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# Recent problems solved by 'tutorcecilia'

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 Linear-equations/49068: Determine the equation of the line through (0,9) that is parallel to the line 3x + 5y =15. 1 solutions Answer 32523 by tutorcecilia(2152)   on 2006-08-15 14:38:05 (Show Source): You can put this solution on YOUR website!Re-write the first equation in slope-intercept format (y=mx+b): 3x + 5y =15 y = -3/5x -15/5 y = -3/5x + 3 The slope (m) = (-3/5) . Since parallel lines have the same slope, the slope of the second line will also equal (-3/5). . Use the slope-intercept formula to find the equation of the second line: y = mx + b [Plug-in the values (0, 9) and the slope (-3/5). 9 = (-3/5)(0) + b [Solve for b] 9 = b. So, the equation of the second line is: y = (-3/5)x + 9
 Graphs/49024: This question is from textbook Beginning Algebra How do I write the equation of the line that passes through point (0, 4) with a slope of 8?1 solutions Answer 32484 by tutorcecilia(2152)   on 2006-08-14 19:41:31 (Show Source): You can put this solution on YOUR website!Given point (0, 4) with a slope(m) of 8 (y2-y1) = m(x2-x1 [Use the point-slope format] (y2-4) = 8(x2-0) [Plug-in the values] y2 - 4= 8x - 0 [Simplify] y-4 = 8x [Solve for y] y = 8x+4 [Slope-intercept formula for the equation of a line]
 Graphs/49026: This question is from textbook Beginning Algebra Please help me find the y-intercept. x – y = 4 1 solutions Answer 32483 by tutorcecilia(2152)   on 2006-08-14 19:37:12 (Show Source): You can put this solution on YOUR website!To find the y-intercept, first, rewrite in the slope-intercept format: y=mx+b [Slope-intercept format where: y = any y value of the line m = the slope of the line x = the corresponding x value of the line b = the y-intercept of the line . x – y = 4 [Isolate the "y" in order to re-write in the slope-intercept form] -y=-x+4 -y/-1 = -x/-1 + 4/-1 [Simplify] y = x - 4 Slope (m) = 1 y-intercpet = -4
 Graphs/49027: This question is from textbook Beginning Algebra Please help find the slope and the y-intercept. y = –5x + 9 1 solutions Answer 32482 by tutorcecilia(2152)   on 2006-08-14 19:32:27 (Show Source): You can put this solution on YOUR website!y = mx + b [Slope-intercept format] y = any y value of the line m = the slope of the line x = any corresponding x value of the line b = the y-intercpet (where the line crosses the y-axis . y = mx + b y = –5x + 9 -5 = the slope (m) 9 = the y-intecept (b)
 Graphs/49022: This question is from textbook Beginning Algebra Please help write equation of: the line with x-intercept (3, 0) and y-intercept (0, 2).1 solutions Answer 32481 by tutorcecilia(2152)   on 2006-08-14 19:29:35 (Show Source): You can put this solution on YOUR website!Given point (3, 0) and y-intercept (0, 2) Since you are given two points, first find the slope: m =(y2-y1)/(x2-x1)[Slope formula] m = (2-0)/(0-3) [Plug-in the values] m = 2/-3 or -2/3 . Next, use the slope-intercept format: y = mx + b 0 = (-2/3)(3) + b [Plug-in the values using one of the points and the slope] 0 = -2 + b [Simplify] 2 = b [Solve for "b"] y = (-2/3)x + 2 [Plug-in the values of "m" and the y-intercept for the equation of the line]
 Graphs/49015: This question is from textbook Beginning Algebra How do I determine which two equations represent parallel lines? y = 4x – 8 y = –4x + 8 y = 4x + 5 y = x – 8 1 solutions Answer 32480 by tutorcecilia(2152)   on 2006-08-14 19:22:33 (Show Source): You can put this solution on YOUR website!Make sure each line is in the slope-intercept formate: y=mx+b. The "m" represents the slope value. If not, re-write it. The lines with the same slopes will be parallel. . y = 4x – 8: m = 4 y = –4x + 8: m = -4 y = 4x + 5: m = 4 y = x – 8: m = 1 . So, y = 4x-8 and y = 4x+5 are parallel because they have the same slope.
