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# Recent problems solved by 'tutorcecilia'

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 Graphs/82964: Can someone please, please show me how to do this? graph the equations y=3x y=x+3 1 solutions Answer 59539 by tutorcecilia(2152)   on 2007-05-22 10:14:22 (Show Source): You can put this solution on YOUR website!y=3x or y=3x+0 Compared to the equation of a line formula: y=mx+b y=any y value m=the slope of the line x=any corresponding x-value b=the point where the line intersects the y-axis For y=3x+0, the line will cross or intersect the y=axis at (0, 0), starting from that point, use the slope of 3 or 3/1. That is, from (0, 0,) go up +3 and over +1 and plot that point (1,3) From (1, 3) go up +3 and over +1 and plot that point (2, 6). . Now for the bottom of the graph, start again at (0, 0), and using the slope -3/-1 (same as +3), go down -3 and to the left (-1); plot this point (-1, -3). Repeat this pattern by going down -3 and over to the left -1; plot this point (-2, -6). . Connect the lines. . y=x+3 or y=1x+3 The slope = 1 or 1/1 The line crosses or intersects the y-axis at (0, 3) So, repeat the instructions from above, only start at point (0, 3) and go up 1 and over 1, etc. Graphing:
 Graphs/82790: Solve 3(x-5)+3x=4x+51 solutions Answer 59438 by tutorcecilia(2152)   on 2007-05-21 14:32:53 (Show Source): You can put this solution on YOUR website!3(x-5)+3x=4x+5 3x-15+3x=4x+5 6x-15=4x+5 6x-4x-15=4x-4x+5 2x-15=5 2x-15+15=5+15 2x=20 2x/2=20/2 x=10 . check by plugging (x=10) back into the original equation and solve: 3(10-5)+3x=4x+5 3(5)+3(10)=4(10)+5 15+30=40+5 45=45 [checks out]
 test/82794: 5(4) divided by 2-4^2...I need help with this, my options are: (a)100 (b)36 (c)5 (d)-61 solutions Answer 59434 by tutorcecilia(2152)   on 2007-05-21 14:20:43 (Show Source): You can put this solution on YOUR website! 10-16 -6
 Rectangles/82802: A rectangle has sides of 3x-4 and 7x+10. Find the expression that represents its perimeter.1 solutions Answer 59430 by tutorcecilia(2152)   on 2007-05-21 14:11:16 (Show Source): You can put this solution on YOUR website!Perimeter of a rectangle: P=2(length+width) So, Lenght=3x-4 and Width= 7x+10 . P=2[(3x-4)+(7x+10)] P=2(10x+6)
 Coordinate-system/82823: Find the distance between (1,4) and (-3,1).1 solutions Answer 59428 by tutorcecilia(2152)   on 2007-05-21 14:04:47 (Show Source): You can put this solution on YOUR website!Use the distance formula: d= . d= [plug-in the values(1,4) and (-3,1)and solve] . d= . d= . d= d=5
 Linear-equations/82825: How do I calculate the slope of a line graph?1 solutions Answer 59423 by tutorcecilia(2152)   on 2007-05-21 13:55:11 (Show Source): You can put this solution on YOUR website!If you are given the line in the slope-intercept format: y=mx+b, the m-term represents the slope . If you are given two points (x1, y1) and x2, y2), use the slope formula: Slope=m=
 Coordinate-system/82844: This one really confused me - please help! Write the equation of the line that satisfies the given condition: contains the point (2,6) and is perpendicular to the line 4x-5y=7. Thank you!1 solutions Answer 59422 by tutorcecilia(2152)   on 2007-05-21 13:52:13 (Show Source): You can put this solution on YOUR website!Lines that are perpendicular have slopes that are the negative reciprocal of each other: For example: if slope #1 = 2, then the perpendicular slope = -1/2 . Line #1 4x-5y=7 [re-write in the y=mx+b format] 4x-4x-5y=-4x+7 -5y=-4x+7 -5y/-5=-4/-5x+7/-5 y=4/5x-7/5 Slope # 1 = 4/5 . So, slope of Line #2 =-5/4 [because I flipped 4/5 and multiplied it by (-1)] y=mx+b [plug-in the values (2, 6) and (m=-5/4) and solve for the b-term] 6=(-5/4)(2)+b 6=-5/2+b 5/2+6=b 17/2=b Plug-in just the values of the slope and the b-term: y=-5/4x+17/2
