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solver91311 answered: 17063 problems
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Parallelograms/444485: "The pairs (-2, -3), (-2, 2), (4, -3) can serve as three of four vertices for three different parallelograms. Find the fourth vertex of each parallelogram." I am completely lost. I know the fourth set is (4, 2), but what else do I have to solve for? The question says 3 parallelograms? There is nothing in my book regarding this...help please? Liz 1 solutions Answer 306369 by solver91311(17077)   on 2011-05-03 16:41:04 (Show Source): You can put this solution on YOUR website! "I know the fourth set is (4,2)" is not precisely correct. What you know is that one possibility for the fourth ordered pair is (4,2). But how about (-8,2) which makes a different parallelogram with the three given points? There is yet another point that combines with the three given points to give yet another different parallelogram. I'll leave that to you to find. John My calculator said it, I believe it, that settles it

Numbers_Word_Problems/444464: the sum of two numbers is 25. One number is twice the second plus seven. What are the two numbers 1 solutions Answer 306363 by solver91311(17077)   on 2011-05-03 16:03:23 (Show Source): You can put this solution on YOUR website! Can't tell. Your problem statement is ambiguous. Do you mean that to obtain one of the numbers I have to multiply the other number by 2 and then add 7, or do I have to add 7 to the other number and then multiply that sum by 2. The way your problem is stated, it could be either way. One way has integer answers and the other way has rational answers, but you don't specify other than to say they are "numbers" which could be anything. John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/444435: 20. Solve the following inequality. x2 - 5x ≥ -6 A. [2, 3] B. (-∞, 2] or [3, ∞) C. [3, ∞) D. (-∞, 2] 21. Solve the following inequality. (a + 7)(a - 5)(a - 6) > 0 A. (-7, 5) or (6, ∞) B. (-∞, -7) or (5, 6) C. (-∞, 5) D. (6, ∞) 22. Solve the following inequality. x2 + 8x + 15 > 0 A. (-∞, -5) or (-3, ∞) B. (-3, ∞) C. (-∞, -5) D. (-5, -3) 23. Solve the following inequality. x3 + 4x2 - 45x > 0 A. (-5, 0) or (9, ∞) B. (-9, 0) or (5, ∞) C. (-9, ∞) D. (-∞,-9) or (0, 5) 1 solutions Answer 306360 by solver91311(17077)   on 2011-05-03 15:53:26 (Show Source): You can put this solution on YOUR website! No, we are not doing your whole assignment for you. Ask a specific question about a concept you don't understand, then we'll help. John My calculator said it, I believe it, that settles it

Inequalities/444434: 17. Solve the following inequality. x2 - 16 > 0 A. (-∞, -16) or (16, ∞) B. (-16, 16) C. (-∞, -4) or (4, ∞) D. (-4, 4) 18. Solve the following inequality. x2 - 49 ≤ 0 A. (-∞, -7] or [7, ∞) B. (-∞, -49] or [49, ∞) C. [-7, 7] D. [-49, 49] 19. Solve the following inequality. 30(x2 - 1) > 11x A. (- 6/5, 5/6) B. (-∞, -6/5) or (5/6, ∞) C. (-∞, - 5/6) or (6/5, ∞) D. (-5/6, 6/5) 1 solutions Answer 306359 by solver91311(17077)   on 2011-05-03 15:53:00 (Show Source): You can put this solution on YOUR website! No, we are not doing your whole assignment for you. Ask a specific question about a concept you don't understand, then we'll help. John My calculator said it, I believe it, that settles it

Inequalities/444431: Solve the following inequality. (x - 1)(x - 2) > 0 A. (2, ∞) B. (-∞, 1) or (2, ∞) C. (1, 2) D. (-∞, 1) 16. Solve the following inequality. x2 + 2x ≤ 0 A. (-∞, 0] or [2, ∞) B. (-∞, -2] or [0, ∞) C. [0, 2] D. [-2, 0] 1 solutions Answer 306358 by solver91311(17077)   on 2011-05-03 15:52:34 (Show Source): You can put this solution on YOUR website! No, we are not doing your whole assignment for you. Ask a specific question about a concept you don't understand, then we'll help. John My calculator said it, I believe it, that settles it

Inequalities/444446: 16<3x-2<19 1 solutions Answer 306356 by solver91311(17077)   on 2011-05-03 15:50:42 (Show Source): You can put this solution on YOUR website! Add 2 to each of the three parts of the compound inequality. Divide each section of the compound inequality by 3. John My calculator said it, I believe it, that settles it