 Graphs/49016: This question is from textbook Beginning Algebra Please help write the equation of the line that passes through point (0, –7) with a slope of -7/2 .1 solutions Answer 32479 by tutorcecilia(2152)   on 2006-08-14 19:19:01 (Show Source): You can put this solution on YOUR website!Given point (0, –7) with a slope of -7/2 (y-y)=m(x-x] [Use the point-slope formula] (y-(-7)=(-7/2)(x-0) [Plug-in the points] y+7 = -7/2x - 0 [Simplify] y+7 = -7/2x y = -7/2x - 7 [Solve for y][Final answer]
 expressions/48999: hey this is exactly what my worksheet says. Simplifying Expressions. 1.(7x-2y+5)+(2x+5y-4) 2.(3x+5xy+2y)+(4-3xy-2x) 3.-2[2a-(4a-2)-2(7-3a)]1 solutions Answer 32478 by tutorcecilia(2152)   on 2006-08-14 19:11:17 (Show Source): You can put this solution on YOUR website!1.(7x-2y+5)+(2x+5y-4) [Combine like-terms only] 9x+3y+1 . 2.(3x+5xy+2y)+(4-3xy-2x) [Combine like-terms only] x+2xy+2y+4 . 3. -2[2a-(4a-2)-2(7-3a)] [Use the order of operations (PEMDAS)] -2[2a-4a+2)-2(7-3a)][Multiply within the brackets] -2[2a - 4a + 2 - 14 + 6a] [Combine like-terms] -2[-2a - 12 + 6a)] [Combine like-terms] -2[4a - 12] [Multiply outside of the brackets] -8a + 24
 absolute-value/49012: This question is from textbook algebra the sum of 3 and a number 1 solutions Answer 32477 by tutorcecilia(2152)   on 2006-08-14 18:51:43 (Show Source): You can put this solution on YOUR website!Sum = addition "a number" = unknown number = x So, 3+x
 Numeric_Fractions/48995: 9 1/3-7 3/4=?1 solutions Answer 32463 by tutorcecilia(2152)   on 2006-08-14 16:21:51 (Show Source): You can put this solution on YOUR website! [Change to an improper fraction] [Cross-multiply] [Multiply the denominators] [Simplify] [Combine fractions with the same denominator] [Simplify] [Final answer]
 Quadratic_Equations/48976: Solve using the quadratic formula, writing the answer as a simplified radical expression. 1 solutions Answer 32462 by tutorcecilia(2152)   on 2006-08-14 16:12:52 (Show Source): You can put this solution on YOUR website![Set the equation equal to zero by subtracting 16 from both sides] . . [Add the term (0x) to make it easier to work with] . a=7 b=0 c=-25 [Plug-in the values] . [Simplify] . . . x = +26.4575/14 = 1.8898 x = -26.4747/14 = -1.8898
 percentage/48993: please help! How much water should be added to 50ml of 25% acid solution to dilute it to a 10% acid solution? A 75 ml B. 7.5 ml C impossible to do Thank you!1 solutions Answer 32461 by tutorcecilia(2152)   on 2006-08-14 15:44:40 (Show Source): You can put this solution on YOUR website!Use this basic formula: (% or rate of A)(Amount of A)+ (% or rate of B)(Amount of B) = C C can equal (% or rate of C)(A+B) or C can equal (% or rate of C)(Amount of C) . Change percentages to decimals: Example: 10% = .10 . Water is 0% acid. . (0%)(xml) + (25%)(50ml) = (10%)(xml + 50ml) (0)(x) + (.25)(50) = (.10)(x + 50) 0 + 12.50 = .10x + 5.0 12.50 = .10x + 5.0 [Solve for "x"] 7.5 = .10x 75ml = x So, add 75ml of water (0% acid) to 50ml of a 25% acid to yield 125ml of a 10% acid. . Check by plugging in all of the variables back into the original equation: (%A)(Amount A) + (%B)(Amount B) = (%C)(A+B) (0%)(75) + (.25)(50) = (.10)(125) 12.5 = 12.5 [Checks out]
 Exponents/48983: Factor 1 solutions Answer 32460 by tutorcecilia(2152)   on 2006-08-14 15:26:47 (Show Source): You can put this solution on YOUR website!Factor {Use the quadratic formula] .. [Plug-in the values] . [Simplify] . . [Reduce] . x = 7/5
