom equation (both sides) by -5 So after multiplying we get this: Notice how 15 and -15 add to zero (ie ) Now add the equations together. In order to add 2 equations, group like terms and combine them Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether. So after adding and canceling out the x terms we're left with: Divide both sides by to solve for y Reduce Now plug this answer into the top equation to solve for x Plug in Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out on the left side. Multiply the terms on the right side So our answer is , which also looks like (, ) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle). and we can see that the two equations intersect at (,). This verifies our answer.

Geometry_proofs/656010: AB+BC=AC AB=XY XY+BC=AC What is the reason? 1 solutions Answer 409336 by MathLover1(6625)   on 2012-09-23 22:06:03 (Show Source): You can put this solution on YOUR website! reason: use of transitive property of segment length

Graphs/655963: what is the equation of a line passing through (-2, -1) and (6, 3)? 1 solutions Answer 409315 by MathLover1(6625)   on 2012-09-23 20:28:46 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: FIND EQUATION of straight line given 2 points hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-2, -1) and (x2, y2) = (6, 3). Slope a is . Intercept is found from equation , or . From that, intercept b is , or . y=(0.5)x + (0) Your graph:

expressions/655947: By which property is the equation 1 • 0 • (-1) = 0 true? A. Identify Property of Multiplication B. Multiplication Property of Zero C. Multiplication Property of -1 D. Inverse Property of Addition 1 solutions Answer 409311 by MathLover1(6625)   on 2012-09-23 20:21:13 (Show Source): You can put this solution on YOUR website! ....since one multiplier is , your answer is: B. Multiplication Property of Zero

Length-and-distance/655727: M is the midpoint of RT. RM = x and RT = 4x - 6. Find the value of x. 1 solutions Answer 409258 by MathLover1(6625)   on 2012-09-23 14:58:20 (Show Source): You can put this solution on YOUR website! if is the midpoint of , then given: and Find: the value of ---------------------------------------- if , then ..solve for

Sequences-and-series/655658: Write a linear function where f(2)=4,f(4)=2 and f(3)=3. 1 solutions Answer 409227 by MathLover1(6625)   on 2012-09-23 12:59:30 (Show Source): You can put this solution on YOUR website! If ,, , then the graph of the function contains the point (,),(,), and (,). Use the two point form of an equation of a straight line and the points (,),(,): where (x1,y1)and (x2,y2) are the coordinates of the given points. here is a proof that all three of given points lie on this line Solved by pluggable solver: To determine if 3 points lie in a line The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line. In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope. Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal. Slope of line taking points (X1,Y1) and (X2,Y2) is ........................(1) Slope of line taking points (X3,Y3) and (X1,Y1) is ........................(2) From conditions (1) and (2) The slopes are equal hence the 3 points can lie on same line. If the slope calculated from points (X2,Y2) and (X3,Y3) comes out to be same then it is confirmed that the 3 points lie on a same line. ........................(3) From (1),(2) and (3) Hence, It is proved that the 3 points lie on same line. To read more on equations of a line refer to articles on wikipedia

test/655406: Through :(-4,-4), parallel to x=0 1 solutions Answer 409112 by MathLover1(6625)   on 2012-09-22 18:23:48 (Show Source): You can put this solution on YOUR website! Slope Intercept form: =? =? Find: Since you know your line is parallel to then we know it is a line on the that has points of [(0,1), (0,2), etc...] take points: (0,1) and given point (-4,-4) ... So.... back to Finally or or, you can find it this way: first slope, then equation of line through the given point and slope Solved by pluggable solver: FIND a line by slope and one point What we know about the line whose equation we are trying to find out: it goes through point (-4, -4) it has a slope of -0.75 First, let's draw a diagram of the coordinate system with point (-4, -4) plotted with a little blue dot: Write this down: the formula for the equation, given point and intercept a, is (see a paragraph below explaining why this formula is correct) Given that a=-0.75, and , we have the equation of the line: Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . Here's the graph:

Expressions-with-variables/655417: what is the distance between(7,3) and (-1,-4)? 1 solutions Answer 409101 by MathLover1(6625)   on 2012-09-22 17:58:57 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Distance Formula to determine length on coordinate plane The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

Equations/655421: Find f(3) when f(x)=x^2-4x+7 1 solutions Answer 409099 by MathLover1(6625)   on 2012-09-22 17:57:31 (Show Source): You can put this solution on YOUR website! when then

