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jim_thompson5910 answered: 28493 problems
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Radicals/286501: How do I simplify 1 solutions Answer 207792 by jim_thompson5910(28504)   on 2010-03-29 14:35:37 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor 54 into 2*27 (note how 27 is a perfect cube) and factor into Break up the root. Take the cube root of 27 to get 3. Take the cube root of to get . Rearrange the terms and combine the roots. So

Quadratic_Equations/286500: A model rocket is projected straight upward from the ground level according to the height equation h= -16t^2+192t, where t is greater than or = to 0. What is the maximum height of the rocket and after how many seconds does the rocket reach maximum height? I am just somewhat frustrated because it seems as thought the book and my lecture do not have sufficient information to answer this question, and I could really use some help. Thanks. 1 solutions Answer 207790 by jim_thompson5910(28504)   on 2010-03-29 14:32:10 (Show Source): You can put this solution on YOUR website! Note: I'm using 'x' instead of 't' and 'y' instead of 'h' The max height will occur at the vertex since the vertex is the highest/lowest point on the parabola. So we must find the vertex. To find the vertex, we'll use the formula which is the x coordinate of the vertex. Since is in the form where , and , we can plug these values in to get So the 'x' coordinate of the vertex is . So the highest point occurs when or equivalently when (since I replaced 't' with 'x'). So the rocket reaches the max height at 6 seconds. From here, just plug into to find the height 'h' at that given 't' value. Note: the vertex will be (6, h) where 'h' is the height at 6 seconds, but you probably don't need this info.

Graphs/286485: how do i write an inequality for this problem i want to buy a car no less than $5000 and no more than $10000 1 solutions Answer 207781 by jim_thompson5910(28504)   on 2010-03-29 14:13:41 (Show Source): You can put this solution on YOUR website! Let 'x' be the price of the car "no less than $5000" means that the price must be equal to or more than $5000 which means that . Alternatively, you can write it as Also, "no more than $10000" means that the price cannot exceed $10000. So Now combine the two inequalities to get

Polynomials-and-rational-expressions/286486: Not sure how to proceed with this question: y + 10x _______ = 4 x + y 1 solutions Answer 207777 by jim_thompson5910(28504)   on 2010-03-29 14:11:12 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by Distribute. Subtract from both sides Subtract from both sides Combine like terms. Divide both sides by -3 to isolate 'y' Reduce So the solution is

Exponential-and-logarithmic-functions/286482: i must express this as a single logorithm or expression log2(5) +log2(8) please help 1 solutions Answer 207775 by jim_thompson5910(28504)   on 2010-03-29 14:10:11 (Show Source): You can put this solution on YOUR website! Hint: Use the identity

Exponents/286479: Divide. (x^3 - 1)/(x - 1) 1 solutions Answer 207773 by jim_thompson5910(28504)   on 2010-03-29 14:06:08 (Show Source): You can put this solution on YOUR website! Hint: You can factor using the difference of cubes formula . So

Points-lines-and-rays/286471: b is a point between ac if ab=6x and bc=x^2 and ac=27 find x 1 solutions Answer 207769 by jim_thompson5910(28504)   on 2010-03-29 13:58:50 (Show Source): You can put this solution on YOUR website! Since b is somewhere on ac, this means that by the segment addition postulate (ie the parts of a line segment add up to the total line segment) So which then becomes . Factor to get . Now use the zero product property and solve to get or Since we're dealing with lengths, the only sensible answer is

Graphs/286470: How do I solve 4T+3X=-4 . 1 solutions Answer 207768 by jim_thompson5910(28504)   on 2010-03-29 13:56:18 (Show Source): You can put this solution on YOUR website! Which variable do you want to solve for?

Probability-and-statistics/286469: For a standard normal distribution, what is the area the lies to the right of 0.59? Could you please explain how to get this I am lost! THANKS! 1 solutions Answer 207764 by jim_thompson5910(28504)   on 2010-03-29 13:42:51 (Show Source): You can put this solution on YOUR website! Step 1) Calculate the area that lies to the left of 0.59 using the cdf function on your calculator. Step 2) Subtract this result from 1 to get your answer.

Probability-and-statistics/286467: For the standard normal distribution, what is the area tha tlies between 0 adn 3.01? I am getting 0.4987 but I don't know how? HELP LOL 1 solutions Answer 207763 by jim_thompson5910(28504)   on 2010-03-29 13:41:53 (Show Source): You can put this solution on YOUR website! You are correct. Simply use the cdf function on your calculator.

Inequalities/286466: -3 -2y>9 1 solutions Answer 207762 by jim_thompson5910(28504)   on 2010-03-29 13:37:49 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add 3 to both sides. Combine like terms on the right side. Divide both sides by -2 to isolate y. Remember that dividing both sides by a negative number flips the inequality sign. Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Probability-and-statistics/286462: 10 white balls, 20 blue balls, 20 red balls are placed in a urn. If two balls are drawn, with replacement, what is teh probability of drawing 2 white balls? and how did we figure this out? 1 solutions Answer 207761 by jim_thompson5910(28504)   on 2010-03-29 13:26:26 (Show Source): You can put this solution on YOUR website! P(2 white balls) = P(white ball AND white ball) = P(white ball)*P(white ball) = (10/50)(10/50) = 100/2500 = 1/25 = 0.04 So the probability is 1/25 which is a 4% chance.