 Graphs/48919: This question is from textbook Beginning Algebra Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept Slope:-2;y-intercept:(0,4)1 solutions Answer 32433 by tutorcecilia(2152)   on 2006-08-14 12:10:36 (Show Source): You can put this solution on YOUR website!Method #1: Slope:-2;y-intercept:(0,4) (y-y) = m(x-x) [Use the point-slope formula for the equation of the line] (y-4) = (-2)(x-0) [Plug-in the values] y-4 = -2x [Simplify] y = -2x + 4 [Solve for "y"] [Final answer in slope-intercept form] . Method #2: Slope:-2;y-intercept:(0,4) y=mx+b [Use the slope-intercept formula for the equation of the line] y = -2x + 4 [Plug-in the values for the slope and the y-intercept] . .
 expressions/48962: Solve for x: 2x – 3 = -41 solutions Answer 32430 by tutorcecilia(2152)   on 2006-08-14 11:51:57 (Show Source): You can put this solution on YOUR website!Solve for x: 2x – 3 = -4 [solve for x] . 2x – 3 + 3 = -4 + 3 2x = -1 2x/2 = -1/2 x = -1/2 . Check by pluggin-in (x=-1/2) back into the original equation.
 Exponents-negative-and-fractional/48929: This question is from textbook algebra 1 b-7 when b = 241 solutions Answer 32429 by tutorcecilia(2152)   on 2006-08-14 11:46:36 (Show Source): You can put this solution on YOUR website!b-7 when b = 24 (24)-7 = 17 [Plug-in the value of "b"]
 Graphs/48956: hwo do i graph this inequality? y>-3x+4 -1 solutions Answer 32428 by tutorcecilia(2152)   on 2006-08-14 11:38:37 (Show Source): You can put this solution on YOUR website!y>-3x+4 [Re-write as an equality] y=-3x+4 y=-3(0)+4 [Let (x=0) and solve for "y"] y = 4 Plot the point (0, 4) . y=-3x+4 0=-3x+4 [Let (y=0) and solve for "x"] x = 4/3 Plot the point ((4/3), 0) . Draw a dashed line for the line. Since "y" is greater than (-3x+4), color or shade everything above and to the right of the dashed line. . The diagram below only shows the boundary line. Your line should be a dashed line with shading above the line. . .
 Linear-equations/48954: what is the equation of the line going through (5,3) and (7,-8) 1 solutions Answer 32425 by tutorcecilia(2152)   on 2006-08-14 11:26:19 (Show Source): You can put this solution on YOUR website!(5,3) and (7,-8) [Points on a line] m = (y2-y1)/x2-x1) [Formula for the slope of a line] m = ((-8)-3)/(7-5) [Plug-in the values] m = -11/2 [The slope of the line] . y = mx+b [The slope-intercept formula for the equation of a line] y = the y-value of a point on the line m = the slope of the line x = the corresponding x-value for a point on the line b = the y-intercept; it is where the line crosses the y-axis (0, b) . y = mx + b 3 = (-11/2)(5) + b [Pick a point and plug-in the values] 3 = (-55/2) + b [Solve for "b"] (55/2) + (3) = b 61/2 = b . y=(-11/2)x + (61/2) [Plug-in the values of the slope and y-intercept][Final answer] . Check by plugging the values for either of the original points
 Rational-functions/48938: 2x^2+7x-2=0 skolve for x using quadratic formula if there is more than one solution separate with commas1 solutions Answer 32419 by tutorcecilia(2152)   on 2006-08-14 11:00:31 (Show Source): You can put this solution on YOUR website!2x^2+7x-2=0 [The quadratic formula] . Values: a=2 b=7 c=-2 . [Plug-in the values] . [Simplify] . . Two answers: x = 0.2656 . or . x=-3.766 . Check each value of x by plugging (x=0.2656) or (x=-3.766) back into the original equation.