Numeric_Fractions/444458: 3y/5 - y/5 = ? 1 solutions Answer 306355 by solver91311(17077)   on 2011-05-03 15:49:01 (Show Source): You can put this solution on YOUR website! Just like finding the difference of any pair of fractions with identical denominators. The difference of the numerators over the common denominator. John My calculator said it, I believe it, that settles it

Angles/444455: What are all the angles like suppementay and what are they 1 solutions Answer 306353 by solver91311(17077)   on 2011-05-03 15:46:22 (Show Source): You can put this solution on YOUR website! Two angles are supplementary if and only if the sum of their measures is 180 degrees or radians. John My calculator said it, I believe it, that settles it

Exponential-and-logarithmic-functions/444436: I have to solve the equation, using properties of logarithms. ln x- ln(x-1)= 2 Thank you so much if you can help me. 1 solutions Answer 306351 by solver91311(17077)   on 2011-05-03 15:42:19 (Show Source): You can put this solution on YOUR website! The difference of the logs is the log of the quotient: Use the definition of logarithms: to write: And then do the algebra to obtain: Use your calculator if you need a numeric approximation. John My calculator said it, I believe it, that settles it

Surface-area/444010: About how much edging would be required to enclose a rectangular garden whose area is about 17 square feet? 1 solutions Answer 306178 by solver91311(17077)   on 2011-05-02 19:19:07 (Show Source): You can put this solution on YOUR website! Depends on the shape of the rectangle. The closer the shape is to square, the smaller the perimeter for a given area. So if you had a 6" wide by 34' garden, you would need 65 feet of fence, but if you have a square garden, on a side, then you would need feet. If you can figure a way to express the length as some function of the width, I can help you. Just write back. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/443994: If an animal h feet high at the shoulder and N=the steps taken per second the animal takes while walking and can be estimated by N(h)=1.6h^-1/2 Estimate the stepping frequency per second of a dog that is 1.9 feet high at the shoulders. Thanks a lot. 1 solutions Answer 306174 by solver91311(17077)   on 2011-05-02 19:12:24 (Show Source): You can put this solution on YOUR website! Replace with 1.9 and do the arithmetic. John My calculator said it, I believe it, that settles it

Quadratic_Equations/443940: 13x^2+14x+13=0 1 solutions Answer 306139 by solver91311(17077)   on 2011-05-02 17:34:34 (Show Source): You can put this solution on YOUR website! Let me open by saying there is absolutely nothing wrong with the other tutor's answer. However, allow me to give you an alternate way to look at how you present your answer. But then recognizing that 480 is equal to 16 times 30, we can write: and which are the simplified exact answers as contrasted with the numerical approximations given. John My calculator said it, I believe it, that settles it

test/443930: what is the number of complex roots, real roots and imaginary roots for this equation, x^3-6x^2+x+34=0 1 solutions Answer 306136 by solver91311(17077)   on 2011-05-02 17:21:12 (Show Source): You can put this solution on YOUR website! Use the rational roots theorem. If a polynomial equation with rational coefficients has a rational root, then that root will be of the form where is an even divisor of the constant term of the equation and is an even divisior of the lead coefficient. Possible rational roots are , , , and . Use synthetic division to find the first real and rational root. This is an equation of odd degree with rational coefficients, hence there must be at least one real root and it must be rational. Review the process of synthetic division at Purple Math: Synthetic Division Be certain to review all four pages. The quotient from your successful synthetic division will provide the coeffients of a quadratic equation. From these coefficients, you can calculate the discriminant to determine the character of the remaining two roots. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/443924: how long does it take if you drive 75 mph to drive 430 miles 1 solutions Answer 306129 by solver91311(17077)   on 2011-05-02 16:57:51 (Show Source): You can put this solution on YOUR website! Divide 430 by 75. Although the real answer depends on how long each Highway Patrolman makes you wait while s/he writes your speeding citiation. John My calculator said it, I believe it, that settles it

Rectangles/443925: if the perimeter of a rectangle is 34 meters, what is the largest area it can cover? 1 solutions Answer 306128 by solver91311(17077)   on 2011-05-02 16:56:57 (Show Source): You can put this solution on YOUR website! The largest area for a rectangle with a given perimeter is a square where each side is one-fourth of the perimeter. John My calculator said it, I believe it, that settles it

Inequalities/443917: How do you write an open sentence involving absolute value? 1 solutions Answer 306126 by solver91311(17077)   on 2011-05-02 16:55:03 (Show Source): You can put this solution on YOUR website! Write an open sentence, put absolute value bars in it somewhere. Make sure you haven't written something impossible so as to make it always false or always true. For example, don't write: That is because the absolute value of anything is ALWAYS positive, hence no expression contained in absolute value can take on a negative value. The example is a sentence involving absolute value but it is a closed sentence because it is always false. Also, don't write: any real-valued expression That is because no matter what is in the absolute value bars in the example, the value will always be positive. This is also a sentence that involves absolute value but is a closed sentence, this time because it is always true. Now all you have to do is write one where you cannot say the sentence is always true or always false. John My calculator said it, I believe it, that settles it

