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Numbers_Word_Problems/214696: A total of 54 monks and clerics were in the tower. If three times the number of clerics exceeded the number of monks by ten, how many of each were in the tower? 1 solutions Answer 162131 by solver91311(16897)   on 2009-09-18 14:43:08 (Show Source): You can put this solution on YOUR website! Let represent the number of clerics Let represent the number of monks Then and Solve the system for and . HINT: Use the elimination method. John

Graphs/214192: Find an equation for the circle: the points (6,5), (7,2), (9,6), and (10,3) are verices of an inscribed square 1 solutions Answer 162098 by solver91311(16897)   on 2009-09-18 10:52:44 (Show Source): You can put this solution on YOUR website! If a square is inscribed in a circle, a diagonal of the square is a diameter of the circle. The midpoint of a diameter is the center of a circle. The segment with endpoints (6,5) and (10,3) is a diagonal of the square. Use the midpoint formula: and and So the midpoint of the diagonal, hence the midpoint of a diameter, hence the center of the circle is at (8, 4) The measure of a radius of the circle is the distance from the center to any of the four vertices. Use the distance formula: The equation of a circle with center at and radius is: So: John

Linear-systems/214520: Hello im having trouble coming up with the second equation and solving this please help:] the terminal tower is 242 ft. shorter than the key tower. the total heights of the two buildings is 1658. what are the heights of both buildings. this is the equation i got x+y= 1658 please help me find the second equation 1 solutions Answer 162040 by solver91311(16897)   on 2009-09-17 19:31:47 (Show Source): You can put this solution on YOUR website! Presuming that represents the height of the terminal tower, you could say: John

Numeric_Fractions/207612: Roots A.)Find each root - sq root 25 B) Quotient Rule for Radicals Simplify each radical. All variables represent positive real numbers. ^3sq root -27y^36 over 1000 C) Rational Exponents Evaluate each expression. (-16)^ one fourth D)Simplify each expression. Write your answers with positive exponents. Assume that all variables represent positive real numbers. (-27x^9)^ one third E)Simplify each expression. Write your answers with positive exponents. Assume that all variables represent positive real numbers. (-27x^9)^ one third F)Adding and Subtracting Radicals All variables in the following exercises represent positive numbers. Simplify the sums and differences. Give exact answers. sq root 5 - 3 sq root 5 G)Simplify each expression. (3 - 2sq root 7)(3 + 2sq root 7) H)Simplifying Radicals Write each radical expression in simplified radical form. sq root 2 over sq root 18 I)Simplify sq root 6 over sq root 7 . sq root 14 over sq root 3 J)The Even-Root Property Find all real solutions to each equation. A^2 – 40 = 0 K)Equations Involving Radicals Solve each equation and check for extraneous solutions. 3 sq root w + 1 = 6 L)Find all real or imaginary solutions to each equation. Use the method of your choice. W^2 = -225 M)Find all real or imaginary solutions to each equation. Use the method of your choice. sq root 7x + 29 = x + 3 N)Solve each equation by using the quadratic formula. X^2 + 4x + 3 = 0 O)Number of Solutions Find b^2 – 4ac and the number of real solutions to each equation -3x^2 + 7x = 0 P)Equations Quadratic in form X^2 + x + sq root x^2 + x - 2 = 0 Q)Find all real and imaginary solutions to each equation. B^4 + 13b^2 + 36 = 0 1 solutions Answer 162039 by solver91311(16897)   on 2009-09-17 19:29:29 (Show Source): You can put this solution on YOUR website! Whatever gave you the idea that someone was going to do your entire homework assignment for you? John

Equations/214516: A block of platinum is 21.45g/cm^3. Calculate its density in kilograms per cubic meter. 1 solutions Answer 162038 by solver91311(16897)   on 2009-09-17 19:24:19 (Show Source): You can put this solution on YOUR website! This is a question for a Chemistry site. John