 Exponents/48902: Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process. 1 solutions Answer 32372 by tutorcecilia(2152)   on 2006-08-13 13:09:48 (Show Source): You can put this solution on YOUR website! = =2 . Looking closer at the exponent of (1/2), the numerator represents the power or degree; the denominator represents the radical. So, "1" is the power, and "2" is the square root. . Another example is: = = 3
 Rational-functions/48696: a+4/2 = a+4/a 1 solutions Answer 32264 by tutorcecilia(2152)   on 2006-08-10 16:00:42 (Show Source): You can put this solution on YOUR website!a+4/2 = a+4/a [Find the lowest common denominator (LCD)] (2*a) = LCD (2a)(a+4)/2 = (2a)(a+4)/a [Multiply each fraction by the LCD] (a)(a+4) = (2)(a+4) [Cancel wherever necessary] a^2 + 4a = 2a + 8 [Simplify] a^2 + 4a - 2a - 8 = 0 [Isolate all of the terms on one side of the equation] a^2 + 2a - 8 = 0 [Combine like-terms] (a-2)(a+4) = 0 [Factor] . [Set each factor equal to zero and solve for "a"] a-2=0 a=2 . or a+4=0 a=-4 . So, a=2 or a=-4 . Check by plugging (a=2) or (a=-4) back into the original equation. a=2 (2)+4/2 = (2)+4/(2) 6/2 = 6/2 3 = 3 [Checks out] . a= -4 (-4)+4/2 = (-4)+4/(-4) 0/2 = 0/-4 0=0 [Checks out]
 Functions/48718: Solve: 3x - 7 = 2x + 81 solutions Answer 32257 by tutorcecilia(2152)   on 2006-08-10 15:23:43 (Show Source): You can put this solution on YOUR website!3x - 7 = 2x + 8 [Move all of the variables to one side of the equation] 3x - 7 + 7 = 2x + 8 + 7 [Add 7 to both sides] 3x = 2x + 15 3x - 2x = 2x - 2x + 15 x = 15 Check by plugging in (x-15) back into the equation. 3(15) - 7 = 2(15) + 8 38 = 38 [Checks out]
 Expressions-with-variables/48675: This question is from textbook y+81 solutions Answer 32252 by tutorcecilia(2152)   on 2006-08-10 15:07:19 (Show Source): You can put this solution on YOUR website!y+8=0 [Solve for y] y+8-8=0-8 [Isolater the "y" by subtracting 8 from both sides] y = -8 . Check by plugging (y=-8) back into the original equation. (-8)+8 = 0 0=0 [Checks out]
 Equations/48614: How do you solve (-5)(-3)(+2)?1 solutions Answer 32193 by tutorcecilia(2152)   on 2006-08-09 15:53:37 (Show Source): You can put this solution on YOUR website!Follow the rules for multiplying integers: Negative x Negative = Positive Positive x Positive = Positve Negative x Positive = Negative Postive x Negative = Negative The same rules also apply for dividing integers. . (-5)(-3)(+2) (15)(+2) 30
 Graphs/48595: How do you interpret the solution of a system of equations by the corresponding graph? 1 solutions Answer 32185 by tutorcecilia(2152)   on 2006-08-09 13:29:30 (Show Source): You can put this solution on YOUR website!Find the point of interception. That is, at which point do the lines cross?