 Linear-equations/82836: Identify the slope of each direct variation 1. a. y = 7x b.y= -3x c. y= x d. y= 1/2x e. y= -1.4x f.y= 2.673x g. y= 3 2/3x h. y= -8x 1 solutions Answer 59419 by tutorcecilia(2152)   on 2007-05-21 13:19:13 (Show Source): You can put this solution on YOUR website!Use the formula y=mx+b where the m-term represents the value of the slope . 1. a. y = 7x Slope = 7 . b.y= -3x Slope = m=-3 . c. y= x Slope=m=1 . d. y= 1/2x Slope=m=1/2
 Proportions/82838: Multiply to find the missing value. Include units in your answer. 3. a.72 hr * \$4/1 hr b. 55 mi/1 hr * 7 hr/1 day c. 35 people/1 party * 2.5 pizzas/10 people1 solutions Answer 59417 by tutorcecilia(2152)   on 2007-05-21 13:16:43 (Show Source): You can put this solution on YOUR website!3. a. [cancel out the hour units; the dollar units are left] . \$288/1 [multiply straight across \$288 . b. [convert days to hours] [cancel out the units wherever possible (hours and days cancel out] . [you are left with miles/hour] 16.0416 mi/hr [multiply straight across] . c. 35 people/1 party * 2.5 pizzas/10 people [cancel units wherever possible (people units)] . 35 /1 party * 2.5 pizzas/10 35 people/1 party * 2.5 pizzas/10 people 8.75 pizzas/party [multiply straight across]
 Coordinate-system/82843: Change the equation to a slope-intercept form: 8x-11y=51 solutions Answer 59415 by tutorcecilia(2152)   on 2007-05-21 13:02:02 (Show Source): You can put this solution on YOUR website!8x-11y=5 [solve for the y-term] 8x-8x-11y=-8x+5 -11y=-8x+5 -11y/-11=-8x/-11+5/-11 y=(8/11)x-5/11
 Polynomials-and-rational-expressions/82839: it asked to factor by grouping and i dont understand how to do it 8x^3+6x^2-12x-91 solutions Answer 59414 by tutorcecilia(2152)   on 2007-05-21 13:00:16 (Show Source): You can put this solution on YOUR website! [factor out the least common multiply amongst each factor and divide each term by it] . [this re-grouping doesn't work becasue each group has a different factor] . . Try to re-arrange the terms, re-group and factor again: [re-factor again; this factoring works because the groups now have a common factor (2x-3)]
 Graphs/82568: Determine which two equations represent parallel lines: (a)y=-9x+4 (b)y=9x+4 (c)y=1/9x+4 (d)y=-9+51 solutions Answer 59173 by tutorcecilia(2152)   on 2007-05-18 13:48:01 (Show Source): You can put this solution on YOUR website!Lines that are parallel have the same slope. In the y=mx+b formula, the "m" is the slope. So look at each equation and find matching slopes: (a)and (d) have matching slopes, so these two lines are parallel.
 Quadratic_Equations/82523: Solve the system by addition or substitution. –6x + 3y = 12 y = 2x + 3 1 solutions Answer 59169 by tutorcecilia(2152)   on 2007-05-18 13:18:05 (Show Source): You can put this solution on YOUR website!–6x + 3y = 12 [re=write] -6x+6x+3y=6x+12 3y=6x+12 3y/3=6x/3+12/3 y=2x+4 . y=2x+4 y=2x+3 ______ . . (-1)y=2x+4 y=2x+3 ______ . . -y=-2=-4 y=2x+3 ________ 0y=0x+-1 o=-1 [untrue statement, so there is no solution or no points in common] . Also, note that the lines have the same slope (2), therefore the lines are parallel and will never intersect.