Expressions-with-variables/286461: 2+3/x-5 / 4-1/x-5 2/1 + 3/x-5 / 4/1 - 1/x-5 2x-7 / 4x-21 My email was incorrect of the one I just sent I need to know if this is correct and it is reduced as far as it can be? 1 solutions Answer 207758 by jim_thompson5910(28504)   on 2010-03-29 13:22:06 (Show Source): You can put this solution on YOUR website! You are correct in saying that and no further simplification is possible.

Rational-functions/286453: For the function f(x)=x squared + 2/x-1 How do I check for symmetry and find the y-intercept? I think I was able to find the x-intercept by plugging in the function equation x=0. 1 solutions Answer 207751 by jim_thompson5910(28504)   on 2010-03-29 13:07:42 (Show Source): You can put this solution on YOUR website! Hint: If f(x) is symmetric with respect to the 'x' axis, then (ie negate the 'y' value). If f(x) is symmetric with respect to the 'y' axis, then . Finally, if f(x) is symmetric with respect to the origin (ie you can rotate the graph 180 degrees and it won't change), then

Expressions-with-variables/286447: b=3 c= -12 a=-2 d=18 what is 2bc/ad 1 solutions Answer 207748 by jim_thompson5910(28504)   on 2010-03-29 12:59:31 (Show Source): You can put this solution on YOUR website! Simply plug in the values and use the order of operations to simplify. So which means that when b=3 c= -12 a=-2 d=18

Exponential-and-logarithmic-functions/286434: i must solve for x logx32=5 how do you do this the x is little 1 solutions Answer 207744 by jim_thompson5910(28504)   on 2010-03-29 12:50:44 (Show Source): You can put this solution on YOUR website! Recall that can be rewritten as . In this case, this means that can be rewritten as . Also, take note that . So which means that (take the 5th root of both sides)

Surface-area/286437: The perimeter of a square is 100 inches. How many square tiles 1 inch on each edge are needed to cover its area? 1 solutions Answer 207743 by jim_thompson5910(28504)   on 2010-03-29 12:48:30 (Show Source): You can put this solution on YOUR website! The perimeter of a square is which means that . Solve for s to get . So the length of the side is 25 inches long. The area of a square is . In this case, . So the area of the square is 625 square inches. Since each tile has a side length of 1 inch, the area of each individual tile is square inch. So you'll need tiles to cover the square.

Parallelograms/286436: In parallelogram ABCD, angle A=x degrees and angle B=(3x) degrees. Find m A. 140 degrees B. 135 degrees C. 70 degrees D. 45 degrees Thank you so much for all your help!!!! 1 solutions Answer 207742 by jim_thompson5910(28504)   on 2010-03-29 12:45:16 (Show Source): You can put this solution on YOUR website! Hint: Since A and B are adjacent angles, this means that A and B are supplementary ie . Or in this case,

Rational-functions/286441: y is directly proportional to the square of x and inversely proportional to the cube of w, y=18 when x=9 and w=3. Find y when x=3 and w=5 1 solutions Answer 207741 by jim_thompson5910(28504)   on 2010-03-29 12:42:44 (Show Source): You can put this solution on YOUR website! Hint: "y is directly proportional to the square of x and inversely proportional to the cube of w" means that for some fixed value of 'k' (which you find when you plug in the given 'x', 'y' and 'w' values).

Expressions-with-variables/286440: if a= -2 and b= 3 what is 3a+2b 1 solutions Answer 207740 by jim_thompson5910(28504)   on 2010-03-29 12:40:16 (Show Source): You can put this solution on YOUR website! So when and

Trigonometry-basics/286433: How many nanoseconds (1 nanosecond = 10^-9 s) does it take a computer signal to travel 60 cm at a rate of 2.4*10^10 cm/s ? Thank you 1 solutions Answer 207739 by jim_thompson5910(28504)   on 2010-03-29 12:39:19 (Show Source): You can put this solution on YOUR website! Recall that distance = rate*time or D = rt In this case, D=60 cm and cm/sec. Plug these values in to get Now divide both sides by 2.4 to get Now divide both sides by to isolate 't' to get From here, it helps to remember that negative exponents effectively flip fractions. Eg. . This means that we can write as So the value of 't' is seconds. Now just multiply this answer by (this is the given conversion factor) to convert the answer into nanoseconds to get nanoseconds So it takes about 2.5 nanoseconds.

Quadratic_Equations/286362: If (x − 7)(y + 7) < 0, then which of the following must be true? A. x > 7 B. y < −7 C. x < 7 D. y > −7 E. None of these. 1 solutions Answer 207735 by jim_thompson5910(28504)   on 2010-03-29 12:21:27 (Show Source): You can put this solution on YOUR website! If , then either (ie is negative) or (ie is negative), but not both. If they are both negative, then the result is positive. Also, if they're both positive, then the product is positive. So if , then which is choice C) and if , then which is is choice B) So the answers are B and C (if you're allowed multiple answers), but not at the same time. If you aren't allowed multiple answers, then there's a typo somewhere.

