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 Equations/595634: write an equation for the line hrough the given point.(5,7),(6,8)1 solutions Answer 377516 by jim_thompson5910(28536)   on 2012-04-07 00:42:53 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 7 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and
 Radicals/596100: Here's an equation: x=sqrt(15-2x) This is how I solved it: x^2=15-2x x^2+2x-15=0 (x+5)*(x-3)=0 therefore x=-5 or x=3 and after checking I found that both solutions satisfies the original equation [because 3=sqrt(9) and -5=sqrt(25)] But after checking the answers, I found that -5 is considered as an extraneous root as -5 is not equal to sqrt(25), namely 5. But the square root of 25 can be both 5 or -5. Can anyone tell me why?1 solutions Answer 377513 by jim_thompson5910(28536)   on 2012-04-07 00:08:13 (Show Source): You can put this solution on YOUR website!Actually, the square root of 25 is only 5 because the square root function is what it says it is: a function. A function takes one input and spits out only ONE output. So it can't take in the input 25 and spit out both 5 and -5 at the same time. So When we want the plus/minus to be in there, we have to explicitly add it like so $\LARGE \pm\sqrt{25}=\pm 5$
 Exponents/596096: Please help me solve this equation: 8x^6y^2/2x^3y^4 i Know that you subtract the exponents so it becomes: 4x^3/y^-2 then i THINK you're suppose to bring the negative exponent up, turning into: 4x^3 y^2 but i am not to sure, please help me.1 solutions Answer 377506 by jim_thompson5910(28536)   on 2012-04-06 23:40:45 (Show Source): You can put this solution on YOUR website!You are very close. You just made one minor mistake. When you subtract exponents, it's all done in reference to the numerator. Basically, you should have Now you flip the fraction to get to make the exponent negative giving you the final answer
 Miscellaneous_Word_Problems/596067: Island dinner booked a party and was charging the group a fix cost of 1,680. Later the number of people in the group increased by 50 people and the average cost decreased by $10 per person. How many people were booked originally. a. 33 b. 70 c. 120 d. 168 The answer is B. 70. Can't figure out how to get 70. Can someone please help me out with this problem. Can't figure this one out1 solutions Answer 377484 by jim_thompson5910(28536) on 2012-04-06 20:30:13 (Show Source): You can put this solution on YOUR website!Let c = cost per person (before the increase of 50 people) and let n = number of people (originally -- before the increase of 50 people) Since the total cost is 1680, and this cost is distributed evenly among 'n' people, this means that each person will pay dollars. Adding 50 people to the group increases the count to n+50 and it decreases the cost per person by$10. So the cost per person is now c-10 The same cost of 1680 is now distributed amongst n+50 people and the cost per person is now c-10 This means that Let's use this equation and to solve for n Now use the quadratic formula to solve for n or or or or Toss out the negative solution since you can't have a negative number of people. Therefore, the only solution is So there were originally 70 people.
 Quadratic_Equations/596066: Please solve tis equation: 8p^2+2p-15=01 solutions Answer 377483 by jim_thompson5910(28536)   on 2012-04-06 20:21:28 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "p": 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 solutions are or
 Linear_Equations_And_Systems_Word_Problems/596064: 0.3x-0.4=0.2x+7 1 solutions Answer 377482 by jim_thompson5910(28536)   on 2012-04-06 20:20:51 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 10 to clear out the decimals. Distribute and multiply. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is
 Quadratic_Equations/596063: Please help me solve the problem: 12c^2+8c+1=01 solutions Answer 377481 by jim_thompson5910(28536)   on 2012-04-06 20:20:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "c": Start with the quadratic formula Plug in , , and 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 solutions are or
 Money_Word_Problems/596055: How much must you invest today in order to have $50,000 in 20 years, if your savings account pays 3% interest compounded daily? 1 solutions Answer 377469 by jim_thompson5910(28536) on 2012-04-06 19:35:47 (Show Source): You can put this solution on YOUR website! So you'll need to invest$27,441.26
 Distributive-associative-commutative-properties/596045: how to solve and check answer 12-16=4y+8+3y1 solutions Answer 377462 by jim_thompson5910(28536)   on 2012-04-06 18:43:04 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Exponents/596043: which of the following is equivelent to 2.6 X 10 to the power of 4 1 solutions Answer 377461 by jim_thompson5910(28536)   on 2012-04-06 18:42:12 (Show Source): You can put this solution on YOUR website!$\LARGE 2.6 \times 10^{4} = 26,000$ To get this answer, start with 2.6 and move the decimal point 4 spots to the right.