 Rational-functions/82564: Express 10/3 - 5/2 as a simplified rational number. I got the answer of 0.8333, but I don't know if it is right. 1 solutions Answer 59167 by tutorcecilia(2152)   on 2007-05-18 13:06:43 (Show Source): You can put this solution on YOUR website!I agree. Good job!! 0.83333
 Expressions-with-variables/82571: Solve the system by substitution: 2x+2y=0 y=4x+01 solutions Answer 59165 by tutorcecilia(2152)   on 2007-05-18 13:02:47 (Show Source): You can put this solution on YOUR website!2x+2y=0 [substitute (y=4x+0) for the y-term and solve for the x-term] . 2x+2(4x+0)=0 2x+2(4x)=0 2x+8x=0 10x=0 10x/10=0/10 x=0 . solve for the y-term by plugging x=0 back into one of the original equations: 2x+2y=0 2(0)+2y=0 2y=0 2y/2=0/2 y=0 . check by plugging the values for x and y back into either eiquation and solve: 2x+2y=0 2(0)+2(0)=0 0=0 [checks out]. and y=4x+0 0=4(0)+0 0=0 [also checks out]
 Quadratic_Equations/82577: Given g(x) = –2x + 1, find g(2a).1 solutions Answer 59162 by tutorcecilia(2152)   on 2007-05-18 12:49:18 (Show Source): You can put this solution on YOUR website! g(x) = –2x + 1 g(2a)=-2(2a)+1 g(2a)=-4a+1 . checking: -4a+1=-2x+1 -4a=-2x -4a=-2(2a) -4a=-4a [checks out]
 Quadratic_Equations/82575: The length of a rectangle is 4 in. more than twice its width. If the perimeter of the rectangle is 56 in., find the width of the rectangle. Answer: The width is ______ Show work: 1 solutions Answer 59161 by tutorcecilia(2152)   on 2007-05-18 12:45:13 (Show Source): You can put this solution on YOUR website!Formula for the perimeeter of a rectangle: P=2[(length + width)] P=56 Length=2w+4 Width=w . so, 56=2[(2w+4)+w)] 56/2=2/2(2w+4+w)] 28=3w+4 28-4=3w 24=3w 24/3=3w/3 8=w . So, P=56 Length=2w+4 = 2(8)+4=16+4=20 Width=w=8 . Plugging everything back into the formula for a perimeter: P=2[(length + width)] 56=2(20+8) 56=2(28) 56=56 [checks out]
 Equations/82585: I have to solve this: √x-1=x-3 This is what I have done so far. Am I on the right track? What do I do now? "The radical symbol is only over the x-1" √x-1=x-3 (√x-1)^2=(x-3)^2 x-1 = (x-3)(x-3) x-1 = x^2-6x+9 x-1 = x^2-6x+9 0=x^2-7x+10 1 solutions Answer 59160 by tutorcecilia(2152)   on 2007-05-18 12:37:23 (Show Source): You can put this solution on YOUR website!Good job!! I agree with your answer. You correctly initially squared both sides of the equation in order to get rid of the radical; used FOIL on the left side; and solved for the x-term. . If your instructor/book wanted you to solve for the x=term, just continue the process: 0=x^2-7x+10 (x-5)(x-2)=0 x-5=0 x=5 or x-2=0 x=2 . Try plugging each x-value back into the original equation to make sure each solution is a true solution. One of the values of x could possibly be an erroneous solution: . = Let x=5 = =[the square root of 4 is either a plus or minus 2] 2=2 [so, x=5 checks out] . = Let x=2 = [the square root of 1 is either a plus or minus (1). In this case, the (-1) works] -1 = -1 [ture, so x=2 is also a solution]
 Radicals/82584: I have to simplify this problem please help. Can anybody show me how to do equations like this one? The ones with letters and that are on top of each other are really hard. √75a / √51 solutions Answer 59158 by tutorcecilia(2152)   on 2007-05-18 12:22:29 (Show Source): You can put this solution on YOUR website! [factor out a perfect square (25)] [multiply by in order to get rid of the radical in the denominator] . [cancel out wherever possible] . or, just cancel out radicals wherever possible:
