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Radicals/104781: Solve. x^2 + 6 = 42 1 solutions Answer 76247 by Fombitz(13828)   on 2007-10-17 16:26:31 (Show Source): You can put this solution on YOUR website! and

Proportions/104785: Iam trying to help my son with problem x-(-6)=32.5 thanks for any help 1 solutions Answer 76246 by Fombitz(13828)   on 2007-10-17 16:23:36 (Show Source): You can put this solution on YOUR website! Negative times negative equals positive. Remember what you do to one side of the equation, you must do to the other. Use the additive inverse of 6 or (-6).

Polynomials-and-rational-expressions/104765: Multiply.-3a^2b/35a^5 x 14a^3b^2/-9b^4 1 solutions Answer 76245 by Fombitz(13828)   on 2007-10-17 16:19:05 (Show Source): You can put this solution on YOUR website! A couple of exponentiation rules will help. Let's break this down to simplify. First let's multiply the numerators then denominators. Numerator: Denominator: Put it together Simplify.

Polynomials-and-rational-expressions/104756: Factor completely. x^2 + 7x – 30 1 solutions Answer 76242 by Fombitz(13828)   on 2007-10-17 16:03:54 (Show Source): You can put this solution on YOUR website! Look for a solution When the equation is expanded with a,b, Compare that to your equation and you find that, Look for integer factors (a,b) of 30 (1,30) (2,15) (3,10) (5,6) Factors (3,10) look promising since their difference is 7. Now to get the signs right. The smaller number needs to be negative for the sum to positive. (a,b)=(-3,10)

Polynomials-and-rational-expressions/104761: The profit on a watch is given by P = x^2 – 13x – 80, where x is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss? 1 solutions Answer 76241 by Fombitz(13828)   on 2007-10-17 15:52:34 (Show Source): You can put this solution on YOUR website! For a $50 loss, then the profit was -50. Find x such that P(x)=-50. Two solutions x=15 and x=-2. Selling (-2) watches doesn't make sense, so your only answer is 15 watches sold. Check your answer. Good answer.

Polynomials-and-rational-expressions/104746: Simplify (y^3/z^5)^4 1 solutions Answer 76235 by Fombitz(13828)   on 2007-10-17 15:41:03 (Show Source): You can put this solution on YOUR website! Following the exponentiation rule,

Graphs/104744: PLEASE HELP!!!!! L HAS Y-INTERCEPT (0,-3) AND IS PARALLEL TO THE LINE WITH THE EQUATION Y= 2/3x + 1 1 solutions Answer 76233 by Fombitz(13828)   on 2007-10-17 15:36:26 (Show Source): You can put this solution on YOUR website! Parallel lines have the same slope. For your line, when x=0, y=-3. Using the point-slope equation of a line, We can use your information and substitute. .

Mixture_Word_Problems/104741: for the floor plans given in exercise determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3, 18). THE FLOOR PLANS IN THE GIVEN EXERCISE ARE (2,3), (11,6), (-3, 18) AND (8,21) 1 solutions Answer 76231 by Fombitz(13828)   on 2007-10-17 15:33:28 (Show Source): You can put this solution on YOUR website! Line 1 is through (2,3) and (11,6). Line 2 is through points (2,3) and (-3, 18). For lines to be perpendicular, their slopes are negative reciprocals, or Let's calculate the slope of both lines and see if this relationship holds. The formula for the slope is : For Line 1, For Line 2, When we look at the product of their slopes We find that they are negative reciprocals and therefore the lines are perpendicular, as you can see by the graph below.

