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# Recent problems solved by 'MathLover1'

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 Trigonometry-basics/682391: solution set for cos(theta/2)=1/2 where theta is greater than or equal to 0 and less than 2pi1 solutions Answer 423171 by MathLover1(6638)   on 2012-11-18 18:58:28 (Show Source): You can put this solution on YOUR website! , ,
 test/682350: 2 and 2/3 divided by 1/3.. Could you please show me how to do this equation 1 solutions Answer 423134 by MathLover1(6638)   on 2012-11-18 17:07:04 (Show Source): You can put this solution on YOUR website! first writ and as or then divided by ..multiply outer terms of fractions and write a product as a nominator, and a product of inner terms as a denominator =....simplify = = =
 Equations/682249: Find values for m and b in the following system so that the solution to the system is (–4, 5). mx + 5y = 21 and –4x – 4y = b1 solutions Answer 423112 by MathLover1(6638)   on 2012-11-18 14:59:05 (Show Source): You can put this solution on YOUR website!(,)= (,) .......eq. 1 and ....eq. 2 __________________________________ .......eq. 1..plug in and .......solve for .....plug in and ......solve for
 Quadratic_Equations/682268: Greetings, I am doing homework on a website. Here is the problem: Write a quadratic function to model the graph (a graph is provided but is not vital for the tutor to understand my question.). The coordinates of the vertex are (h,k)= (3,2) when substituted the values into the equation the equation becomes Why is h=3 in the ordered pair of the vertex but it is 9 in the vertex form equation? 1 solutions Answer 423110 by MathLover1(6638)   on 2012-11-18 14:47:03 (Show Source): You can put this solution on YOUR website! whoever put it in the vertex form equation is wrong if you are given the equation and the vertex at (,)= (,), means that and then you have , NOT ; here is squared and that is incorrect
 Age_Word_Problems/682258: the sum of anna's and jeff's age is 23. the product is 132. anna is one year younger. how old is anna1 solutions Answer 423109 by MathLover1(6638)   on 2012-11-18 14:35:06 (Show Source): You can put this solution on YOUR website! let be anna's and jeff's age given: anna is one year younger; means .............1 the sum of anna's and jeff's age is , means .......substitute from 1 ....solve for .........anna's age so, if ........jeff's age check the product: the product is
 Divisibility_and_Prime_Numbers/682241: Compute 2007^2 − 1993^2. Compute the value of A divided by B given that A = 666666^6 and B = 222222^6 Compute 3200^8 − 3200^5 ---------------- 3200^5 − 3200^21 solutions Answer 423099 by MathLover1(6638)   on 2012-11-18 13:34:00 (Show Source):
 Triangles/682234: two triangles are similar and the ratio of the corresponding side is 1:3 . what is the ratio of their perimeter ? 1 solutions Answer 423093 by MathLover1(6638)   on 2012-11-18 13:08:26 (Show Source): You can put this solution on YOUR website! The ratio of the perimeters is the as the similarity ratio; so, it is .
 Miscellaneous_Word_Problems/682060: A donkey and a horse were carrying some bales of cloth. The donkey said to the horse "If you give me one of your bales, i shall carry half as much as you." If you give me one of yours, replied the horse, I will be carrying 3x's as much as you. How many bales was each animal originally carrying? THANKS FOR YOUR HELP!! 1 solutions Answer 423024 by MathLover1(6638)   on 2012-11-17 23:13:12 (Show Source): You can put this solution on YOUR website! a donkey carrying bales of cloth and a horse were carrying bales of cloth The donkey said to the horse "If you give me one of your bales, i shall carry half as much as you." ..............1 If you give me one of yours, replied the horse, I will be carrying 3x's as much as you. ..............2 solve the system: ..............1 ..............2 ______________________________ ..............1..both sides multiply by and solve for ....substitute in 2 ..............2..solve for ......the number of bales that donkey was carrying now find ......the number of bales that horse was carrying
 test/682050: the question says," sketch the ellipses. identify the center vertices and foci." 9(x+4)^2+(y+7)^2=81 (x-3)^2/9 + (y+3)^2/16 = 11 solutions Answer 423017 by MathLover1(6638)   on 2012-11-17 22:27:56 (Show Source): You can put this solution on YOUR website! , , , and Center: (, )=(, ) Vertices: (-4, -7 ± 9) or (,), (,) Co-vertices: (-4 ± 3, -7) or (,), and (,) Length of Major Axis: Length of Minor Axis: 2. , , , and Center: (, )=(, ) Vertices: (3, -3 ± 4) or (,), (,) Co-vertices: (3 ± 3, -3) or (,), and (,) Length of Major Axis: Length of Minor Axis:
Functions/682023: whats the domain and range of the function. f(x)= 3/5x^2
1 solutions