 Linear-equations/82221: Please some assistance is needed. Plot the point with coordinates (-3,-3)1 solutions Answer 58948 by tutorcecilia(2152)   on 2007-05-16 14:15:19 (Show Source): You can put this solution on YOUR website!Starting at the origin of (0,0) on the graph, go three spaces to the left (-3) and than down three spaces (-3). Plot the point. . For coordinate points, (x, y) the first number tells you how many spaces to move on the x-axis (left or right). The second number tells you how many spaces to move on the y-axis (up or down)
 Polynomials-and-rational-expressions/82235: This question is from textbook please assist me with the following: 1.factor: y2-4y-5 2. factor 3a2+9a+6 3.evaluate: x(x+1)(x-1) 4.facctor: 6y2-2yz1 solutions Answer 58947 by tutorcecilia(2152)   on 2007-05-16 14:11:10 (Show Source): You can put this solution on YOUR website!1.factor: y2-4y-5 (y-5)(y+1) . 2. factor 3a2+9a+6 (3a+3)(a+2) . 3.evaluate: x(x+1)(x-1) set each factor equal to zero and solve for the x-term: x=0 x+1=0 x=-1 and x-1=0 x=1 So, x= 0, -1 and 1 . 4.factor: 6y2-2yz factor out (2y) (2y)(3y-z) .
 Linear-equations/82273: This question is from textbook algebra 2 Write the equation in standard form. 10. y=2/3x+11 solutions Answer 58946 by tutorcecilia(2152)   on 2007-05-16 14:00:05 (Show Source): You can put this solution on YOUR website!Standard for is: Ax+By=C y=2/3x+1 [get the variables to one side and the constant (1) to the other side] -2/3x+y=-2/3x+2/3x+1 -2/3x+y=1
 Quadratic_Equations/82238: This question is from textbook please assist me with the following: 1. factor 6f2+5f+1 2. factor 12w2+10w-8 3. factor: 20y2-33y+10 factor: -x2-x-61 solutions Answer 58938 by tutorcecilia(2152)   on 2007-05-16 13:26:34 (Show Source): You can put this solution on YOUR website!1. factor 6f2+5f+1 (3f+1)(2f+1)=0 [use trial-and-error to find the factors that have a product (multiplied) of the first and last term; and a sum (add) of the middle term] Example: factor =(3f)(2f) factor the last term of (1) = (1)(1) Try to find the combination of the factors that, when added togeter, will equal the middle term of 5f. (3f+1)(2f+1) . factor 12w2+10w-8 (6w+8)(2w-1) [use trial-and-error to find the factors that have a product (multiplied) of the first and last term; and a sum (add) of the middle term] Example: 12 = (6)(2) or (12)(1) or (3)(4) and -8 = (-1)(8) or (1)(-8) or (-4)(2) or (-2)(4) Try to find the combinations that, when added, will equal the middle term of (10w) . 3. factor: 20y2-33y+10 (5y-2)(4y-5)[use trial-and-error to find the factors that have a product (multiplied) of the first and last term; and a sum (add) of the middle term] . factor: -x2-x-6 (-x-3)(x-2)[use trial-and-error to find the factors that have a product (multiplied) of the first and last term; and a sum (add) of the middle term]