Triangles/214506: This question is from textbook The lengths of the sides of an isosceles triangle are represented by 2x + 5, 2x - 6, and 3x-3. What are the lengths of the sides of the triangle? 1 solutions Answer 162035 by solver91311(16897)   on 2009-09-17 19:23:31 (Show Source): You can put this solution on YOUR website! If this is an isosceles triangle, then two of the sides must be equal to each other. That is an absurdity, no value of x makes the statement true, so those are not the two equal sides. The side of a triangle cannot have a negative measure, so those are not the two equal sides. So these are the equal sides and they measure 21. The third side is John

Length-and-distance/214514: Consumer Application: Televisions and computer screens are usually advertised based on the length of their diagonals. If the height of a computer screen is 11in. and the width is 14in., What is the length of the diagonal? Round to the nearest inch. 1 solutions Answer 162032 by solver91311(16897)   on 2009-09-17 19:13:16 (Show Source): You can put this solution on YOUR website! Presuming the screen is a rectangle and therefore has right angle corners, Pythagoras says: You can run a calculator as well as I can. John

Equations/214510: What periodic element has an atomic number of 11, a mass number of 23, 11 protons, 10 electrons, 12 neutrons, and a net charge of 1+? 1 solutions Answer 162030 by solver91311(16897)   on 2009-09-17 19:11:16 (Show Source): You can put this solution on YOUR website! Don't know. Go find a Chemistry site and ask them. John

Miscellaneous_Word_Problems/214513: The caterer for your class picnic charges $1 for each hot dog and $2 for each hamburger. You have $48 to spend. Write a model that shows the different numbers of hot dogs and hamburgers that you could purchase. 1 solutions Answer 162029 by solver91311(16897)   on 2009-09-17 19:10:03 (Show Source): You can put this solution on YOUR website! John

Rectangles/214496: This question has been killing me for 2 hours now, please help: A rectangular sheet of tin is 15cm long and 9cm wide. A uniform strip is to be cut off around the sheet. The remaining area is to be 112cm^2. Calculate the width of the strip. 1 solutions Answer 162026 by solver91311(16897)   on 2009-09-17 19:08:16 (Show Source): You can put this solution on YOUR website! If the uniform width is then the new length and width must be and . The area is the length times the width, so: In standard form: Solve the quadratic for . You will get two roots. One of them is larger than 9, so twice that, subtracted from either 9 or 15 is less than zero. Exclude that root. The other one is your answer. John

Travel_Word_Problems/214475: boat travels 135 miles upstream, then back, in 24 hours. Current is 3 mph. What is the boat's still speed? 1 solutions Answer 162004 by solver91311(16897)   on 2009-09-17 18:08:12 (Show Source): You can put this solution on YOUR website! Use distance = rate times time, or Describe the upstream trip. The upstream trip is against the current, so the actual rate of travel is the boat's still water speed () minus the current, so . We can say that the upstream trip took hours, giving us: Describe the downstream trip. The downstream trip is with the current, so the actual rate of travel is the boat's still water speed plus the current, so . If the upstream trip took hours and the entire trip took 24 hours, then the downstream trip must have taken hours, giving us: Solve the two equations for : Now we have two expressions in both equal to , so set them equal to each other: Apply the LCD of : Combine everything on the left: Combine the numerators: Multiply both sides by the denominator, leaving you with a quadratic in . It is ugly, but it does factor. Solve the quadratic for and exclude the negative root (the boat certainly doesn't go backwards in still water). The positive root is the boat's still water speed. John

Geometry_proofs/214429: Given: in ΔXYZ, ∠XYZ is a right angle. Prove: ∠YXZ and ∠YZX are complementary. 1 solutions Answer 162000 by solver91311(16897)   on 2009-09-17 17:32:00 (Show Source): You can put this solution on YOUR website! The sum of the measures of the interior angles of any triangle is 180° A right angle measures 90°, so in any right triangle, the sum of the two acute angles must be 180° - 90° = 90°. The sum of the measures of two angles is 90° if and only if the two angles are complementary. John