Exponential-and-logarithmic-functions/286430: i am supposed to write in logorithmic form 1/2^4=1/16 please help if possible i dont understand 1 solutions Answer 207733 by jim_thompson5910(28504)   on 2010-03-29 12:16:07 (Show Source): You can put this solution on YOUR website! Hint: Remember that can be rewritten as

Exponential-and-logarithmic-functions/286368: i must write in exponential form and simplify cuberoot x^5y^5. please help if possible. thanks 1 solutions Answer 207732 by jim_thompson5910(28504)   on 2010-03-29 12:14:54 (Show Source): You can put this solution on YOUR website! Recall that . So You could go one step further and multiply the exponents to get On the other hand, you can pull all of the exponents out to get Either way, they're all equivalent. It'll just depend on what you're book or teacher is looking for.

test/286396: lim 2x^6+6x^3 / 4x^5+3x^3 x→0 1 solutions Answer 207731 by jim_thompson5910(28504)   on 2010-03-29 12:10:28 (Show Source): You can put this solution on YOUR website! Hint: If you directly substitute , then you'll find that you'll have an indeterminate value. Instead, simplify and then apply the substitution.

Graphs/286429: Help me graph this equation, Y=-1/4+4. I can't get the correct coordinates so that I can plot the line. 1 solutions Answer 207729 by jim_thompson5910(28504)   on 2010-03-29 12:08:46 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Graphing Linear Equations In order to graph we only need to plug in two points to draw the line So lets plug in some points Plug in x=-8 Multiply Add Reduce So here's one point (-8,6) Now lets find another point Plug in x=-4 Multiply Add Reduce So here's another point (-4,5). Add this to our graph Now draw a line through these points So this is the graph of through the points (-8,6) and (-4,5) So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 4 units to get to the next point), the y-intercept is (0,)and the x-intercept is (,0) We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,). So we have one point (0,) Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go down 1 units and to the right 4 units to get to our next point Now draw a line through those points to graph So this is the graph of through the points (0,4) and (4,3)

Quadratic_Equations/286427: Find and label the vertex and the line of symmetry. Graph the function. -2(X+2)^2 1 solutions Answer 207727 by jim_thompson5910(28504)   on 2010-03-29 12:07:43 (Show Source): You can put this solution on YOUR website! Hint: The vertex of is (h,k) and the axis of symmetry is . Note: rewrite as

Linear-systems/286418: Solve using the Substitution Method 3x+2y=13 x+y=5 1 solutions Answer 207726 by jim_thompson5910(28504)   on 2010-03-29 12:06:17 (Show Source): You can put this solution on YOUR website! Step 1) Pick an equation and a variable to solve for. I'm going to solve for 'y' in the second equation. So solve for 'y' in to get Step 2) Plug in (ie substitute) into the other equation . In other words, replace each 'y' with to effectively eliminate every 'y' term. After doing so, you should get Step 3) Solve for 'x'. This can be easily done as is a simple linear equation with one variable. Step 4) Take the solution found in step 3 and use it to find the solution in terms of 'y'.

Linear-equations/286207: Find an equation of the line described. Write the equation in the slope-intercept formif possible. through (6, -14) and (3, -2)? 1 solutions Answer 207547 by jim_thompson5910(28504)   on 2010-03-28 18:28:32 (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 Rewrite as Distribute Multiply Subtract 14 from both sides. Combine like terms. So the equation that goes through the points and is

Functions/286185: Find the domain of the function g(x)=8 'over' 2-3x I'm so lost...Thank you in advance!! 1 solutions Answer 207512 by jim_thompson5910(28504)   on 2010-03-28 16:41:46 (Show Source): You can put this solution on YOUR website! Reminder: The domain is the set of all allowable inputs. You can think of this as the set of all possible 'x' values (that produce some number as an output). Remember that you CANNOT divide by zero. So if the denominator , then (solve for 'x'). This means that if , then . In other words, if , then the denominator is zero (which is not allowed). So we must exclude this value from the domain. Since there are no other values that make the denominator zero, this means that the only value to exclude from the domain is So the domain is the set of all real numbers except We denote this in interval notation as Basically, this is the interval with the number taken out of it.

Exponents/286155: Help.... (-4m^2n^4)^3 (-3m^3n^2)^2 / (-6m^2n^3)^6 1 solutions Answer 207484 by jim_thompson5910(28504)   on 2010-03-28 16:01:34 (Show Source): You can put this solution on YOUR website! Hint: Use the four identities 1. . Basically, you can either multiply first, then exponentiate, OR, exponentiate and then multiply. (note: this can expand to any number of terms inside the parenthesis. So you could have 50 terms in the parenthesis if you wanted). Example: 2. . When you raise an exponential expression to another exponent, you're going to multiply the exponents. Example: 3. . When you multiply monomials (with a common base), you're going to add the exponents. Example: 4. . When you divide monomials (with a common base), you're going to subtract the exponents. Example: