Tutor:

New! Get regular updates about newly solved problems via algebra.com's RSS system.

---

Recent problems solved by 'robertb'

robertb answered: 4011 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019, >>Next

Travel_Word_Problems/356055: how far would you travel in 2.4 hours at 25 mph? 1 solutions Answer 254148 by robertb(4012)   on 2010-10-13 20:16:08 (Show Source): You can put this solution on YOUR website! miles.

Numbers_Word_Problems/356053: find 3 consecutive even integers whose sum is: a. 156 b. 258 c. -60 1 solutions Answer 254146 by robertb(4012)   on 2010-10-13 20:14:46 (Show Source): You can put this solution on YOUR website! three consecutive even integers are x, x+2, x+4. Their sum is x+x+2+x+4 = 3x+6. a. , , . Therefore the consecutive even integers are 50, 52, 54. b. , , . Therefore the consecutive even integers are 84, 86, 88. c. , , . Therefore the consecutive even integers are -22, -20, -18.

Equations/356054: what's the solution to a + 5 = -5a + 5 1 solutions Answer 254144 by robertb(4012)   on 2010-10-13 20:09:48 (Show Source): You can put this solution on YOUR website! , , , .

Complex_Numbers/355616: show that the integration of ( cos3x / (x^2 + 1 )^2 ) = 2pi / e^3 would any one help >>?? . 1 solutions Answer 253939 by robertb(4012)   on 2010-10-13 02:19:43 (Show Source): You can put this solution on YOUR website!

Numeric_Fractions/355622: 4(x^-4)^3(-2x)^4 1 solutions Answer 253935 by robertb(4012)   on 2010-10-13 00:55:58 (Show Source): You can put this solution on YOUR website! = = =

Travel_Word_Problems/355624: A running track has the shape with straight sides and semicircular ends. if the length of the track is 440 yd the two straight parts are each 110 yd long, what is the radius of the semicircular parts(to the nearest yd)? 1 solutions Answer 253932 by robertb(4012)   on 2010-10-13 00:52:53 (Show Source): You can put this solution on YOUR website! the two straight parts are each 110 yards. Thus each of the two congruent semicircular parts must also be 110 yards each. Now circumference , or . This means that , or . To the nearest yard, this is equal to 35 yards.

Numeric_Fractions/355623: (8x)^-7(8x)^3= ??? 1 solutions Answer 253931 by robertb(4012)   on 2010-10-13 00:47:29 (Show Source): You can put this solution on YOUR website!

Linear-equations/355462: write an equation of the line that passes through ( 6,-10) and is perpendicular to the line that passes through ( 4,-6) and (3,-4) 1 solutions Answer 253871 by robertb(4012)   on 2010-10-12 19:52:10 (Show Source): You can put this solution on YOUR website! The slope of the line pasing through (4,-6) and (3, -4) is . The slope of the line perpendicular to this is equal to its negative reciprocal: 1/2. Therefore the equation of the line with slope 1/2 and passing through (6,-10) is , or , , .

Equations/355459: How do you do this problem need help asap Equations and functions y = x+7 identify the domain and range 1 solutions Answer 253870 by robertb(4012)   on 2010-10-12 19:46:09 (Show Source): You can put this solution on YOUR website! Both domain and range are equal to the set of all real numbers.

Graphs/355447: Identify the correct x intercept and y intercept of the equation 4x - 3y = 24. 1 solutions Answer 253868 by robertb(4012)   on 2010-10-12 19:42:25 (Show Source): You can put this solution on YOUR website! To get the y-intercept, let x = 0: 4(0)-3y = 24, or -3y=24, or y = -8. Therefore, the y-intercept is the point (0, -8). To get the x-intercept, let y = 0: 4x - 3(0) = 24, or 4x = 24, or x = 6. Therefore, the x-intercept is the point (6, 0).

Linear-equations/355448: How do you solve the following equation using the Elimination Method: -5x + 12y = 20 x - 2y = -6 1 solutions Answer 253867 by robertb(4012)   on 2010-10-12 19:39:16 (Show Source): You can put this solution on YOUR website! Multiply the bottom equation by 5, with the purpose of eliminating x. Then we get 5x -10y = -30. Add corresponding sides with the top equation, to get 12y - 10y = 20 - 30, or 2y = -10, or y = -5. Use the bottom equation to solve for x: x - 2(-5) = -6, or x + 10 = -6, or x = -16. Therefore the solution is the ordered pair (-16, -5).

