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# Recent problems solved by 'funmath'

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 Quadratic_Equations/60913: Please, please help with this question. I do not know where to go. When a ball is thrown vertically upward, its height (h, in feet) above the ground after t seconds is described by the mathematical formula h = - 16t2 + 96t + 80. At what times is the ball 103 feet above the ground?1 solutions Answer 41865 by funmath(2925)   on 2006-11-11 15:15:04 (Show Source): You can put this solution on YOUR website!When a ball is thrown vertically upward, its height (h, in feet) above the ground after t seconds is described by the mathematical formula h = - 16t2 + 96t + 80. At what times is the ball 103 feet above the ground? Use the quadratic formula: a=16, b=-96, c=23 and and and x=.25 s and x=5.75 s One the way up, the ball hits 103 ft in .25 s, on the way back down it hits it again in 5.75 s. Since this came out to rational answers this could have been factored. When the numbers are more difficult to deal with the quadratic formula is easier to use than factoring. Here's what it looks like factored. 4t-1=0 and 4t-23=0 4t=1 and 4t=23 t=1/4 s and t=23/4 s Happy Calculating!!!
 Polynomials-and-rational-expressions/60752: Trying to add this rational expresion not sure my solution is correct?? would appreciate some help thanks!!!! x+4/(x^2-7x+x)+4x+7/(x^2-6x+5) reads x+4 over x^2-7x+6 plus 4x over x^2 -6x+5 my solution 5x^2-18x-62/[(x-1)(x-6)((x-5)]1 solutions Answer 41860 by funmath(2925)   on 2006-11-11 14:53:53 (Show Source): You can put this solution on YOUR website! 1st factor the denominators. The LCD is (x-1)(x-5)(x-6), whatever you do to the denominator you must also do to the numerator. You're right! Happy Calculating!!!
 Polynomials-and-rational-expressions/60874: HELP!! Please!! Missed lecture and nothing makes sense. The following apply for the listed problems...let f(x)=x+5; let g(x)=X^2-2; let h(x)=-3x 1. ((f)*(g))*x I tried to write this and got and then looked for a gun. I don't know where to go. Are we solving for x or simplifying? 2. h(h(5)) 3. g(h(-1)) 4. (f*(4)) + (g*(6)) Thanks so much in advance!1 solutions Answer 41856 by funmath(2925)   on 2006-11-11 14:23:17 (Show Source): You can put this solution on YOUR website!Let f(x)=x+5; let g(x)=X^2-2; let h(x)=-3x 1. ((f)*(g))(x) <---I think this is what you meant. : 2. h(h(5)) First find h(5) h(h(5))=h(-15) Now substitute that value into the h function. h(h(5))=-3(-15) h(h(5))=45 : 3. g(h(-1)) h(-1)=-3(-1) h(-1)=3 g(h(-1))=g(3) Substitute 3 into the g function. g(h(-1))=9-2 g(h(-1))=7 : 4. (f(4)) + (g(6)) (4+5)+(36-2) 9+34 43 : Happy Calculating!!!
 Complex_Numbers/60893: I have one final question that I could really use assistance with. How do I work the following problem? (4x-5)^2=-321 solutions Answer 41852 by funmath(2925)   on 2006-11-11 14:04:24 (Show Source): You can put this solution on YOUR website! 4x-5=+- 4x=5+- and Happy Calculating!!!
 Linear-equations/60897: Find the slope and y-intercept. –x – 4y = –32 1 solutions Answer 41851 by funmath(2925)   on 2006-11-11 13:55:11 (Show Source): You can put this solution on YOUR website!The slope intercept form of a line is , m=slope, and (0,b) is the y-intercept. Find the slope and y-intercept. –x – 4y = –32 x-x-4y=x-32 -4y=x-32 , the slope m=-1/4 , the y-intercept is (0,b)=(0,8), some teachers are happy with 8. Happy Calculating!!!