Rectangles/104654: This question is from textbook W x (L=9) = 36 2 length is 9 inches greater than the width area 36in2. Can you please break down how this is done (the formula). Thank you 1 solutions Answer 76226 by Fombitz(13828)   on 2007-10-17 15:15:58 (Show Source): You can put this solution on YOUR website! The area of a rectangle is equal to A=L*W. The area of your rectangle is 36 sq.inches. Your first equation is 1. You say that the length is 9 inches greater than the width, or 2. Substitute your equation (2) into (1) and solve for W. Distributive property. Additive inverse of 36. Factor the quadratic equation. Solutions are W=-12, W=3. Since a negative width does not make sense, we throw out that solution. W=3 inches L=12 inches

Equations/104730: Given f(x) = –x^3+3x^2+x+7 find f(–3), f(0), and f(1) 1 solutions Answer 76218 by Fombitz(13828)   on 2007-10-17 14:39:55 (Show Source): You can put this solution on YOUR website! For x=-3, For x=0, For x=1,

Equations/104731: The base of an isosceles triangle is 8 in. less than the length of the equal sides. If the perimeter of the triangle is 28 in., find the length of each of the sides. 1 solutions Answer 76217 by Fombitz(13828)   on 2007-10-17 14:19:52 (Show Source): You can put this solution on YOUR website! Since the triangle is isoceles, you know that two sides have the same length, L. You also mention that the base, B, is 8 inches shorter than the length and the perimeter is 28 inches. The perimeter of this triangle is, But you also know that Use that equation and plug the value for B into the perimeter equation. Additive inverse of (-8). Multiplicative inverse of 3. Then use your base equation, Your solution is L=12 inches and B=4 inches.

Polynomials-and-rational-expressions/104687: page 330 # 64 - factor each polynomial x^2 - 5xs -24s^2 1 solutions Answer 76216 by Fombitz(13828)   on 2007-10-17 14:11:44 (Show Source): You can put this solution on YOUR website! We want to find the values for a and b that make this true. If we expand the equation in terms of a and b, we can find what relationships need to be met to solve the problem. Note, the terms a and b will also include an s term for each. Don't let that throw you off, it acts like a constant. Let's compare terms in the original equation: 1. or 2. Let's use equation 2 and look for factors of that when summed equal -5s (Equation 1). Integer factors of are (1s,24s),(2s,12s),(3s,8s),(4s,6s). (3s,8s) looks promising since their difference is 5s. Now we need to get the signs right. and

Equations/104636: Solve for R? 100=70/(1+R)+60/(1+R)^2 1 solutions Answer 76215 by Fombitz(13828)   on 2007-10-17 13:51:15 (Show Source): You can put this solution on YOUR website! Multiply both side by . Expand. Distribute. Group terms on both sides. Group terms on one side. where a=10, b=13, c=-3 First solution Second solution Let's check one solution Good answer. You can also check the other answer.

Miscellaneous_Word_Problems/104723: A homeowner has 120 feet of fence to enclose a rectangular garden. Come up with a function that gives the area of the garden as a function of the width (Area in terms of width). What I know length*2 + width*2=120 feet 2W=120-2L Divide everything by 2 W=60-L Is this complete or do I need to do something else for the answer? Thank you. 1 solutions Answer 76214 by Fombitz(13828)   on 2007-10-17 13:21:51 (Show Source): You can put this solution on YOUR website! Yes, you still need to come up with the area equation for the rectangular garden using width and length. Once you have the area equation, substitute for width, with (60-L), as you derived. You're almost there.

Polynomials-and-rational-expressions/104680: FIND EACH QUOTIENT (14Y + 8Y^2 + Y^3 + 12) DIVIDED BY (6 + Y) 1 solutions Answer 76212 by Fombitz(13828)   on 2007-10-17 13:16:26 (Show Source): You can put this solution on YOUR website!

Polynomials-and-rational-expressions/104688: factor each polynomial completely -4w^3 - 16w^2 + 20w 1 solutions Answer 76211 by Fombitz(13828)   on 2007-10-17 12:24:30 (Show Source): You can put this solution on YOUR website! Factor out (-4w) from all terms. Factor the quadratic equation.

