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Polynomials-and-rational-expressions/156948: Solve by factoring and using the principle of zero products. 18d^2 + 30d + 12 = 0 1 solutions Answer 115708 by jim_thompson5910(28715)   on 2008-09-14 19:36:24 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor the left side Now set each factor equal to zero: or or Now solve for d in each case So our answers are or

Expressions-with-variables/156931: I have a problem 4a^2+18a+8/a+4 could you please work this out and show me step by step how you did this Thanks 1 solutions Answer 115702 by jim_thompson5910(28715)   on 2008-09-14 19:01:32 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. Reduce Distribute So simplifies to . In other words, where .

Quadratic_Equations/156932: Evaluate the discriminate b^2-4ac. Then use the answer to state how many real number solutions exist for the rquation y=x^2+8x+16 1 solutions Answer 115700 by jim_thompson5910(28715)   on 2008-09-14 18:55:36 (Show Source): You can put this solution on YOUR website! From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Subtract from to get Since the discriminant is equal to zero, this means that there is one real solution.

Equations/156933: 45-3x=30 1 solutions Answer 115699 by jim_thompson5910(28715)   on 2008-09-14 18:54:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is

Polynomials-and-rational-expressions/156935: Could someone please show me how to solve this equation? This is not coming up the way i need it to but the 7 is supposed to like a cubed square root. I am supposed to rewrite with rational exponents. 1 solutions Answer 115698 by jim_thompson5910(28715)   on 2008-09-14 18:52:52 (Show Source): You can put this solution on YOUR website! Remember, So in this case,

Polynomials-and-rational-expressions/156872: Find the variation constant and an equation of variation where y varies directly as x and y=12 when x=3. The variation constant is k= ??? the equation of variation is y=??? 1 solutions Answer 115659 by jim_thompson5910(28715)   on 2008-09-14 14:35:49 (Show Source): You can put this solution on YOUR website! The statement " y varies directly as x" translates to Start with the given equation Plug in and Divide both sides by 3 to isolate "k" So the variation constant is which means that the equation is

Polynomials-and-rational-expressions/156870: This question is from textbook college algebra rule of signs to state the numbier of possible positive and negative real zeros of each polynomial function P(x)=10x6 -9x5 -14x4 -8x3-18x2+x+6 I used my calculator to find the possible zeros and I understand there are 6 possible zeros so far x=-1,-.6, .5, 2 1 solutions Answer 115658 by jim_thompson5910(28715)   on 2008-09-14 14:15:40 (Show Source): You can put this solution on YOUR website! Possible Zeros: Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 6 (the last coefficient): Now let's list the factors of 10 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur

Number-Line/156865: How can I change an algebraic expression to the common languaje? 1 solutions Answer 115656 by jim_thompson5910(28715)   on 2008-09-14 13:44:58 (Show Source): You can put this solution on YOUR website! Post a problem so we can walk you through it

Distributive-associative-commutative-properties/156864: 10r-4(12+9r) 1 solutions Answer 115655 by jim_thompson5910(28715)   on 2008-09-14 13:44:10 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms

real-numbers/156862: The depth of a pool varies directly with how many gallons of water it will hold. If a 6 foot deep pool holds 10,000 gallons of water, a pool that holds 12,500 gallons of water should be __________inches deep, according to this theory. ?? 1 solutions Answer 115654 by jim_thompson5910(28715)   on 2008-09-14 13:43:14 (Show Source): You can put this solution on YOUR website! We have the follow ratio: number of gallons of pool # 1 number of gallons of pool # 2 --------------------------- = ------------------------------- depth of pool # 1 depth of pool # 2 Plug in the given information Multiply both sides by x Multiply both sides by 6 Multiply Divide both sides by 10000 Divide So a pool that is 7.5 feet deep will hold 12,500 gallons of water