Answer 422982 by MathLover1(6638)   on 2012-11-17 20:12:38 (Show Source):
You can put this solution on YOUR website!
if you have

 Solved by pluggable solver: Plot a graph of any function AND its DOMAIN Here's a graph of function (3/5x^2). The domain is shown on the x axis by a green horizontal line.

the domain:
and
the range:

but, if you have

 Solved by pluggable solver: Plot a graph of any function AND its DOMAIN Here's a graph of function ((3/5)x^2). The domain is shown on the x axis by a green horizontal line.

the domain:
and
the range:

 Linear-systems/681944: How would you solve the substitution equation: x+y=1 X^2+xy-y^2=-1 Thank you.1 solutions Answer 422970 by MathLover1(6638)   on 2012-11-17 19:07:52 (Show Source): You can put this solution on YOUR website!...............1 ........2 _________________________________ ...............1...solve for .......substitute in 2 ______________________________ ........2 .........solve for ...use quadratic formula solutions: and now find if : if : so, solution pairs are: 1. and 2. and
 test/681992: it says, "Sketch the graphs, using the function and three points: two roots and the turning point. f(x)= x^2-2x-8 f(x)= x^2-2x-151 solutions Answer 422938 by MathLover1(6638)   on 2012-11-17 17:47:16 (Show Source): You can put this solution on YOUR website!1. ...factor completely, replace with .......group ....set if ..=>... if ..=>... so, the roots are and and points are (,) and (,) let , solve for and find third point so, third point is (,) now, graph it 2. ...factor completely, replace with .......group ....set if ..=>... if ..=>... so, the roots are and and points are (,) and (,) let , solve for and find third point so, third point is (,) now, graph it
 Permutations/681934: we want to form a 4 letter password using letters from A,B,C,D,E,F without repetition, what is the probability that the first letter of the password is A and the last letter is F??1 solutions Answer 422868 by MathLover1(6638)   on 2012-11-17 14:47:01 (Show Source): You can put this solution on YOUR website!4 letter password using letters from A,B,C,D,E,F By assuming that the first letter is "A", and the last letter is “F", Therefore, one has to find two more letters from the remaining 4 letters. Of the 4 letters, there are 1 B, 1 C, 1 D, and 1 E . The second and third positions can have two different letters. When the two letters are different. One has to choose two different letters from the 4 available different choices. This can be done in 4 * 3=12 ways. Total number of possibilities is 12. 1. A,B,C,F 2. A,C,B,F 3. A,B,D,F 4. A,D,B,F 5. A,C,D,F 6. A,D,C,F 7. A,C,E,F 8. A,E,C,F 9. A,D,E,F 10. A,E,D,F 11. A,B,E,F 12. A,E,B,F
 Radicals/681910: square root of x divided by the cube root of x1 solutions Answer 422855 by MathLover1(6638)   on 2012-11-17 10:49:34 (Show Source): You can put this solution on YOUR website! or, you can do it this way:
 �t�e�s�t/681906: A radioactive isotope decays at a rate that is modeled by the following formula. A(t) = 30e^ -.001t 1. How much material was present initally ? 2. How much will be present in 2000 years ? 1 solutions Answer 422848 by MathLover1(6638)   on 2012-11-17 10:26:27 (Show Source): You can put this solution on YOUR website! ..........lambda=λ where: = the activity = the activity at time, 1. How much material was present initially ? 2. How much will be present in 2000 years ? if ..............
 Exponents/681869: (5x^-3 yz^2)^-2 please tell how to solve1 solutions Answer 422842 by MathLover1(6638)   on 2012-11-17 09:16:49 (Show Source):
 test/681890: what is natural numbers1 solutions Answer 422839 by MathLover1(6638)   on 2012-11-17 08:57:07 (Show Source): You can put this solution on YOUR website! The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... or to the set of nonnegative integers 0, 1, 2, 3, ... e.g., Regrettably, there seems to be no general agreement about whether to include 0 in the set of natural numbers. In fact, Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 in P." The set of natural numbers (whichever definition is adopted) is denoted N. Due to lack of standard terminology, the following terms and notations are recommended in preference to "counting number," "natural number," and "whole number." set................................ name.............. symbol ..., -2, -1, 0, 1, 2, ......... integers.......... Z 1, 2, 3, 4, ............ positive integers.. Z-+ 0, 1, 2, 3, 4, .......... non-negative integers... Z-* 0, -1, -2, -3, -4, ......... non-positive integers...... -1, -2, -3, -4, ........... negative integers......... Z--
 test/681888: natural numbers1 solutions Answer 422838 by MathLover1(6638)   on 2012-11-17 08:55:57 (Show Source): You can put this solution on YOUR website! The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... or to the set of nonnegative integers 0, 1, 2, 3, ... e.g., Regrettably, there seems to be no general agreement about whether to include 0 in the set of natural numbers. In fact, Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 in P." The set of natural numbers (whichever definition is adopted) is denoted N. Due to lack of standard terminology, the following terms and notations are recommended in preference to "counting number," "natural number," and "whole number." set................................ name.............. symbol ..., -2, -1, 0, 1, 2, ......... integers.......... Z 1, 2, 3, 4, ............ positive integers.. Z-+ 0, 1, 2, 3, 4, .......... non-negative integers... Z-* 0, -1, -2, -3, -4, ......... non-positive integers...... -1, -2, -3, -4, ........... negative integers......... Z--
 Triangles/681728: Triangle JKL and triangle MNO are similar triangles. What is the measure of side OM? Please Help Me!!1 solutions Answer 422793 by MathLover1(6638)   on 2012-11-16 21:00:12 (Show Source): You can put this solution on YOUR website!.. as you can see, if two triangles are similar, their sides are proportional; so, the measure of side is proportional to the measure of side