Volume/443911: Give the dimensions of a rectangular box that have the same volume as the cylindrical can. (cylindrical can is 8 centimeters high and has a radius of 2 centimeters.) 1 solutions Answer 306117 by solver91311(17077)   on 2011-05-02 16:37:00 (Show Source): You can put this solution on YOUR website! There are an infinite number of possibilities. The only thing you can say for sure is: Let , , and represent the length, width, and height of the rectangular box. Then . One possibility is , , and . But there are an infinite number of other possibilities. John My calculator said it, I believe it, that settles it

Rectangles/443905: If the length and width of a rectangle are both doubled, find the ratio of the area of the new rectangle to the area of the original rectangle. Prove your assertion. 1 solutions Answer 306115 by solver91311(17077)   on 2011-05-02 16:31:48 (Show Source): You can put this solution on YOUR website! 4:1 Let represent the width of the original rectangle. Let represent the length of the original rectangle. The area of the original rectangle is then Then the width of the new rectangle is and the length of the new rectangle is . The area of the new rectangle is John My calculator said it, I believe it, that settles it

Numeric_Fractions/443874: Perimeter of a high school basketball court. The perimeter of a standard high school basketball court is 268 ft. The length is 34 ft longer than the width. Find the dimensions of the court. Source: Indiana High School Athletic Association thank you! 1 solutions Answer 306113 by solver91311(17077)   on 2011-05-02 16:26:14 (Show Source): You can put this solution on YOUR website! Let represent the width. Then must represent the length. Two times the width plus two times the length is the perimeter, so: Solve for , then calculate . John My calculator said it, I believe it, that settles it

Graphs/443774: find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2x^2-16x+37 choose correct line of symmetry? a. y=-5 b. x=-4 c. y=5 d. x=4 the maximum/minimum of f(x) is? Is the value, f(4)=5 minimum or a maximum? 1 solutions Answer 306024 by solver91311(17077)   on 2011-05-02 12:21:36 (Show Source): You can put this solution on YOUR website! Given a quadratic function an equation of the axis of symmetry is The maximum or minimum of a quadratic function is the value of the funcition at the -coordinate of the vertex. The -coordinate of the vertex is found by: And then the value of the funcition at the vertex is the function evaluated at If the lead coefficient, , is positive, then the graph opens upward and the value of the function at the vertex is a minimum. If the lead coefficient is negative, then the graph opens downward and the value of the function at the vertex is a maximum. John My calculator said it, I believe it, that settles it

Linear_Algebra/443750: There are 2 leaves along 3 inches of an ivy vine. There are 14 leaves along 15 inches of the same vine. How many leaves are there along 6 inches of the vine? 1 solutions Answer 305994 by solver91311(17077)   on 2011-05-02 11:16:39 (Show Source): You can put this solution on YOUR website! 5

Numeric_Fractions/442467: What is the sum of the 7 over 8 and 1 over 4? 1 solutions Answer 305179 by solver91311(17077)   on 2011-04-29 14:18:52 (Show Source): You can put this solution on YOUR website! Now that the denominators are the same, you can just add the numerators. John My calculator said it, I believe it, that settles it

Triangles/442432: area of an isosceles triangle is 60sq. cm. the same two side of is 13 cm, what is the other one leangth ?? 1 solutions Answer 305174 by solver91311(17077)   on 2011-04-29 14:08:34 (Show Source): You can put this solution on YOUR website! Construct triangle ABC with the vertex B common to the two congruent sides upward and the unknown side as the base. Construct a perpendicular to the base through the vertex at the top of the triangle. Label the point of intersection of the perpendicular and the base with D. Your picture should look like one of the following: Let represent the measure of segement AD. Let represent segment BD. Since we know from a common geometric proof that the perpendicular from the apex to the base of an isosceles triangle bisects the base, the apex angle, and the triangle itself. Therefore the area of triangle ABD is equal to the area of triangle BCD and the area of each is one-half of the area of the entire triangle ABC. From the formula for the area of a triangle, we have: Hence, And further, From which we can derive: From the fact that segment BD is perpendicular to segment AD, we can deduce that triangle ABD is a right triangle, for which we are given the measure of the hypotenuse is 13 and we have identified the measure of the legs as and . Using Pythagoras: And using what we learned earlier about the relationship between and , we can write: Multiply both sides by : Let , substitute, and put the resulting quadratic into standard form: Factor: Then or Discarding the negative roots because we are attempting to calculate length, we have or . Having previously determined that segment BD bisects segment AC, and by construction, AD plus DC is equal to AC, we can deduce that AC is equal to two times AD. Therefore the base measurement that we seek as an answer to this problem is two times the value of or John My calculator said it, I believe it, that settles it

test/442303: Please I need help in algebra 1 on problems of complete the square I don't get it all and I don't anything thank you 1 solutions Answer 305038 by solver91311(17077)   on 2011-04-28 23:20:34 (Show Source): You can put this solution on YOUR website! Step 1: Move the constant term to the RHS Step 2: Divide by the lead coefficient Step 3: Divide the 1st degree coefficient by 2, square the result, and add that result to both sides of the equation. is the 1st degree coefficient. Divide by 2: . Square: Step 4: Factor the perfect square trinomial in the LHS: Step 5: Apply the LCD in the RHS Step 6: Take the square root of both sides. Remember to consider both positive and negative roots. Step 7: Add the opposite of the constant term in the RHS to both sides: Of course, when you do it with a problem that has specific numbers rather than general representations of the coefficients, you have to do the arithmetic and simplify the answer as much as possible. John My calculator said it, I believe it, that settles it

Square-cubic-other-roots/442060: I am having a problem solving this equation: I need to factor this but am getting nowhere. Is it not factorable? 1 solutions Answer 304943 by solver91311(17077)   on 2011-04-28 17:15:42 (Show Source): You can put this solution on YOUR website! The problem with your question is that the answer is both yes and no. I suspect you mean Is it factorable over the rational numbers, in which case the answer is no. But all quadratic trinomials are factorable if you allow complex number factors. A large subset of these are factorable over the real irrational numbers. And only a tiny fraction of these are factorable over rational numbers. The given quadratic actually has a pair of irrational factors: John My calculator said it, I believe it, that settles it

decimal-numbers/442055: I know there is now a section, but can I get help with the following question? 3 Find the derivative of the function. f(x) = (3x - 2)(3x + 1) 1 solutions Answer 304941 by solver91311(17077)   on 2011-04-28 16:54:55 (Show Source): You can put this solution on YOUR website! There are two ways to go about this. You can use the formula for the derivative of a product: If then So if you let and Then Or you could first multiply the two denominators and then take the derivative of the resulting 2nd degree polynomial function. Hence Achieving the same result. Whichever seems easiest to you is the way to do it. John My calculator said it, I believe it, that settles it

Pythagorean-theorem/441513: I need to solve for x using the Pythagorean theorem. Here are the measurements: Leg A: x, Leg B: 6, Leg C: 2+x 1 solutions Answer 304741 by solver91311(17077)   on 2011-04-27 18:34:08 (Show Source): You can put this solution on YOUR website! Pythagorean Theorem: So Just solve for John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/441499: 1. A ball is hit upward. Its height h in feet after t seconds is given by h=-16t^2 + 80t + 4. At what times is the ball 100 feet in the air? searcheagle@yahoo.com 1 solutions Answer 304731 by solver91311(17077)   on 2011-04-27 18:09:16 (Show Source): You can put this solution on YOUR website! You have a projectile launched vertically at 80 feet per second initial velocity from a position 4 feet above ground level (height zero). gives the height at seconds if the instant of launch is You want to know the value of when So: Just solve the quadratic for the two values of . Hint: Divide through by -16 and then factor the resulting trinomial. John My calculator said it, I believe it, that settles it

Numbers_Word_Problems/441440: the sum of two numbers is 64. the one number is three times the other number. what are the two numbers? 1 solutions Answer 304725 by solver91311(17077)   on 2011-04-27 17:57:19 (Show Source): You can put this solution on YOUR website! Solve for . Then calculate John My calculator said it, I believe it, that settles it

Linear_Algebra/440948: I need your help, what are the steps to solving the equation 1/2(8w-6)=17 1 solutions Answer 304491 by solver91311(17077)   on 2011-04-26 18:57:49 (Show Source): You can put this solution on YOUR website! Multiply both sides by 2 Add 6 to both sides Multiply both sides by John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/440678: Find the general form of the equation of the line passng through the points (3,-5) and (-1,-2) 1 solutions Answer 304334 by solver91311(17077)   on 2011-04-26 01:27:43 (Show Source): You can put this solution on YOUR website! Use the two point form of an equation of a line: where and are the coordinates of the given points. Then do the arithmetic and arrange the result into whatever form you like. John My calculator said it, I believe it, that settles it