Travel_Word_Problems/156861: This question is from textbook Two runners leave the starting gate, one running 12mph and the other 10mph. If they maintain the pace, how long will it take for them to be 1/4 mile apart? 1 solutions Answer 115652 by jim_thompson5910(28715)   on 2008-09-14 13:31:17 (Show Source): You can put this solution on YOUR website! Let's set up the equation for the faster runner: Start with the distance-rate-time formula Plug in So after "t" hours, the faster runner has run miles ---------------------------------- Let's set up the equation for the slower runner: Start with the distance-rate-time formula Plug in So after "t" hours, the faster runner has run miles Now if you want to know the distance between them, simply subtract the two expressions to get Since we want the distance to be of a mile, this means that Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which approximates to . So in of an hour (or 7 and half minutes) the distance between the two runners is of a mile

Angles/156860: if angle a and angle b are complementary and angle b and angle c are supplementary how do they look? 1 solutions Answer 115651 by jim_thompson5910(28715)   on 2008-09-14 13:29:24 (Show Source): You can put this solution on YOUR website! If angle a and angle b are complementary, this means that they add to 90 degrees. This also means that they are both acute angles. Since angles b and c are supplementary, and we know that angle b is acute (ie less than 90 degrees), this means that angle c is obtuse Here's one way you could draw the three angles

Exponential-and-logarithmic-functions/156859: This question is from textbook College Algebra what is the simplest form of (x^-2y^-3)over (x^2y^-1)^3 1 solutions Answer 115649 by jim_thompson5910(28715)   on 2008-09-14 13:20:56 (Show Source): You can put this solution on YOUR website! Start with the given expression Rewrite as . Rewrite as . Rewrite as Combine the fractions Distribute the outer exponent 3 to the inner exponents in the denominator Multiply the first fraction by the reciprocal of the second fraction. Combine and multiply . Note: Add Divide by subtracting the exponents. Subtract Simplify So simplifies to In other words, where or

Equations/156858: Please help me solve this: -5x + 3y = 7 1 solutions Answer 115648 by jim_thompson5910(28715)   on 2008-09-14 13:09:32 (Show Source): You can put this solution on YOUR website! Do you want to solve for "y"? Start with the given equation. Add to both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. So the solution is

Geometry_Word_Problems/156845: if one leg of a triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs. 1 solutions Answer 115647 by jim_thompson5910(28715)   on 2008-09-14 13:09:14 (Show Source): You can put this solution on YOUR website! Leg 1: Leg 2: (since one leg is 14 m shorter than the other, the other leg is 14 m longer than the first one) Hypotenuse: 26 Start with Pythagorean's Theorem Plug in the given information Square 26 FOIL Combine like terms Subtract 676 from both sides. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible answers are or However, a negative length isn't possible. So the only answer is So the first leg is 10 m, the second leg is 24 m (since ), and the hypotenuse is 26 m

Exponential-and-logarithmic-functions/156857: 12^(m+5)=17 1 solutions Answer 115643 by jim_thompson5910(28715)   on 2008-09-14 12:53:05 (Show Source): You can put this solution on YOUR website! Start with the given equation Take the log of both sides Rewrite the left side using the identity Divide both sides by Use the change of base formula to rewrite the right side Subtract 5 from both sides Use a calculator to evaluate the right side So the exact answer is which approximates to

Equations/156856: Please help me solve this equation: 8x + 4y = 12 1 solutions Answer 115642 by jim_thompson5910(28715)   on 2008-09-14 12:45:57 (Show Source): You can put this solution on YOUR website! Do you want to solve for "y" ? Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce.

Travel_Word_Problems/156854: a car is traveling at a speed of 55 miles per hour. you want to write an algebraic expression to show how far the car will travel in a certain number of hours. what will be your constant? your variable? 1 solutions Answer 115641 by jim_thompson5910(28715)   on 2008-09-14 12:43:18 (Show Source): You can put this solution on YOUR website! Start with the distance-rate-time formula Plug in So in "t" hours, the car will travel miles. For instance, if , then which means in 2 hours the car travels 110 miles. So the algebraic expression for the distance is where is the coefficient (in this case there is no constant) and is the variable

Equations/156853: 6-2 x = -8 - 3 1 solutions Answer 115639 by jim_thompson5910(28715)   on 2008-09-14 12:38:18 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is