 Quadratic-relations-and-conic-sections/681711: I need help with the following. Graph the Elipse I have already tried and cannot get it.1 solutions Answer 422772 by MathLover1(6638)   on 2012-11-16 18:45:07 (Show Source): You can put this solution on YOUR website!Vertical Ellipse .......both sides divide by , so you have , , , and Center: (, )=(, ) Vertices: (, ± ) or (,), (,) Co-vertices: ( ± ,) or (,), and (,) Length of Major Axis: Length of Minor Axis:
 Complex_Numbers/681626: The square root of -2891 solutions Answer 422713 by MathLover1(6638)   on 2012-11-16 12:02:54 (Show Source):
 Travel_Word_Problems/681621: If i am Traveling At 20 feet per second How many MPH am i going?1 solutions Answer 422709 by MathLover1(6638)   on 2012-11-16 11:43:19 (Show Source): You can put this solution on YOUR website! first convert into : so calculate the number of miles in : now convert into : plug both values in your formula:
 Equations/681560: What is the X and y intercept of 4x=7y+9?1 solutions Answer 422689 by MathLover1(6638)   on 2012-11-16 08:25:49 (Show Source): You can put this solution on YOUR website!you will find the and intercept of if you set and solve for , then set and solve for if or .....so, the intercept is at (,) if or .......and the intercept is at (,) let's check it on a graph
 Conjunction/681470: Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. Show complete work and submit your solution to the Dropbox. I) If the cat does not have claws, then the cat cannot scratch the furniture. II) If the cat can scratch the furniture, then the cat has claws. III) If the cat has claws, then the cat can scratch the furniture. a. I and II are equivalent b. I and III are equivalent c. II and III are equivalent d. I, II, and III are equivalent e. None are equivalent (Points : 4) 1 solutions Answer 422672 by MathLover1(6638)   on 2012-11-15 22:47:24 (Show Source): You can put this solution on YOUR website!the statements are: I) If the cat does not have claws, then the cat cannot scratch the furniture. II) If the cat can scratch the furniture, then the cat has claws. III) If the cat has claws, then the cat can scratch the furniture. you can solve this using truth tables. you would do so as follows: p = cat has claws q = cat scratches furniture ~p->~q = I q->p = II p->q = III truth table: p q ~p ~q ~p->~q q->p p->q T T F F T T T T F F T T T F F T T F F F T F F T T T T T  from the truth tables, it appears that ~p->~q is equivalent to q->p because their truth tables are the same. that means that I is equivalent to II III is not equivalent to either one of them because its truth table is different. if we examine the statement, we will see why this is so. the statement are, once again: I) If the cat does not have claws, then the cat cannot scratch the furniture. II) If the cat can scratch the furniture, then the cat has claws. III) If the cat has claws, then the cat can scratch the furniture. statement II looks like it is the contrapositive of statement I. statement I says: if no claws, then no scratch furniture. statement II says: if scratch furniture, then claws. if the statement is: if no claws, then no scratch furniture then the contrapositive to that statement is: if scratch furniture, then claws. if the statement is: if scratch furniture, then claws then the contrapositive to that statement is: if no claws, then no scratch furniture. the statement and its contrapositive are equivalent which means if the statement is true then the contrapositive is also true and vice versa. this is the case between statements I and II. statement III says: if claws, then scratch furniture. the contrapositive to this would be. if no scratch furniture, then no claws. all 3 statements are: I = if no claws, then no scratch furniture II = if scratch furniture, then claws. III = if claws, then scratch furniture. the contrapositive to statement III is: if no scratch furniture, then no claws neither I or II are the contrapositive to statement III, therefore the only equivalent statement are I and II. It's a little convoluted, but that's the way it works out. Use of the truth tables can make sense of the insensible, assuming you know how to use them. p->q is only false if p is true and q is false. q->p is only false if q is true and p is false. ~p->~q is only false if ~p is true and ~q is false. ~q->~p is only false if ~q is true and ~p is false. that's the truth table for the implied statement.l
 Points-lines-and-rays/680995: Sixty concurrent lines in a plane divide the plane into how many regions?1 solutions Answer 422546 by MathLover1(6638)   on 2012-11-15 11:03:30 (Show Source): You can put this solution on YOUR website!three or more lines in a plane are said to be concurrent if they intersect at a single point lines divide the plane into regions check for line .....it’ true that one line divides the plane into two regions check for lines .....it’ true that two lines divides the plane into four regions check for lines .....it’ true that two lines divides the plane into six regions so, now we can check for lines ....so, lines divides the plane into regions
 Numeric_Fractions/680994: 22 cups for 4 people as a fraction in lowest terms1 solutions Answer 422542 by MathLover1(6638)   on 2012-11-15 10:12:21 (Show Source): You can put this solution on YOUR website! cups for people: divide by ....simplify, divide both and by
 Geometry_Word_Problems/680978: if the diagonal of a square garden is 16ft , what is the exact measure of each side1 solutions Answer 422541 by MathLover1(6638)   on 2012-11-15 09:59:57 (Show Source): You can put this solution on YOUR website! two sides of a square along with the diagonal of a square form right angle triangle so, if the of a square garden is , the exact measure of each side could be found using Pythagorean theorem: .....plug in
Equations/680980: what is the answer to 2x-3y=-1 y=x-1
1 solutions