 Exponents/596042: which property is used in this equation? 15-5x=5(3-x)1 solutions Answer 377458 by jim_thompson5910(28536)   on 2012-04-06 18:40:52 (Show Source): You can put this solution on YOUR website!The distributive property is being used here.
 Exponents/596038: what is the slope of (1,4) and (-1,-2)1 solutions Answer 377453 by jim_thompson5910(28536)   on 2012-04-06 17:48:09 (Show Source): You can put this solution on YOUR website!Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is
 Exponents/596036: which of the following numbers are irrational ? A.square root of 25 B.square root of 15 C.7 over 8 D.-41 solutions Answer 377451 by jim_thompson5910(28536)   on 2012-04-06 17:46:21 (Show Source): You can put this solution on YOUR website! is irrational since you cannot represent it as a fraction of integers (or whole numbers)
 Equations/596031: Hello, I am trying to solve this equation for my son who is in high school. He is having a difficult time with algebra and it's been a while since I've touched on this subject.I would greatly appreciated if someone could help us both out. The equation is 2y - 3(2 - y) = 5 + y . Thank you, and if you can show the steps on how this is done instead of just the answer would also be great so that I may in the future be of some help and can learn myself as well.1 solutions Answer 377448 by jim_thompson5910(28536)   on 2012-04-06 17:31:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Probability-and-statistics/596030: A recent national survey found that high school students watched an average (mean) of 7.3 DVDs per month with a population standard deviation of .50 hours. A random sample of 40 college students revealed that the mean number of DVDs watched last month was 6.60. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students and Compute the P-value ? (I know I just asked a very similar question but now I can't find the p-value and i'm not sure what that is)1 solutions Answer 377447 by jim_thompson5910(28536)   on 2012-04-06 17:30:07 (Show Source): You can put this solution on YOUR website!The test statistic found here was z = -8.85437744847147 (approximately) This is very very far from the center value of z = 0. In fact, it's more than 8 standard deviations away from the mean. So it's very unlikely to observe this value if it randomly came up (assuming the null is true). Usually, the most likely values will fall within 3 standard deviations (on either side). But this is more than 8 standard deviations away. This means that the p-value is very small. So small that it's practically zero. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. So we can conclude that college students watch fewer DVDs a month than high school students.
 Probability-and-statistics/596028: A recent national survey found that high school students watched an average (mean) of 7.3 DVDs per month with a population standard deviation of .50 hours. A random sample of 40 college students revealed that the mean number of DVDs watched last month was 6.60. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students and Compute the value of the test statistic ? (I can't find the test statistic part) 1 solutions Answer 377444 by jim_thompson5910(28536)   on 2012-04-06 17:09:04 (Show Source): You can put this solution on YOUR website!Test Statistic: $\LARGE z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$ $\LARGE z = \frac{6.60-7.3}{\frac{0.50}{\sqrt{40}}}$ $\LARGE z = \frac{-0.7}{\frac{0.50}{\sqrt{40}}}$ $\LARGE z = \frac{-0.7}{\frac{0.50}{6.32455532033676}}$ $\LARGE z = \frac{-0.7}{0.0790569415042}$ $\LARGE z = -8.85437744847252$ So the test statistic is approximately $\LARGE z = -8.85437744847252$
 Miscellaneous_Word_Problems/596027: A rectangle has a perimeter of 196 inches. the length is 28 inches more than the width. What is the dimensions?1 solutions Answer 377441 by jim_thompson5910(28536)   on 2012-04-06 16:52:40 (Show Source): You can put this solution on YOUR website!P = 2L + 2W 196 = 2(W+28) + 2W 196 = 2W+56+2W 196 = 56+4W 0 = 56+4W-196 -4W = 56-196 -4W = -140 W = (-140)/(-4) W = 35 --------------- L = W+28 L = 35+28 L = 63 So the length is 63 inches and the width is 35 inches.