Exponents/156852: (3a^-2)^2(b^2c^3)^4/(ab)^-3 c^-4 1 solutions Answer 115638 by jim_thompson5910(28715)   on 2008-09-14 12:37:19 (Show Source): You can put this solution on YOUR website! So

Exponents/156851: K^4K^-5/(K^-2)^2 1 solutions Answer 115636 by jim_thompson5910(28715)   on 2008-09-14 12:30:49 (Show Source): You can put this solution on YOUR website! So where

Triangles/156850: The hypotenuse of a right triangle is twice as long as one of the legs and 10 inches longer than the other. What are the lengths of the sides of the triangle? So far I know that i should use the Pythagorean theorem. I've drawn the triangle and know: 1st Leg: h/2 2nd Leg: h-10 Hypotenuse: h (h-10)^2 + (h/2)^2 = h^2 4(h^2-20h-100+ (h^2/4))=h^2 4h^2-80h-400+h^2=h^2 5h^2-80h-400=h^2 1 solutions Answer 115635 by jim_thompson5910(28715)   on 2008-09-14 12:27:48 (Show Source): You can put this solution on YOUR website! You have the right equations set up, but your work is a little off. Start with the given equation FOIL. Note: the third term is +100 (not -100) Square to get Multiply EVERY term (including the terms on the right side) by the LCD 4 to eliminate the fraction Subtract from both sides Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for h Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) Break up the fraction. Reduce. or Break up the expression. or Now approximate the values of "h" So the possible hypotenuses are or However, if you plug into , you'll get a negative answer. So the only solution is So the length of the hypotenuse is approximately units So the first leg is units long and the second leg is units long

Equations/156849: This question is from textbook Row 1 x = 10 Row 2 1/2 x = 10 Row 3 1/3x = 10 Row 100 1/100x = 10 Row n ? x = ? As n gets larger, to what equation are the equations getting closer and closer? What is happening to the solutions? 1 solutions Answer 115634 by jim_thompson5910(28715)   on 2008-09-14 12:17:03 (Show Source): You can put this solution on YOUR website! I'm assuming that Row 2 is . If that's the case, then Row n is . As "n" get's larger the value of gets smaller and it approaches the value of zero. So the equations are getting closer and closer to zero as "n" increases.

Exponents/156848: (X^-1-X^-2)^-1 1 solutions Answer 115632 by jim_thompson5910(28715)   on 2008-09-14 12:07:58 (Show Source): You can put this solution on YOUR website! So where or

Radicals/156831: I need to find x, AB, and BC, where A, B, and C are points on a line...A is the leftmost point, C is the rightmost point, and B is in between A and C (not necessarily the midway) AB = square root (3x +4) BC = x-6 AC = 6 I was able to write out sqrt(3x+4) + x - 6 = 6, then simplifies to SQRT (3x+4) + x = 12. I don't understand how to eliminate the square root in these radical equations. Please help. Thank you. 1 solutions Answer 115631 by jim_thompson5910(28715)   on 2008-09-14 11:53:24 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add 6 to both sides. Subtract "x" from both sides. Square both sides to eliminate the square root FOIL Subtract from both sides. Subtract from both sides. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible answers are or However, if you plug back into the original equation, you'll find that it doesn't work. So the only solution is Now plug in into AB, BC, and AC So the lengths are , , and Check: Remember, AB+BC=AC AB+BC=AC ... Start with the given equation 5+1=6 ... Plug in , , and 6=6 ... Add Since this equation is true, this verifies the answer.