Angles/214469: 2 angles are supplementary. one angle is 36 more than the other one. find the 2 angles. 1 solutions Answer 161999 by solver91311(16897)   on 2009-09-17 17:27:17 (Show Source): You can put this solution on YOUR website! Let represent one of the angles. The other is . The sum of the measures of two supplementary angles is 180° Solve for to get the smaller angle, add 36 to get the other one. You could also have done: In which case would be the larger angle and subtracting 36 would give you the smaller one. John

Numbers_Word_Problems/214461: The Square of a positive number is six more then five times the positive number, find the number. 1 solutions Answer 161998 by solver91311(16897)   on 2009-09-17 17:21:55 (Show Source): You can put this solution on YOUR website! Let represent the positive number. Then represents the square of the positive number, represents five times the positive number and represents six more than that, and is means "=", so: Put the equation into standard form and then solve for . HINT: This one factors quite tidily. Exclude the extraneous negative root. John

Rectangles/214435: A rectangular bedroom is 7ft longer than it is wide. It's area is 228 ft^2. What are it's dimensions? 1 solutions Answer 161997 by solver91311(16897)   on 2009-09-17 17:15:11 (Show Source): You can put this solution on YOUR website! Let represent the width. Then must represent the length. The area is the product of the length times the width, so: Put it in standard form and then solve the quadratic for . Exclude the extraneous negative root. The positive root will be the width. Add 7 to get the length. John

Length-and-distance/214464: chapter 2 section 2 "definitions and biconditional statements" question... give a counterexample that demonstrates that the converse of the statement is false. problume... if an angle measures 94*, then it is obtuse. my actaully quetion... i cant figure out how to make this false. 1 solutions Answer 161996 by solver91311(16897)   on 2009-09-17 17:10:31 (Show Source): You can put this solution on YOUR website! Given the statement "if then ", the converse of the statement is "if then " In your case, you have If an angle measures 94°, then it is obtuse. So your is "an angle measures 94°" and your is "it is obtuse" Knowing that, let's construct the converse: If an angle is obtuse, then it measures 94° Counter example: 110° is an obtuse angle that does not measure 94° John

Miscellaneous_Word_Problems/214462: Please help me I cannot figure this one out. Going into the final exam, Joann has test scores of 80,84,71,65,and 90. If the final exam is 45% of the overall grade, what does Joann have to score to have a final average of 87? I will appreciate this so much if you could help me. Thank you. 1 solutions Answer 161992 by solver91311(16897)   on 2009-09-17 16:57:32 (Show Source): You can put this solution on YOUR website! If the weight of the final exam is 45%, then the weight of all the other exams must be 55%. Since there are 5 other exams, each of them is worth 55 divided by 5 equals 11%. So you can write the following equation: Solve for and you have your answer. She is going to have to do a LOT better than what she averaged on the first 5 exams. John

Angles/214455: 1) angle 1 is complementary to angle 3,angle 2 is complementary to angle 3. if the measure of angle 2=x+24 and the measure of angle 3=8x-6 what is the measure of angle 1 2)Which of the following statements is not true? A) if x=4, then x^2=6. B) if x^3=-27, then x=3. C) if x=2, then x^2=4. D) If x^2=49 then x=7 1 solutions Answer 161987 by solver91311(16897)   on 2009-09-17 16:34:58 (Show Source): You can put this solution on YOUR website! If both and are complementary to , then . Since and , and they are complementary we can say: Which is to say: Hence and therefore As for your second question, I think you meant which one is true because three of the given statements are false (A, B, and D) and only one is true (C). A: If , then B: If , then C: If , then True D: If , then Half right, therefore half wrong, therefore False John

Numbers_Word_Problems/214452: please help me...I am 2 numbers.The sum of my 2 numbers is 100.The difference between my two numbers is 24. What am I? 1 solutions Answer 161979 by solver91311(16897)   on 2009-09-17 16:06:37 (Show Source): You can put this solution on YOUR website! Let represent one of the numbers. Let represent the other one. Solve the system for and and you have your answer. HINT: Use the elimination method. John