 Linear-systems/596026: Questions & answers Transpose the formula to find s---->Question : a=2(ut-s)/t^2 I got s=l^2(2(ut-s) Word__Problem a)When five is taken from six times a certain number the result is fifteen.What is the number? I GOT LET X BE THE CERTAIN NUMBER 6X-5=15 6X=15+5 6X=20 X=20/6 b)Sidney paid a grocery bill of $3.90 with dimes and quarters.If there were 4 more dimes than quarters,how many coins of each kind did he have? Not sure how to attempt this?1 solutions Answer 377440 by jim_thompson5910(28536) on 2012-04-06 16:43:43 (Show Source): You can put this solution on YOUR website!# 1 ======================================================= # 2 You're very close to the final answer. Reduce to get 20/6 = 10/3 So the answer is 10/3 ======================================================= Let d = # of dimes and q = # of quarters "If there were 4 more dimes than quarters", then The total value of d dimes is 0.1d dollars The total value of q quarters is 0.25q dollars They must add to 3.90, so 0.1d + 0.25q = 3.90 Multiply everything by 100 to get Now use this equation (along with the first) to solve for d and q ... Replace 'd' with 'q+4' (since d = q+4) So there are 10 quarters. and there are 14 dimes  Miscellaneous_Word_Problems/596025: how many 2/3 acres lots can fill a 9 3/4 acres of land?1 solutions Answer 377437 by jim_thompson5910(28536) on 2012-04-06 16:35:44 (Show Source): You can put this solution on YOUR website!Let x = # of lots If each lot is 2/3 of an acre, then x lots will be total of (2/3)x acres We want this to be 9 3/4, so... (2/3)x = 9 3/4 (2/3)x = 9 + 3/4 (2/3)x = 36/4 + 3/4 (2/3)x = 39/4 2x = 3*(39/4) 2x = 117/4 x = (117/4)/2 x = (117/4)*(1/2) x = 117/8 x = (112 + 5)/8 x = 112/8 + 5/8 x = 14 + 5/8 x = 14 5/8 So you need 14 5/8 lots, but you can only have a whole number of lots. So round down to get the final answer of 14 lots.  Probability-and-statistics/596022: Using two independent samples, we test for a hypothesized difference between two population means. The population standard deviations are equal. The number in the first sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value? a.24 b.25 c.26 d.271 solutions Answer 377434 by jim_thompson5910(28536) on 2012-04-06 16:23:10 (Show Source): You can put this solution on YOUR website!Degrees of freedom: df = n1 + n2 - 2 df = 15 + 12 - 2 df = 27 - 2 df = 25 So the answer is choice B Note: the formula only works if the population standard deviations are equal  Travel_Word_Problems/596021: How many hours would it take a truck doing 55 mph to go 911 miles?1 solutions Answer 377433 by jim_thompson5910(28536) on 2012-04-06 16:16:41 (Show Source): You can put this solution on YOUR website!d = rt 911 = 55t 911/55 = t 16.5636 = t t = 16.5636 So it will take approximately 16.5636 hours  Inverses/596020: Please check my work: Evaluation Problem: -8x - 22 = -27 1/3 3[-8x - 22] = 3(-27) x 3(1/3) -24x - 66 = -81 -24x = -81 - +66 -24x = -15 x= 5/81 solutions Answer 377432 by jim_thompson5910(28536) on 2012-04-06 16:13:36 (Show Source): You can put this solution on YOUR website! Let me know if you have any questions.  Travel_Word_Problems/596019: Rene is going to the lake to visit some friends. If the lake is 60 miles away, and Rene is driving at 40 miles per hour the entire time, how long will it take her to get to the lake?1 solutions Answer 377431 by jim_thompson5910(28536) on 2012-04-06 16:05:56 (Show Source): You can put this solution on YOUR website!d = rt 60 = 40t 60/40 = t 3/2 = t t = 3/2 t = 1 1/2 So it will take $\Large 1 \frac{1}{2}$ (one and a half) hours. This is equal to 90 minutes.  Linear-systems/596016: Solve the following equations...this is what i did 1) 4x/x+2 + 3/x-2=4 when i set it up this is what i got 4x(x-2)+3(x+2)=4(x+2)(x-2) 2.)10b-50/b^2-b-20 divided by 15/6b+24 answer: i factored everything and flipped it over since it says to divide and i got 10(b-5)/(b+4)(b-5) X 6(b+4)/15 10(b-5)/15(b-5) where should the 6 go?1 solutions Answer 377428 by jim_thompson5910(28536) on 2012-04-06 15:47:08 (Show Source): You can put this solution on YOUR website!