Linear-equations/355443: How do you solve the following equation using the Elimination Method: -3x + 3y = 3 3x + y = 9 1 solutions Answer 253864 by robertb(4012)   on 2010-10-12 19:34:35 (Show Source): You can put this solution on YOUR website! Add corresponding sides of the two equations. -3x and 3x will cancel each other out, giving 3y+y = 3+9, or 4y = 12, or y = 3. Using the 2nd equation, 3x + 3 = 9, or 3x = 6, or x = 2. Therefore the solution is the ordered pair (2, 3).

Problems-with-consecutive-odd-even-integers/355440: the width, length, and diagonal of a rectangle are consecutive even integers. What are the integers. 1 solutions Answer 253861 by robertb(4012)   on 2010-10-12 19:31:07 (Show Source): You can put this solution on YOUR website! Let w = width of the rectangle, which is also the shortest side of the right triangle. Then the other leg is w +2, and w+4 is the hypotenuse. Then by the Pythagorean Theorem, , , , . Thus w = 6, and the other leg is 8, and the hypotenuse is 10.

Miscellaneous_Word_Problems/355436: a sugar dud has 30 less than twice as many calories as a krunchy krum. if 5 sugar duds have the same number of calories as 8 krunchy krums, how many calories are in each? 1 solutions Answer 253857 by robertb(4012)   on 2010-10-12 19:22:34 (Show Source): You can put this solution on YOUR website! Let s = # calories in a sugar dud k = # calories in a krunchy krum. Then from the given, . From the second sentence, we also know that . Thus by direct substitution, . , , , the number of calories in a krunchy krum. This makes calories for a sugar dud.

test/355432: martha wants to rent a car for a week and to pay no more then $130. how far can she drive if the car rental costs $94 a week plus $.12 a mile? 1 solutions Answer 253852 by robertb(4012)   on 2010-10-12 19:14:37 (Show Source): You can put this solution on YOUR website! $130 - $94 = $36. Then $36/$0.12 per mile = 300 miles.

real-numbers/355106: Could you please give me an example of a real number,that is not an irrational number? 1 solutions Answer 253634 by robertb(4012)   on 2010-10-12 07:23:55 (Show Source): You can put this solution on YOUR website! Any integer would do.

Pythagorean-theorem/355109: Two lines intersect at a point and formed two non-adjacent angles whose measures are (4x-95)and (2x+21)degrees.What is the value of each angle? 1 solutions Answer 253633 by robertb(4012)   on 2010-10-12 07:22:34 (Show Source): You can put this solution on YOUR website! , , . Each of the 2 angles is 137 degrees.

Money_Word_Problems/355108: Nadine found a wallet which contains 1560 pesos in P10 and P20 bills. If there are 110 bills in all, how many bills of each kind were there? 1 solutions Answer 253632 by robertb(4012)   on 2010-10-12 07:19:39 (Show Source): You can put this solution on YOUR website! Let x = # 10 peso bills. Then 110 - x = # 20 peso bills. Also, , after dividing by 10. , , . So there are 64 10-peso bills, and 46 20-peso bills.

Radicals/355006: Divide, then simplify: SQRT(270X^3) / SQRT(30X) 1 solutions Answer 253628 by robertb(4012)   on 2010-10-12 07:02:34 (Show Source): You can put this solution on YOUR website! = = =3x, assuming x is positive.

Probability-and-statistics/355022: how many different ways can 8 speakers be seated on a stage? 1 solutions Answer 253627 by robertb(4012)   on 2010-10-12 06:58:55 (Show Source): You can put this solution on YOUR website! If they're to be seated on a row, then ways.

Rate-of-work-word-problems/355008: it takes 7 people 8.5 hours to complete a job how long would it take 4 people? 1 solutions Answer 253626 by robertb(4012)   on 2010-10-12 06:56:22 (Show Source): You can put this solution on YOUR website! The rate of contribution of a person per hour is . If 4 people are working, then let x = #number of hours to finish job. Then , hours.