Radicals/156834: I need to resolve x, AB, BC and AC, where A, B and C are points on a line. A is leftmost, C is rightmost, and B is somewhere in between. AB = 2x+1 BC = x-2 AC = sqrt (x^2 + 25x + 5) Was able to write, 2x+1+x-2 = sqrt (x^2+25x+5), which reduces to 3x-1 = sqrt (x^2 + 25x + 5). I don't know how to eliminate the square root, especially when there is an exponential along with it. Please help. Thank you. 1 solutions Answer 115630 by jim_thompson5910(28715)   on 2008-09-14 11:44:35 (Show Source): You can put this solution on YOUR website! I'll start where you left off Start with the given equation Square both sides. This will eliminate the square root. FOIL the left side Subtract from both sides. Subtract from both sides. Subtract from both sides. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible answers are or However, if you plug in back into the original equation, you'll find that the equation won't be true. Also, since distance is ALWAYS positive, this means that will not work (since if you plug it into any expression the result is negative) So the only answer is Now plug in into AB,BC, and AC: AB = BC = AC = So the three lengths are , , and Check: Remember, the segment addition postulate is AB+BC=AC (ie the lengths of the pieces of AC should add to the length of AC) AB+BC=AC ... Start with the given equation 9+2=11 ...Plug in AB=9, BC=2, and AC=11 11=11 ... Add. Since this equation is true, this verifies the answer.

Radicals/156836: I need to resolve x, AB, BC and AC, where A, B and C are points on a line. A is leftmost, C is rightmost, and B is somewhere in between. AB = 2x+1 BC = x-2 AC = sqrt (x^2 + 25x + 5) Was able to write, 2x+1+x-2 = sqrt (x^2+25x+5), which reduces to 3x-1 = sqrt (x^2 + 25x + 5). I don't know how to eliminate the square root, especially when there is an exponential along with it. Please help. Thank you. 1 solutions Answer 115629 by jim_thompson5910(28715)   on 2008-09-14 11:43:32 (Show Source): You can put this solution on YOUR website! I'll start where you left off Start with the given equation Square both sides. This will eliminate the square root. FOIL the left side Subtract from both sides. Subtract from both sides. Subtract from both sides. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible answers are or However, if you plug in back into the original equation, you'll find that the equation won't be true. Also, since distance is ALWAYS positive, this means that will not work (since if you plug it into any expression the result is negative) So the only answer is Now plug in into AB,BC, and AC: AB = BC = AC = So the three lengths are , , and Check: Remember, the segment addition postulate is AB+BC=AC (ie the lengths of the pieces of AC should add to the length of AC) AB+BC=AC ... Start with the given equation 9+2=11 ...Plug in AB=9, BC=2, and AC=11 11=11 ... Add. Since this equation is true, this verifies the answer.

Quadratic_Equations/156773: Use the quadratic equation to solve 2x^2-5x=-9 Use i if complex answer. i would appreciate a breakdown of the solution..Thanks 1 solutions Answer 115592 by jim_thompson5910(28715)   on 2008-09-13 23:10:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add 9 to both sides. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root or Break up the expression. So the answers are or which approximate to or

Polynomials-and-rational-expressions/156767: Rewritethe following expression with positive exponents. (5xy)^(-6/7) I think its 1/ 5xy^7/6.... im probally wrong. Please help! 1 solutions Answer 115585 by jim_thompson5910(28715)   on 2008-09-13 22:22:14 (Show Source): You can put this solution on YOUR website! If is negative, then . So in our case:

Quadratic_Equations/156738: write the equation of a quadratic f(x) such that f(0)=8 and a vertex at x=0. 1 solutions Answer 115572 by jim_thompson5910(28715)   on 2008-09-13 19:01:20 (Show Source): You can put this solution on YOUR website! Since the vertex is at and (which means that when , then ), this means that the vertex is at the point (0,8). Now remember, the quadratic has the vertex (h,k). So this means that in this case and Start with the general quadratic in vertex form Plug in and Subtract So the quadratic equation which has the vertex at (0,8) is where "a" can be any number. For example, has the vertex at (0,8)

Exponential-and-logarithmic-functions/156731: equation y=ca^x points on graph = (3,50) and (2,1) Solve for a 1 solutions Answer 115570 by jim_thompson5910(28715)   on 2008-09-13 18:50:27 (Show Source): You can put this solution on YOUR website! Start with the given equation Plug in and Divide both sides by to isolate "c" Rearrange the equation Start with the given equation Plug in and Plug in Multiply Reduce Multiply both sides by "a" So the solution is