Rectangles/214364: question about angels, opposite sides, opposite angels, parallel sides, congruent sides and congruent angles 1 solutions Answer 161978 by solver91311(16897)   on 2009-09-17 16:02:30 (Show Source): You can put this solution on YOUR website! If you really have a question about angels, then you should consult your priest, minister, imam, or other local tribal shaman as befits your belief system. If you have a question about angles, someone here would be very happy to help you if you would only be so kind as to share the specific question with us. John

Geometry_Word_Problems/214444: To find the volume of a box, you can multiply its height, width and length. The measure of the volume of the box is 70. Find the possible dimensions. Thanks 1 solutions Answer 161976 by solver91311(16897)   on 2009-09-17 15:56:29 (Show Source): You can put this solution on YOUR website! Given that there are an infinite number of ordered triples that would satisfy the conditions of this problem even once you had chosen a unit of measure (the volume is 70 what?), it would take a VERY long time to answer you. John

Rational-functions/214439: please help me solve this equation y=3x+2 1 solutions Answer 161975 by solver91311(16897)   on 2009-09-17 15:52:10 (Show Source): You can put this solution on YOUR website! You cannot solve that equation. There are an infinite number of real number ordered pairs that satisfy the equation. You can draw a graph of the solution set, namely a line with slope 3 passing through (0, 2). Is that what you wanted? John

Rational-functions/214447: How do you find the local minimum, local maximum, absolute minimum, absolute maximum, and increasing and decreasing in a function? 1 solutions Answer 161972 by solver91311(16897)   on 2009-09-17 15:48:02 (Show Source): You can put this solution on YOUR website! If the first derivative of a function is positive over an interval, then the function is increasing on that interval. If the first derivative is negative over that interval, the function is decreasing over that interval. A critical point of a function is a point such that or does not exist. An absolute maximum or minimum over an interval is either a critical point in that interval or an endpoint of . If you have a continuous and twice differentiable function, take the first derivative, set it equal to zero, and then solve. The roots will be critical points that can be either local minima or local maxima. Now take the second derivative and evaluate it at the value of each root from the previous step. If the value of the 2nd derivative is positive, then the curve is concave up and you have a local minimum. If the 2nd derivative is negative, you have a local maximum. John

Polynomials-and-rational-expressions/214443: Find all numbers for which the rational expression is undefined. t^3-9t/t^2-16 1 solutions Answer 161969 by solver91311(16897)   on 2009-09-17 15:24:10 (Show Source): You can put this solution on YOUR website! A rational expression is undefined for any value of a variable that makes the denominator zero. The given rational expression is therefore undefined for the solution set of: Solve for both values of to get your answer. John

Complex_Numbers/214423: Add or subtract as indicated and write the result in a , b i form. (4 . 2i) , (2, 5i) 1 solutions Answer 161968 by solver91311(16897)   on 2009-09-17 15:21:48 (Show Source): You can put this solution on YOUR website! You have periods and commas where I would expect + and - signs. Which is which? John

Numbers_Word_Problems/214294: the tens digits of a two digit number is 3 more than 5 times the units digit. if the digits are reversed, the new number is 2 more than twice the tens digit of the original number. find the original number. 1 solutions Answer 161865 by solver91311(16897)   on 2009-09-16 20:59:56 (Show Source): You can put this solution on YOUR website! This one you can do in your head. Digits must be 9 or less. Since 5 times 2 is 10, the most that the units digit can be is 1. 5 times 1 is 5 plus 3 is 8, so your number is 81 -- or 5 times 0 is 0 plus 3 is 3, so your number is 30. Check 81: Twice the original 10s digit is 2 times 8 is 16. 2 more than that is 18 and that is the original number with the digits reversed. This one works. Check 30: Twice the original 10s digit is 2 times 3 is 6. 2 more than that is 5, which is not the original number reversed. This one doesn't work. The answer is 81. John