Square-cubic-other-roots/104710: x-2*sqrt(x-3)=3 solve for zero... I subtract x from both sides which = -2*sqrt(x-3)=3-x then I divide by -2 from both sides sqrt(x-3)=(3-x)/-2 then to get rid of the "sqrt" ^2 on both sides x-3=(9+x^2)/4 then I subtract "x" and add 3 to both sides to solve for zero. 0=(9+x^2)/4-x+3 then I find a common denominator of 4 and solve 0=(9+x^2)/4 -4x/4+12/4 which equals 0=(x^2-4x+21)/4 then I multiply 4/1 on both side the loose the denominator. 0=x^2-4x+21 which can not be factored, but my text book gives a solution set of {7,3}. I cant find were I went wrong, please help. Please note, this question had already been answered but the link to the answer did not work so this is why I am re-submitting it. Thank you. 1 solutions Answer 76201 by Fombitz(13828)   on 2007-10-17 11:13:26 (Show Source): You can put this solution on YOUR website! Here's the step where you got on the wrong path. You're missing a term. Re-work and continue from there. You're on the right track otherwise. Post another question if you get stuck.

Signed-numbers/104707: What is the arithmetic mean of 8,7,7,5,3,2, and 2? 1 solutions Answer 76200 by Fombitz(13828)   on 2007-10-17 11:07:53 (Show Source): You can put this solution on YOUR website! The arithmetic mean is the sum of all of the numbers divided by the total count of numbers. The sum of all of the numbers The total count of all numbers You have seven numbers. Mean = 34/7 = 4.86 (rounded off to two decimal places).

Miscellaneous_Word_Problems/104704: Train A leaves a station traveling at 32 kilometers per hour. 4 hours later, train B leaves the same station traveling in the same direction at 52 kilometers per hour. How long does it take train B to catch up to train A? 1 solutions Answer 76199 by Fombitz(13828)   on 2007-10-17 11:03:41 (Show Source): You can put this solution on YOUR website! Rate x Time = Distance Train A rate : 32 km/h Train A time : t+4 hrs (it's 4 hours ahead of train B) Train A distance : 32(t+4) Train B rate : 52 km/h Train B time : t hrs Train B distance : 52t Train B catches Train A when the distances from the station is equal. Additive inverse of 32t Simplify Multiplicative inverse of 20. hours Always check your answer: Train A travels 32(t+4) km Train B travels 52t km Train A distance = Train B distance. Good answer. t=32/5 hours or 6.4 hours or 6 hrs 24 min

Exponents-negative-and-fractional/104701: Hi there! I am having terrible trouble trying to simplify this expression. Instructions say to simplify and express the answer using positive exponents. [2x^(3/4)*y^(-1/2)]^(-8) 1 solutions Answer 76198 by Fombitz(13828)   on 2007-10-17 10:49:43 (Show Source): You can put this solution on YOUR website! Use the following exponentiation rule, Distribute the exponent. Multiply the exponents. Only positive exponents wanted. Expanded answer.

Linear-equations/104697: David has $16,000 to invest. He invests $11,000 in a mutual fund that pays 12% annual simple interest. If he wants to make a t least $2200 in yearly interest, at what minimum rate does the remainder of the money need to be invested? This was my hardest one. 1 solutions Answer 76197 by Fombitz(13828)   on 2007-10-17 10:30:30 (Show Source): You can put this solution on YOUR website! Let's call the unknown rate R. Interest Equation The rate needs to be at least 17.6%.

logarithm/104689: Could someone please assist me by solving this logarithmic equation step-by-step for future reference. Thank you. log(7y + 1) = 2log(y+3)-log2 1 solutions Answer 76196 by Fombitz(13828)   on 2007-10-17 10:17:40 (Show Source): You can put this solution on YOUR website! Some rules to remember Now let's look at your example. Bring the variable expressions to one side. Power rule from above both sides. Division rule from above. Inverse function both sides. Multiply both sides by Distribute and expand. Group all terms on one side. Factor the equation. and . Two solutions. Verify your answer Power and division rule, right hand side. Good answer. Power and division rule, right hand side. Good answer.

Linear-equations/104691: Including 8% sales tax, a bed-and-breakfast inn charges $172.80 per night Find the inn's nightly cost before the tax is added. I tried and tried 1 solutions Answer 76194 by Fombitz(13828)   on 2007-10-17 09:44:07 (Show Source): You can put this solution on YOUR website! Let's say the bed and breakfast charges X per night. With 8% tax, it's $172.80. Room Charge + Tax = Total The room rate is $160.00 and the tax is ($160)(0.08) or $12.80.