 Linear-equations/60898: how do i write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line. 1 solutions Answer 41849 by funmath(2925)   on 2006-11-11 13:52:04 (Show Source): You can put this solution on YOUR website!The slope intercept form of a line is , m=slope and (0,b)=y-intercept. Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line. m=4 b=-5 To graph, plot the y-intercept (0,-5) From that point use the slope to graph another point. m=4=4/1. Rise (go up) 4 and run (go right) 1, you should be at (1,-1). Plot another point there. Connect the points and you have a line: Happy Calculating!!!
 Linear-equations/60900: how do i find the slope and y-intercept. –x – 4y = –32 1 solutions Answer 41848 by funmath(2925)   on 2006-11-11 13:45:09 (Show Source): You can put this solution on YOUR website!The slope intercept form of a line is , m=slope, and (0,b) is the y-intercept. Find the slope and y-intercept. –x – 4y = –32 x-x-4y=x-32 -4y=x-32 , the slope m=-1/4 , the y-intercept is (0,b)=(0,8), some teachers are happy with 8. Happy Calculating!!!
 Linear-systems/60896: how can i solve the system by graphing. x + y = 4 –x + y = 2 1 solutions Answer 41847 by funmath(2925)   on 2006-11-11 13:38:11 (Show Source): You can put this solution on YOUR website!how can i solve the system by graphing. E1: x + y = 4 E2: –x + y = 2 : For E1, let x=0 and y=? 0+y=4 y=4 Plot (0,4) Now let y=0 and x=? x+0=4 x=4 Plot (4,0) Connect your points and you have this line: For E2, let x=0 and y=? -0+y=2 y=2 Plot (0,2) Now let y=0 and x=? -x+0=2 -x/-1=2/-1 x=-2 Plot (-2,0) Connect these points and you have a second line. The solution is their point of intersection: (1,3) Happy Calculating!!!
 Quadratic_Equations/60819: This question is from textbook i have to find the coordinates of the vertex of y=2x squared1 solutions Answer 41782 by funmath(2925)   on 2006-11-10 18:01:53 (Show Source): You can put this solution on YOUR website!Find the coordinates of the vertex of When the quadratic formula is in standard form: the x-coordinate is found with the formula: a=2, b=0, and c=0 That's the x-coordinate of the vertex. You find the y coordinate by letting x=0. y=0 The vertex is (x,y)=(0,0) Happy Calculating!!!
 Quadratic_Equations/60820: This question is from textbook i have to find the coordinates of the vertex of y=-7xsquared+2x1 solutions Answer 41781 by funmath(2925)   on 2006-11-10 17:54:57 (Show Source): You can put this solution on YOUR website!i have to find the coordinates of the vertex of y=-7x^2+2x The x coordinate of the vertex is found with the formula: The quadratic formula is in standard form: a=-7, b=2, and c=0 The y coordinate is what you get when you substitute the x coordinate into the equation and solve for y. The vertex is (-1/7,-3/7). Happy Calculating!!!
 Square-cubic-other-roots/60811: This question is from textbook 1 solutions Answer 41777 by funmath(2925)   on 2006-11-10 16:48:41 (Show Source): You can put this solution on YOUR website!Type in your problem and directions and we'll help you. We don't have your book.
 Rational-functions/60620: This question is from textbook alegbra concepts and applications PLEASE HELP!!! To divide 7/x+2 by x-2/14, you can multiply 7/x+2 by what?1 solutions Answer 41776 by funmath(2925)   on 2006-11-10 16:46:49 (Show Source): You can put this solution on YOUR website! To divide 7/x+2 by x-2/14, you can multiply 7/x+2 by what? When dividing fractions, you flip the fraction over that's behind the division symbol and multiply. It's called multiplying by the reciprocal. The reciprocal of is So you multiply by Happy Calculating!!!