Probability-and-statistics/355092: how does the sample's shape compare to the population's shape? 1 solutions Answer 253625 by robertb(4012)   on 2010-10-12 06:46:45 (Show Source): You can put this solution on YOUR website! If what you're asking is about the distribution of the sample means coming from some population that is symmetrical or otherwise, then the Central Limit Theorem says that as the sample size increases, the distribution approaches a normal distribution whose mean is the same as that of the underlying population, with a standard deviation equal to the standard deviation of the underlying distribution divided by the square root of the sample size.

Pythagorean-theorem/355096: 1. three angles are in the ratio 2:3:4.If the smallest angle is 24 ,fing the sum of the three angles? 2.the first three triangular are 1,3,6,which of the following is the fourth triangular number? 1 solutions Answer 253624 by robertb(4012)   on 2010-10-12 06:33:15 (Show Source): You can put this solution on YOUR website! 1. Let S = sum of the three angles. Then the smallest angle is 2/9 of the sum, the next is 3/9 of the sum, and the biggest is 4/9 of the sum. Now it is given that , so . 2. The fourth triangular number is 1+2+3+4 = 10. The 5th is 10+5 = 15, etc...

Geometry_Word_Problems/355095: What is the measure of an angle if the measure of its supplement is 39 degrees more than twice the measure of its compliment? (Show your solution) 1 solutions Answer 253623 by robertb(4012)   on 2010-10-12 06:25:54 (Show Source): You can put this solution on YOUR website! Let x = the measure of the angle. Then 180 - x = its supplement, and 90 - x = its complement. From the given, , , , degrees.

Mixture_Word_Problems/355104: How many grams of 50% silver alloy and a 10% silver alloy must be mixed to obtain 24 grams of a 25% silver alloy? 1 solutions Answer 253622 by robertb(4012)   on 2010-10-12 06:19:59 (Show Source): You can put this solution on YOUR website! Let x = # of grams of 50% silver alloy Then 24 - x = # of grams of 10% silver alloy. , , , and . Therefore he has to mix 9 grams of 50% silver alloy, and 15 grams of 10% silver alloy.

Trigonometry-basics/355076: A man is walking away from a lamppost with a light source 6 m above the ground. The man is 2 m tall. How far from the lamppost is the man when his shadow is 5 m long? 1 solutions Answer 253621 by robertb(4012)   on 2010-10-12 06:14:50 (Show Source): You can put this solution on YOUR website! Let x = distance of the man from the base of the lamppost. Then x + 5=distance of the tip of the man's shadow from the base of the lamppost. Then by a direct application of similar triangles, . After cross-multiplication, . . The man is 10 m away from the base of the lamppost.

Pythagorean-theorem/355099: One of the legs of a right triangle has length √19 cm The sum of the lengths of the hypotenuse and the other leg is 19 cm. What is the area of this triangle in square centimeters? 1 solutions Answer 253619 by robertb(4012)   on 2010-10-12 06:03:58 (Show Source): You can put this solution on YOUR website! The legs have measure and b, the hypotenuse, c. We have to find the area . It is given that , and so . From the Pythagorean theorem, , or . By direct substitution, , , , , , after dividing both sides by 19. . This area is then sq. cm.

Circles/355100: A circle has a chord of length 10 cm. This chord is the perpendicular bisector of a radius of that circle. What is the area of the circle in square centimeters? 1 solutions Answer 253617 by robertb(4012)   on 2010-10-12 05:50:38 (Show Source): You can put this solution on YOUR website! The given chord perpendicularly bisects a radius of the circle, so we can form a right triangle where one leg measures 5 cm, the other leg measures , and the hypotenuse measures r. Then by the Pythagorean Theorem, , , , . Now the area of the circle is given by . Substituting into this area formula, we get square centimeters.

Probability-and-statistics/355049: Flip a fair coin 6 times. Find the probability of getting the following outcome. (Round your answer to six decimal places.) at least 4 heads 1 solutions Answer 253614 by robertb(4012)   on 2010-10-12 05:38:55 (Show Source): You can put this solution on YOUR website! = = = = = =0.34375

Coordinate-system/355031: solve 5=1.5x+1 1 solutions Answer 253602 by robertb(4012)   on 2010-10-11 23:55:42 (Show Source): You can put this solution on YOUR website!

Inequalities/355046: 22-3x_< 16 1 solutions Answer 253601 by robertb(4012)   on 2010-10-11 23:53:47 (Show Source): You can put this solution on YOUR website! , since we have divided by a negative number.