Polynomials-and-rational-expressions/104673: Multiply (5a – 3b)^2 1 solutions Answer 76193 by Fombitz(13828)   on 2007-10-17 09:15:15 (Show Source): You can put this solution on YOUR website! Use the FOIL method (First, Outer, Inner, Last) First : Outer : Inner : Last : =First + Outer + Inner + Last A faster way is to compare to the following equation where and

Linear-equations/104683: A basketball court is a rectangle with a perimeter of 86 meters. The length is 13 meters more than the width. Find the width and length of the basketball court. I don't know where to start, please help. 1 solutions Answer 76191 by Fombitz(13828)   on 2007-10-17 08:53:29 (Show Source): You can put this solution on YOUR website! Start with what you know. Court is a rectangle with width and length. Give the variables a name. W-width L-length What is the perimeter of a rectangle in terms of its width and length? P=2L +2W Now look at the specifics of the information you are given. The perimeter is 86. P=2L+2W=86 The length is 13m more than the width. L=13+W So now you have two equations, with two unknowns. 1. 2. Substitute equation 2 in equation 1 and solve for W. 1. Use this result in equation 2 to solve for L. 2. Verify your answer Good answer. L=28 m and W=15 m

Polynomials-and-rational-expressions/104678: FIND EACH PRODUCT (3Y^2 + 1) (3Y^2 - 1) 1 solutions Answer 76188 by Fombitz(13828)   on 2007-10-17 08:29:35 (Show Source): You can put this solution on YOUR website! Use the FOIL method (First, Outer, Inner, Last) First : Outer : Inner : Last = = =

Linear-equations/104649: C=(-4,1),R=SQUARE ROOT OF 7 WRITE THE EQUATION OF A CIRCLE WITH THE INDICATED CENTER AND RADIUS. THANKS 1 solutions Answer 76186 by Fombitz(13828)   on 2007-10-17 08:19:58 (Show Source): You can put this solution on YOUR website! The equation of a circle centered at (h,k) with a radius R is : In your case, h=-4, k=1, and R=

Exponents/104571: What is 2 to the negative 5 times 4 to the negative 3 ? I'm getting an answer in decimal form....4.8828125 to the negative 04 .Please help 1 solutions Answer 76092 by Fombitz(13828)   on 2007-10-16 17:12:32 (Show Source): You can put this solution on YOUR website! You are correct. or in scientific notation x

Linear_Equations_And_Systems_Word_Problems/104568: Hello, I need help with this problem: The height, in feet, of a rocket t seconds after blast-off is given by a formula h=1260t-16t^2. After how many seconds will the rocket first reach a height of 23,400 feet? Thank you 1 solutions Answer 76091 by Fombitz(13828)   on 2007-10-16 17:06:39 (Show Source): You can put this solution on YOUR website! Use the quadratic formula, where a=-16, b=1260, and c=-23400 and t=48.75 seconds t=30 seconds Since your looking for the first time, pick the earliest time. t=30 seconds. Why two answers? First when the rocket is going up and then when the rocket's coming down, as shown in the graph below, with the horizontal axis equal to h=23,400 feet.

Volume/104522: how many pounds is 41 grams of gold 1 solutions Answer 76087 by Fombitz(13828)   on 2007-10-16 16:48:25 (Show Source): You can put this solution on YOUR website! The conversion factor is 1 kg equals 2.2 lbs. To convert grams to pounds, we need another converstion factor, 1000g equals 1kg. 41 grams x(1 kg)/(1000grams)x(2.2lb/kg)=.0902 lbs.

absolute-value/104564: 4 + /r+2/ = 7 1 solutions Answer 76082 by Fombitz(13828)   on 2007-10-16 16:24:09 (Show Source): You can put this solution on YOUR website! Additive inverse of 4. Simplify. The absolute value function is defined as if and if Since we don't know the value of (r+2), we solve for both cases. Assume , then Assume , then Check your answers. r=1 Good answer. r=-5 Good answer.