 Rectangles/60812: The length of a rectangle is 5 cm more than 2 times its width. If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth. Thanks in advance for your WONDERFUL help! ac1 solutions Answer 41775 by funmath(2925)   on 2006-11-10 16:40:46 (Show Source): You can put this solution on YOUR website!Hi ac, The length of a rectangle is 5 cm more than 2 times its width. If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth. : Let the width be: x Then the length is: 2x+5 Area is: 78 cm^2 Area=length*width : 78=x(2x+5) 78=2x^2+5x 0=2x^2+5x-78 This is in standard form: We can use the quadratic formula to solve it: a=2, b=5, and c=-78 You can ignore the negative dimension. x=5.119 The width is: x=5.119 cm Length is:2x+5=2(5.119)+5=15.238 cm Happy Calculating!!!
 Quadratic_Equations/60788: Can you help me find the x-intercepts?? y=x^2+6x+8 and y=x^2-2x+4 Thanks for your help! CH1 solutions Answer 41773 by funmath(2925)   on 2006-11-10 16:02:21 (Show Source): You can put this solution on YOUR website!Hi CH find the x-intercepts?? y=x^2+6x+8 and Let y=0 and solve for x. 0=x^2+6x+8 Factor 0=(x___)(x___) the blank gets filled with two numbers that multiply to get 8 and add to get 6. 2*4=8 and 2+4=6 0=(x+2)(x+4) Let each parentheses=0 x+2=0 and x+4=0 x=-2 and x=-4 The x-intercepts are (-2,0) and (-4,0) : y=x^2-2x+4 This has no x-intercepts. It's not factorable. If you're familiar with the discriminant:, you can tell if a quadratic equation has no x-intercepts if the discriminant is negative. There are no x-intercepts. Happy Calculating!!!
 Functions/60795: Rewrite the equation 4x – 10y = 11 as a function of x. 1 solutions Answer 41772 by funmath(2925)   on 2006-11-10 15:52:53 (Show Source): You can put this solution on YOUR website!Rewrite the equation 4x – 10y = 11 as a function of x. -4x+4x-10y=-4x+11 -10y=-4x+11 <--some books are happy here <--others want the y to be written in function notation. Happy Calculating!!!
 Functions/60797: Given f(x) = –2x + 4, find f(a – 2).1 solutions Answer 41770 by funmath(2925)   on 2006-11-10 15:46:46 (Show Source): You can put this solution on YOUR website!Given f(x) = –2x + 4, find f(a – 2). Replace x with (a-2) in f(x): f(a-2)=-2(a-2)+4 f(a-2)=-2(a)-2(-2)+4 f(a-2)=-2a+4+4 f(a-2)=-2a+8 : Happy Calculating!!!
 Linear-systems/60798: Solve the system by addition. x + y = 4 x – y = 101 solutions Answer 41768 by funmath(2925)   on 2006-11-10 15:40:15 (Show Source): You can put this solution on YOUR website!Solve the system by addition. Add the two equations and the y's are eliminated. Now you can solve for x. x + y = 4 x – y = 10 _____________ 2x+0=14 2x=14 2x/2=14/2 x=7 : Let x=7 in either equation and solve for y. I'm using the first one. 7+y=4 -7+7+y=4-7 y=-3 : The solution is (x,y)=(7,-3) HGappy Calculating!!!
 Linear-equations/60810: How does the graph of the quadratic function or the absolute value function change if you subtract something from them?1 solutions Answer 41764 by funmath(2925)   on 2006-11-10 15:33:54 (Show Source): You can put this solution on YOUR website!How does the graph of the quadratic function or the absolute value function change if you subtract something from them? They cause a vertical shift down that many units. y=x^2 and y=x^2-3 are graphed below the -3 caused a vertical shift down 3 units Y=|x| and y=|x|-3 are graphed below and the -3 caused the same vertical shift down three units. : When the 3 is subtracted from the x it causes a horizontal shift to the right three units. y=x^2 and y=(x-3)^2 are graphed below. y=|x| and y=|x-3| are graphed below. Happy Calculating!!!