Answer 422540 by MathLover1(6638)   on 2012-11-15 09:43:55 (Show Source):
You can put this solution on YOUR website!

you have a system of linear functions and solution will be coordinates (,) of their intersection point

.....=>......

 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 Add to 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)

Linear-equations/680824: I need to write an equation in point intercept form for the line that is parallel to the given line and that passes through the given point for 4y=x (4,0) I got y=1/4x-0. is that correct?
1 solutions

Answer 422478 by MathLover1(6638)   on 2012-11-14 21:52:09 (Show Source):
You can put this solution on YOUR website!
given:
line that passes through (4,0)
you got which is slope-intercept form where slope and y-intercept is
now find an equation in point-intercept form for the line that is parallel to the given line and that passes through the given point

 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 (4,0), 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 (,)

 logarithm/680759: log 4 base 81 solutions Answer 422472 by MathLover1(6638)   on 2012-11-14 21:44:25 (Show Source):
 Quadratic_Equations/680405: A toy rocket is launched from ground level. Its distance in feet from the ground in t seconds is given by the formula s(t)=-16t^2+208t (a) make a sketch of what is happening (b) When will the rocket be 550 feet from the ground (c) After how many seconds will the rocket strike the ground?1 solutions Answer 422327 by MathLover1(6638)   on 2012-11-14 13:24:14 (Show Source): You can put this solution on YOUR website! (a) make a sketch of what is happening (b) When will the rocket be 550 feet from the ground solution: .........the rocket be 550 feet from the ground when it goes up or ........the rocket be 550 feet from the ground when it goes down after it reaches maximum height (c) After how many seconds will the rocket strike the ground? solution: or .......the rocket strike the ground in ; on a graph, that will be a point (,)