Angles/214297: Find the measure of an angle whose supplement is 10 degrees more than twice its complement. Let 90 - x equal the degree measure of its complement and 180-x equal the degree of measure of its supplement. how do I write the equation? 1 solutions Answer 161863 by solver91311(16897)   on 2009-09-16 20:52:16 (Show Source): You can put this solution on YOUR website! Just like it is written in words: An angle whose supplement () is (=) 10 more than (10 + ) twice its complement (). John

Polynomials-and-rational-expressions/214295: Factor the trinominal 2(m+p)^2-7(m+p)-30 1 solutions Answer 161858 by solver91311(16897)   on 2009-09-16 20:45:25 (Show Source): You can put this solution on YOUR website! Looks uglier than a mud fence. But a simple little substitution will help us tame this beast. Let , then Not so bad anymore, hmmm? We know that we need something that looks like or We know this because in order to get as a first term, one binomial has to have and the other must have as the first terms. We also know that the signs in the two binomials must be opposite because the constant term of the trinomial is negative. We have several choices for factors of -30: -5 and 6, 5 and -6, -3 and 10, 3 and -10, -2 and 15, 2 and -15, -1 and 30, 1 and -30. 2 times one of the factors plus the other factor has to equal -7. Looking over the possibilities, it looks like 2 times -6 is -12 plus 5 is -7, so: Ah ha!! Now just substitute back: John

Linear-equations/214284: I tried to start it, but I really don't know what to do!? Write the slope for a perpendicular line. 2x+4y=8 and I have one more question if it's not to much. Find the equation of the line that is perpendicular to the line y=-1/3x+5 and goes through the point (1,2). -1/3 is a fraction thanks!! 1 solutions Answer 161848 by solver91311(16897)   on 2009-09-16 20:20:40 (Show Source): You can put this solution on YOUR website! The slopes of two lines perpendicular to each other are negative reciprocals. Write your equation in slope-intercept form, that is, solve for so it looks like this: . The part will be the slope. Take the negative of the reciprocal of that slope and you will have the slope of any line perpendicular to the given line. In your second problem, your given equation is already in slope-intercept form and we can see that the slope of that line is . The reciprocal of is -3 and the negative of that is 3, so we know that the slope of the desired line is 3. Now use the point-slope form of a line to derive the desired equation: Where is the slope and is the given point. Just substitute what you know: Now you can put it into whatever form your instructor requires -- or just leave it like it is. John

Circles/214271: Find the equation of each circle described. Passes through the origin and is concentric with the circle x^2-6x+y^2-4y+4=0 1 solutions Answer 161843 by solver91311(16897)   on 2009-09-16 20:01:15 (Show Source): You can put this solution on YOUR website! The equation of a circle centered at with radius is: Let's begin by determining the center of the given circle, which is the center of the circle we want because they are concentric. Take the equation of the given concentric circle: and complete both squares. First put the constant term on the right. Remember for a squared binomial, the third term of the resulting trinomial is one-half of the second term coefficient squared. -6 divided by 2 is -3; -3 squared is 9, so add 9 to both sides. And -4 divided by 2 is -2; -2 squared is 4, so add 4 to both sides. Now factor the two trinomials: Hence, the the given circle is centered at (3, 2) with radius 3. Since the desired circle passes through the origin, the line segment with endpoints at the origin and at (3, 2) is a radius of the desired circle. We need to know the measure of the radius which is the distance from (0, 0) to (3, 2). Use the distance formula: Now that we know the center and radius of the desired circle we can write the equation: Expand the binomials: Simplify: John

Word_Problems_With_Coins/214256: Two fifth of the coins are dimes. Half of the coins are pennies. The rest are nickles. What is the total value of the coins? 1 solutions Answer 161825 by solver91311(16897)   on 2009-09-16 19:25:40 (Show Source): You can put this solution on YOUR website! Depends. How many total coins are there? You did not share the entire problem. If there were 100 coins, you would have 40 dimes for $4.00, 50 pennies for $0.50, and 10 nickels for $0.50 making a total of $5.00, but if you only had 50 coins you would have 20 dimes for $2.00, 25 pennies for $0.25, and 5 nickels for $0.25 making a total of $2.50. That's only two examples out of an infinite number of possibilities. John