 Linear-systems/60805: graph each system of equations and describe it as consistent and independent,consistent and dependent, or inconsistent. y=-x-2 x+y=-4 1 solutions Answer 41755 by funmath(2925)   on 2006-11-10 15:01:22 (Show Source): You can put this solution on YOUR website!graph each system of equations and describe it as consistent and independent,consistent and dependent, or inconsistent. y=-x-2 x+y=-4 : For y=-x-2 Let x=0 and y=? y=-(0)-2 y=-2 Plot (0,-2) Now let x=-2 and y=? y=-(-2)-2 y=2-2 y=0 Plot (-2,0) Connect the points and you have this line. For x+y=-4 Let x=0 and y=? (0)+y=-4 y=-4 Plot (0,-4) Let y=0 and x=? x+(0)=-4 x=-4 Plot (-4,0) Connect the points and you have a second line. Notice that the lines a parallel and will never intersect. This system has no solution and is inconsistent (and independent). Happy Calculating!!!
 Radicals/60809: I have tried this problem a million times and I can not get the answer that the book gives, can someone please show me??? the book says that the answer is 21 solutions Answer 41754 by funmath(2925)   on 2006-11-10 14:51:09 (Show Source): You can put this solution on YOUR website! (a-2)(a-18)=0 a-2=0 and a-18=0 a=2 and a=18 Check for extraneous solutions: a=2 is a valid solution. a=18 is extraneous. The only valid solution is a=2. Happy Calculating!!!
 Polynomials-and-rational-expressions/60726: Solve: (a+b)^3 Thanks1 solutions Answer 41698 by funmath(2925)   on 2006-11-09 19:44:08 (Show Source): You can put this solution on YOUR website!Solve: (a+b)^3 Most people end up having to memorize this, this is how you derive it. (a+b)(a+b)(a+b) Multiply the second two. (a+b)(a^2+ab+ab+b^2) (a+b)(a^2+2ab+b^2) distribute the a then the b from the first parentheses. a(a^2+2ab+b^2)+b(a^2+2ab+b^2) a^3+2a^2b+ab^2+a^2b+2ab^2+b^3 a^3+2a^2b+a^2b+ab^2+2ab^2+b^3 a^3+3a^2b+3ab^2+b^3 If you're in algebra II it's worth memorizing. Happy Calculating!!!
 Trigonometry-basics/60592: use the reference angles to find the exact value of the expression: csc 4pi over 31 solutions Answer 41695 by funmath(2925)   on 2006-11-09 19:27:07 (Show Source): You can put this solution on YOUR website!use the reference angles to find the exact value of the expression: This falls in Quad. III, sine and its reciprocal is negative there. csc(= = = Happy Calculating!!!
 Polynomials-and-rational-expressions/60705: Hey!..can u please help me with this problem?..it has to be factored completely. 8b^2+12b+4 thanks!1 solutions Answer 41691 by funmath(2925)   on 2006-11-09 19:15:14 (Show Source): You can put this solution on YOUR website!factor completely. 2b*b=2b^2 and 1*1=1 and 2b*1+b*1=3b, so Happy Calculating!!!
 Polynomials-and-rational-expressions/60723: multiplying polynomials r^3(2r^2-5r-1)1 solutions Answer 41688 by funmath(2925)   on 2006-11-09 19:08:12 (Show Source): You can put this solution on YOUR website! multiplying polynomials Happy Calculating!!!
 Quadratic_Equations/60718: 6x2 - 13x + 6 = 01 solutions Answer 41686 by funmath(2925)   on 2006-11-09 19:01:53 (Show Source): You can put this solution on YOUR website!6x^2-13x+6=0 We need to factor the left side which is in standard form: a=6, b=-13, and c=6 Replace the middle term with two numbers that multiply to give you a*c=6*6=26, but add to give you b=-13. -4*-9=36 and -4+-9=-13 6x^2-4x-9x+6=0 Factor by grouping (6x^2-4x)+(-9x+6)=0 group 2x(3x-2)-3(3x-2)=0 factor out the GCF in each group (3x-2)(2x-3)=0 Factor the 3x-2 out of each. 3x-2=0 and 2x-3=0 3x=2 and 2x=3 3x/3=2/3 and 2x/2=3/2 x=2/3 and x=3/2 Happy Calculating!!!