 Systems-of-equations/48596: Is there a difference between solving a system of equations by the algebraic method and the graphical method? Why?1 solutions Answer 32184 by tutorcecilia(2152)   on 2006-08-09 13:28:16 (Show Source): You can put this solution on YOUR website!Yes, the algebraic method is more precise. When you "solve" a system you are really identifying the points that all of the lines have in common. In other words, the point at which the lines intersect. . Finding the solution with graphs is not precise, but should usually be close enough if that is what is asked.
 Graphs/48589: Solve the system by graphing 2x + 4y = 2 x + 2y = 1 Thanks 1 solutions Answer 32180 by tutorcecilia(2152)   on 2006-08-09 11:43:32 (Show Source): You can put this solution on YOUR website!2x + 4y = 2 Let x=0 and solve for y Let y=0 and solve for x Plot the two points:(0, 1/2) and (1,0) . x + 2y = 1 Let x=0 and solve for y Let y=0 and solve for x Plot the two points:(0, 1/2) and (1, 0)
 Exponents-negative-and-fractional/48534: 1/8 - 3/5 = 1/x1 solutions Answer 32179 by tutorcecilia(2152)   on 2006-08-09 11:18:56 (Show Source): You can put this solution on YOUR website!1/8 - 3/5 = 1/x [Find the Least Common Denominator (LCD)] 1/8 - 3/5 = 1/x} [LCD = 8*5*x = 40x] (40x)(1/8) - (40x)(3/5) = (40x)(1/x) [Multiply each term by the LCD] 5x - (8x)(3) = (40) [Cancel out wherever possible] 5x-24x=40 [Simplify] -19x=40 x=-40/19 . Check by plugging (x=-40/19) back into the original equation and solve] 1/8 - 3/5 = 1/(-40/19) -.475 = -.475
 Linear-equations/48538: how do you find the slope of the line passing through (7,3) and (9,-2)1 solutions Answer 32178 by tutorcecilia(2152)   on 2006-08-09 11:04:47 (Show Source): You can put this solution on YOUR website!m = (y2-y1)/x2-x1) [Use the slope of a line formula] m = (-2-3)/(9-7) [Plug-in the values] m = -5/2 = the slope . y=mx+b [Use the slope-intercept formula to find the equation of the line] 3=(-5/2)(7) + b [Plug-in the values] 3=(-5/2) + b [Solve for b] 41/2 = b y=mx+b [Plug-in the values for the slope and y-intercept (b) only] y=(-5/2)x + 41/2 [Equation of the line]
 Linear-equations/48551: Graph these two problems of inequality. & Graph the inequality x > 2 2x + 3y > 6 I do not understand graph no matter how hard I study. 1 solutions Answer 32177 by tutorcecilia(2152)   on 2006-08-09 10:49:33 (Show Source): You can put this solution on YOUR website!x>2 [Re-write the inequality as an equation] x=2 [Graph using a dashed line. Shade everything above the line] . 2x + 3y > 6 [Solve for y] y > -2/3x + 2 [Re-write the inequality as an equation] y = -2/3x + 2 [Graph using a dashed line. Shade everything above the line] . The reason you shade above the line is because the final inequalities are "greater than". If the inequality was "less than", than you would shade below the line.
 Square-cubic-other-roots/48578: apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x^2 + 4 g(x) = x^2 + x + 12 1 solutions Answer 32176 by tutorcecilia(2152)   on 2006-08-09 10:32:14 (Show Source): You can put this solution on YOUR website!f(x) = x^2 + 4 Let: a=1 b=0 c=4 . [Plug-in the values] . [Simplify] [Cancel out] x = +-2i [x = -2i or x = +2i] [Final answers] . . . g(x) = x^2 + x + 12 Let: a = 1 b = 1 c = 12 . . . . . . . .