Linear-equations/655358: x+y= 1 solutions Answer 409094 by MathLover1(6625)   on 2012-09-22 17:31:49 (Show Source): You can put this solution on YOUR website! your question is incomplete!!! post it again

expressions/655412: 2(x − 3) 2x − 6 Prove, in complete sentences, whether the left expression is equal to the right expression and discuss which property applies. 1 solutions Answer 409092 by MathLover1(6625)   on 2012-09-22 17:30:36 (Show Source): You can put this solution on YOUR website! ...left expression ... right expression if the left expression is equal to the right expression, then will be ...first multiply ...both sides of the equation are same, means it is true consequently, we can say that left expression to right expression

Quadratic_Equations/655375: Suppose x1 and x2 are two solutions of the equation x^2+bx+c=0.Find x_1+x_2 and x_1 x_2. Hint: What are the solutions? 1 solutions Answer 409087 by MathLover1(6625)   on 2012-09-22 16:55:14 (Show Source): You can put this solution on YOUR website! and are two solutions of the equation ...since , we have so, the solutions are: now find and and

Polynomials-and-rational-expressions/655345: finding zeros of a polynomial function f(x)=5x^4+15x^2 +10 1 solutions Answer 409082 by MathLover1(6625)   on 2012-09-22 16:13:18 (Show Source): You can put this solution on YOUR website! set to fins solutions: if ...->.....->.... or ..complex roots if ...->.......->.......->.... or ....complex roots so, roots are: complex roots

Surface-area/655350: PLEASE HELP! The diameter of a circle is (x+2) units. Express the area of the square in the figure as a polynomial it is a circle with a line going through the middle, and two arrows going opposite directions below that with x+2 in the center. http://i49.tinypic.com/2w7pyjp.png < This is a picture for a visual thanks. 1 solutions Answer 409079 by MathLover1(6625)   on 2012-09-22 15:33:14 (Show Source): You can put this solution on YOUR website! you are given: the diameter of a circle is units you need to express the area of the square in the figure as a polynomial as you know, the area of the square is where is the side of the square if you take a close look at your picture, you will see that units so,the area of the square will be: so, your answer is:

Surface-area/655352: PLEASE HELP- Whats the area of the shaded figure? Round your answer to the nearest tenth. Can anyone show me step by step how to figure this out? 12.5cm is in the inside. 8.4 is at the bottom. THANKS! http://i46.tinypic.com/2u8koes.png < picture of the problem with multiple choice answers 1 solutions Answer 409078 by MathLover1(6625)   on 2012-09-22 15:22:18 (Show Source): You can put this solution on YOUR website! if you look closely at shaded area, you will see that that area could be calculated as following: you have a square inside ellipse with sides and , so its area is: than you have two half circles with same diameter of that you should deduct from the area of the square, and these two halves make one full circle with area where so, we have find their difference: finaly, you have two half circles, one on left and one on right side of the square, that make one full circle...its diameter is ; so, its radius is and the area will be now, your shaded area will be: ...round to one decimal place so, your answer is

Equations/655303: Help me solve this equation: x/8 + 12 = -5 1 solutions Answer 409066 by MathLover1(6625)   on 2012-09-22 13:31:06 (Show Source): You can put this solution on YOUR website!

Linear-systems/655332: which ordered pair is a solution to hte system 3x+2y=-9 and 5x-3y=4 1 solutions Answer 409062 by MathLover1(6625)   on 2012-09-22 13:10:55 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Solve the System of Equations by Graphing Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

Square-cubic-other-roots/655284: the sum of the square of x and 5 in word problem 1 solutions Answer 409028 by MathLover1(6625)   on 2012-09-22 09:55:33 (Show Source): You can put this solution on YOUR website! if you have "the sum", put + sign between and if you have square of , write it as then you have:

Linear-systems/655283: I need help on understanding how to solve this problem using substitution and elimination. Please show me how: 4x+5y=13 4x+3y=9 1 solutions Answer 409026 by MathLover1(6625)   on 2012-09-22 09:51:21 (Show Source): You can put this solution on YOUR website! solving linear system by substitution: Solved by pluggable solver: Solving a linear system of equations by subsitution Lets start with the given system of linear equations Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y. Solve for y for the first equation Subtract from both sides Divide both sides by 5. Which breaks down and reduces to Now we've fully isolated y Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x. Replace y with . Since this eliminates y, we can now solve for x. Distribute 3 to Multiply Reduce any fractions Subtract from both sides Make 9 into a fraction with a denominator of 5 Combine the terms on the right side Make 4 into a fraction with a denominator of 5 Now combine the terms on the left side. Multiply both sides by . This will cancel out and isolate x So when we multiply and (and simplify) we get <---------------------------------One answer Now that we know that , lets substitute that in for x to solve for y Plug in into the 2nd equation Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out 3 on the left side. Multiply the terms on the right side Reduce So this is the other answer <---------------------------------Other answer So our solution is and which can also look like (,) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle. and we can see that the two equations intersect at (,). This verifies our answer. ----------------------------------------------------------------------------------------------- Check: Plug in (,) into the system of equations Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Since the solution (,) satisfies the system of equations this verifies our answer. solving linear system by elimination: Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero. So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 4 and 4 to some equal number, we could try to get them to the LCM. Since the LCM of 4 and 4 is 4, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -1 like this: Multiply the top equation (both sides) by 1 Multiply the bottom equation (both sides) by -1 So after multiplying we get this: Notice how 4 and -4 add to zero (ie ) Now add the equations together. In order to add 2 equations, group like terms and combine them Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether. So after adding and canceling out the x terms we're left with: Divide both sides by to solve for y Reduce Now plug this answer into the top equation to solve for x Plug in Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out on the left side. Multiply the terms on the right side So our answer is , which also looks like (, ) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle). and we can see that the two equations intersect at (,). This verifies our answer.