 Equations/60719: how do you solve a problem like this: 3m=(-84)1 solutions Answer 41681 by funmath(2925)   on 2006-11-09 18:49:58 (Show Source): You can put this solution on YOUR website!how do you solve a problem like this: 3m=(-84) Notice that this means 3 times a number = -84. To isolate the m we need to do the opposite of 3 times on both sides of the equation. We divide both sides of the equation byt 3. : Sanity Check, do both sides of the = sign equal when m=-28? 3(-28)=-84 -84=-84 We're right. Happy Calculating!!!
 Inverses/60712: This question is from textbook What would a x value, that is undefined, be for the equation y=2/(1-2x)?1 solutions Answer 41679 by funmath(2925)   on 2006-11-09 18:42:51 (Show Source): You can put this solution on YOUR website!What would a x value, that is undefined, be for the equation y=2/(1-2x)? The fraction is undefined when the denominator=0 1-2x=0 -2x=-1 -2x/-2=-1/-2 x=1/2 The equation is undefined when x=1/2 Happy Calculating!!!
 Numeric_Fractions/60715: This question is from textbook algebra 1/2 I need help in figuring out these kind of problem please. can I get a example of how to do this. problem 12/16 times 4/3 divided by 5/6. 1 solutions Answer 41678 by funmath(2925)   on 2006-11-09 18:39:14 (Show Source): You can put this solution on YOUR website!12/16 times 4/3 divided by 5/6 divided by : If your observant it's faster to reduce first. Happy Calculating!!!
 Quadratic-relations-and-conic-sections/60702: I need to graph each function y=x2-5x+6 (I tried to subscript the 2 but it didnt work) f(x)=x2+4 (I tried to subscript the 2 but it didnt work) 1 solutions Answer 41673 by funmath(2925)   on 2006-11-09 18:26:02 (Show Source): You can put this solution on YOUR website!Graph each function y=x^2-5x+6 <--you can use ^ to raise something to a power. This is a parabola. Because x^2 is positive, we know it opens up. The y-intercept can be found by letting x=0 y=0^2-5(0)+6 y=0+0+6 y=6 Plot (0,6) : To find the x-intercept, let y=0 0=x^2-5x+6 0=(x-3)(x-2) x-3=0 and x-2=0 x=3 and x=2 Plot (3,0) and (2,0) The axis of symmetry and x coordinate of the vertex can be found using the formula a=1, b=-5, and c=6 x=2.5 y=6.25-12.5+6 y=-.25 Plot (2.5,-.25) You now know that it looks like this. : f(x)=x^2+4 x^2 is positive, so it opens up. The y-intercept is: f(0)=0^2+4 f(0)=4 Plot (0,4) : There is no x-intercept because 0=x^2+4 has no real solution. : The vertex is the y intercept because there's no b. Because you only know one point. Plot some points on the left and right side of x=0. f(1)=1^2+4 f(1)=1+4 f(1)=5 Plot (1,5) f(-1)=(-1)^2+4 f(-1)=1+4 f(-1)=5 Plot(-1,5) I'll let you find and plot f(-2) and f(2). Connect your points and you have: Happy Calculating!!!
 Linear-systems/60700: In the equation x/2 + y/3 = 1, how do you find the x and y intercepts?1 solutions Answer 41669 by funmath(2925)   on 2006-11-09 17:57:08 (Show Source): You can put this solution on YOUR website!In the equation x/2 + y/3 = 1, how do you find the x and y intercepts? Let x=0 and solve for y to get the y-intercept. The y-intercept is (0,3) Let y=0 and solve for x to get the x-intercept. The x-intercept is (2,0) Here's what it looks like graphically, notice the line crosses the y axis at (0,3) and the x axis at (2,0). Happy Calculating!!!
 Exponents/60664: PLEASE HELP SOLVE: (3PQ)Q^2 / 6P^2 Q^41 solutions Answer 41668 by funmath(2925)   on 2006-11-09 17:48:42 (Show Source): You can put this solution on YOUR website! Happy Calculating!!!