# 1 You're on the right track. Now foil/expand, simplify and get into standard form The x squared terms cancel and we're left with a linear equation. I'll let you solve this. Tell me what you get. ============================================================================================================== # 2 The 6 is in the numerator of the second fraction (in step 2). So it should stay in the numerator. You can multiply it with the 10 in the numerator of the first fraction to get 10*6 = 60 So you'll end up with 60(b-5)/15(b-5) which can be simplified further (I'll let you take over from here. Let me know what you get)  Numeric_Fractions/595983: Please help me solve (a+3)^31 solutions Answer 377426 by jim_thompson5910(28536) on 2012-04-06 15:36:24 (Show Source): You can put this solution on YOUR website!(a+3)^3 (a+3)(a+3)(a+3) (a+3)(a^2+6a+9) a(a^2+6a+9)+3(a^2+6a+9) a^3+6a^2+9a+3a^2+18a+27 a^3+9a^2+27a+27 So (a+3)^3 = a^3+9a^2+27a+27 for all values of 'a'  absolute-value/595979: abs(x-2)+ 4 = 2x I tried but I keep getting different things and then I got a negative but I know that isn't right because I have answer choices and there no negatives so please help. I don't get the x on the 2 at all and I have no idea how to solve this.1 solutions Answer 377425 by jim_thompson5910(28536) on 2012-04-06 15:34:23 (Show Source): You can put this solution on YOUR website! or or or or or or or or So the only solution is really  Linear-systems/596010: I Factored these questions and here are my answers 1)15^3-60x 15x(x^2-4) 2)5x^3-2x^2+5x-2 x^2(5x-2) (5x-2) (x^2+1)(5x-2) 3)3x^2+x-2 ac=3(-2)=-6 b=1 3x^2+3x-2x-2 3x(x+1)-2(x+1) (3x-2)(x+1) Simplify a)(x+y)(x^2-5y^4) answer:(x^3-xy^4)+(x^2 -5y^5) 4)write the set {...,-3,-1,1,3,5,7,...}using set builder notation.1 solutions Answer 377421 by jim_thompson5910(28536) on 2012-04-06 15:20:31 (Show Source): You can put this solution on YOUR website!# 1 you can keep going and factor x^2-4 into (x-1)(x+1) So the final answer is 15x(x-1)(x+1) ======================================================= # 2 Correct ======================================================= # 3 Correct ======================================================= # 4 $\LARGE \{...,-3,-1,1,3,5,7,...\} = \{2k+1 | k\in\mathbb{Z}\}$  Miscellaneous_Word_Problems/596012: Messenger: jim_thompson5910 Values on the horizontal axis range from$0 to \$25,000 show what the curve would look like if the decision maker was risk averse, risk seeking, or risk neutral1 solutions Answer 377420 by jim_thompson5910(28536)   on 2012-04-06 15:16:48 (Show Source): You can put this solution on YOUR website!I'm not exactly familiar with the topic at hand, but take a look at this page. Let me know if it helps. Thanks.
 Rational-functions/595876: SOLVE. 3x^2+x=-9 ANSWER CHOICES A.(1 + i√109)/6 , (1-i√109)/6 B.(1 + i√107)/6 , (1-i√107)/6 C.(-1 + i√107)/6 , (-1-i√107)/6 D.(-1 + i√109)/6 , (-1-i√109)/61 solutions Answer 377359 by jim_thompson5910(28536)   on 2012-04-06 00:06:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Get every term to the left side. Notice that the quadratic is 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 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) or Break up the expression. So the solutions are or
 Equations/595883: Solve simultaneously I dont understand..\ y=x^2-4x-2 y=x-21 solutions Answer 377358 by jim_thompson5910(28536)   on 2012-04-06 00:05:08 (Show Source): You can put this solution on YOUR website!If y=x^2-4x-2 and y = x-2, then we can say x - 2 = x^2-4x-2 This is because the two are both simultaneously equal to y. So they must be equal to each other. From here, solve for x or or ------------------------------------------------------- If x = 0, then y = x-2 = 0-2 = -2 So if x = 0 then y = -2 So one ordered pair solution is (0, -2) ------------------------------------------------------- If x = 5, then y = x-2 = 5-2 = 3 So when x = 5, the value of y is y = 3 So another ordered pair solution is (5, 3)
 Travel_Word_Problems/595888: A car is traveling at a constant velocity of 100 km/hr. What is the distance it will travel in one minute? 1 solutions Answer 377357 by jim_thompson5910(28536)   on 2012-04-06 00:03:48 (Show Source): You can put this solution on YOUR website!60 min = 1 hour 1 min = 1/60 hours d = rt d = 100(1/60) d = 100/60 d = 5/3 d = 1.667 So it will travel roughly 1.667 kilometers.