 Graphs/82257: how do I graph the inequality y<1?1 solutions Answer 58936 by tutorcecilia(2152)   on 2007-05-16 12:53:59 (Show Source): You can put this solution on YOUR website!y<1 First, establish a boundary line by using an equal sign: y=1 (see the graph: . In this case, the boundary line will be a dashed line because the inequality is "less than" "1". If the inequality had been just "less than or equal to", the boundary line would have been a solid line instead. . Now, shade every thing below or less than the line (which is everything < 1) since "y" is every point less than the line (see the graph below):
 Equations/82249: 3x=6x-15 then x+8=1 solutions Answer 58933 by tutorcecilia(2152)   on 2007-05-16 12:34:51 (Show Source): You can put this solution on YOUR website!3x=6x-15 [solve for the x-term= 3x-6x=6x-6x-15 -3x=-15 -3x/-3=-15/-3 x=5 [checking: 3(5)=6(5)-15 15=30-15 15=15 [checks out] . So, x=5 and x+8= 5+8=13
 Graphs/82252: Graph f(x)=3x+21 solutions Answer 58932 by tutorcecilia(2152)   on 2007-05-16 12:28:03 (Show Source): You can put this solution on YOUR website!Using the formula: y=mx+b; y=any y-value on the line m=the slope of the line x=any corresponding x-value b=the y-intercept . f(x)= f(x)=3x+2 y=mx+b The slope = 3 The y-intercept = 2 Graphing:
 Graphs/82258: How do I graph f(x)=-2x+2?1 solutions Answer 58930 by tutorcecilia(2152)   on 2007-05-16 12:18:23 (Show Source): You can put this solution on YOUR website! Using the formula: y=mx+b; y=any y-value on the line m=the slope of the line x=any corresponding x-value b=the y-intercept . f(x)=-2x+2 y=mx+b The slope = -2 The y-intercept = 2 Graphing:
 Rectangles/82261: The length of a rectangle is 3in more than twice its width. If the perimeter of the rectangle is 36in, find the width of the rectangle. (a)7in (b)6in (c)4in (d)5in1 solutions Answer 58928 by tutorcecilia(2152)   on 2007-05-16 12:14:41 (Show Source): You can put this solution on YOUR website!Use the formula for the perimeter of a rectangle: P=2(length+width) P=36 Length = 3in more than twice its width = 2 x Width +3 = 2w+3 Width=w . P=2(l+w) [plug-in the values and solve for the width(w)] 36=2[(2w+3)+w] 36/2=2/2(2x+3+w) 18=2w+3+w 18=3w+3 18-3=3w 15=3w 15/3=3w/3 5=w . checking: Length = 2w+3=2(5)+3=13 Width=5 . 36=2(13+5) 36=2(18) 36=36 [checks out]
 Radicals/82256: How do i work this? 10 square root of 2 divided by square root of 81 solutions Answer 58921 by tutorcecilia(2152)   on 2007-05-16 11:45:00 (Show Source): You can put this solution on YOUR website! [multipliply the entire fraction by the denominator in order to get rid of the radical in the denominator] . [simplify wherever possible] 5
 Graphs/82253: Given f(x)=-x-4, find f(a-3)1 solutions Answer 58920 by tutorcecilia(2152)   on 2007-05-16 11:43:33 (Show Source): You can put this solution on YOUR website! f(x)=-x-4 [substitute (a-3) for the x-term and solve as much as possible f(a-3)=-x-4 f(a-3)=-(a-3)-4 f(a-3)=-a+3-4[multiply through by (-1) f(a-3)=-a-1 f(a-3)=a+1 [multiply through by (-1)
 Linear-systems/82250: solve the system by substitution 8x-4y=16 y=2x-41 solutions Answer 58919 by tutorcecilia(2152)   on 2007-05-16 11:38:17 (Show Source): You can put this solution on YOUR website!y=2x-4 [substitute for the y-term in the first equation] 8x-4y=16 8x-4(2x-4)=16 [simplify] 8x-8x+16=16 0+16=16 16=16 [Infinate number of solutions because the equations represent the same line]