Equations/655267: Explain and answer the question [3a * -7b + b] * [{(sqrt 3)/2}* a^2*b] note in the second bracket, you have to find the square root of 3 and then divide in by 2 after that multiply by a square . then multiply by b 1 solutions Answer 409022 by MathLover1(6625)   on 2012-09-22 09:46:43 (Show Source): You can put this solution on YOUR website! now, if you set it equal to zero, you can calculate the values of and if ...->... and if ...->...->...

Probability-and-statistics/655216: Construct a scatterplot for the (x, y) values below, and answer the following questions. You needn’t submit your scatterplot with your answer. x y 1 4 2 6 3 8 4 10 5 11 - Based on the scatterplot, would the correlation between x and y be positive or negative? - How would you interpret these data in terms of linear regression? Please be sure to see the model in problem 6 of practice items posted in the P&S area Could you please show work 1 solutions Answer 408995 by MathLover1(6625)   on 2012-09-22 00:03:02 (Show Source): You can put this solution on YOUR website! x | y 1 | 4 2 | 6 3 | 8 4 | 10 5 | 11 .... find the slope find the equation: Solved by pluggable solver: FIND a line by slope and one point What we know about the line whose equation we are trying to find out: it goes through point (1, 4) it has a slope of 3 First, let's draw a diagram of the coordinate system with point (1, 4) plotted with a little blue dot: Write this down: the formula for the equation, given point and intercept a, is (see a paragraph below explaining why this formula is correct) Given that a=3, and , we have the equation of the line: Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . Here's the graph: Correlation: since as x rises, y rises

Rational-functions/655221: How do I determine f(-20) from a graph? 1 solutions Answer 408978 by MathLover1(6625)   on 2012-09-21 23:35:10 (Show Source): You can put this solution on YOUR website! tells you that construct a vertical line at and see where it meets the graph

Radicals/655220: Square root (8x+1) =5 Please show work on how to solve for x 1 solutions Answer 408974 by MathLover1(6625)   on 2012-09-21 23:33:07 (Show Source): You can put this solution on YOUR website! .......raise both sides to power of

Reduction-of-unit-multipliers/655201: How do you solve 2(v-8)+3(9-v)=3 -2(k-3) = k-5 1 solutions Answer 408973 by MathLover1(6625)   on 2012-09-21 22:47:53 (Show Source): You can put this solution on YOUR website! ...first multiply

Numeric_Fractions/655188: -8c^-3 divided by 2c^4 1 solutions Answer 408972 by MathLover1(6625)   on 2012-09-21 22:40:33 (Show Source): You can put this solution on YOUR website!

Functions/655172: f(x)= 4|x-4| Increasing? Decreasing? Constant? On? 1 solutions Answer 408971 by MathLover1(6625)   on 2012-09-21 21:53:04 (Show Source): You can put this solution on YOUR website! assuming is real: global minimum: min{..} is at Increasing? Decreasing? Constant? On? (, ] Thus function is decreasing on this interval in its domain. [, ) Thus function is increasing on this interval in its domain. The function is continuous on its entire domain (,)

Volume/655154: Find the outside surface area. Note that the container may not have a top. Assume a = 4 in., b = 5 in http://www.webassign.net/smithnm11/9-3-041combo_6alt.gif 1 solutions Answer 408964 by MathLover1(6625)   on 2012-09-21 20:00:42 (Show Source): You can put this solution on YOUR website! since you have square pyramid (and assume a = 4 in, b = 5 in) which is a container that may have a top, means you will not need the area of the base so, you will calculate lateral area: if you include base area of a square pyramid (square): you will have: Total Surface Area of a square pyramid:

Conjunction/655143: construct a truth table for ~(p v q)↔ (~p ^ ~q) 1 solutions Answer 408958 by MathLover1(6625)   on 2012-09-21 18:10:46 (Show Source): You can put this solution on YOUR website! click on this link and you will see your solution: W3C Web site