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# Recent problems solved by 'Alan3354'

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Rate-of-work-word-problems/305501: Thank you in advance for your help. I have attacked this problem many different ways and still come up short. The problem is:
The members of a bicycle club rode a 20-mile round trip route. On the way back, they had a tailwind and averaged 3 mph faster than on the first 10 miles of the trip. If the entire trip took them 1 1/2 hours, what was their average speed on the first half of the ride?
1 solutions

Answer 218740 by Alan3354(31532)   on 2010-05-17 16:17:09 (Show Source):
You can put this solution on YOUR website!
The members of a bicycle club rode a 20-mile round trip route. On the way back, they had a tailwind and averaged 3 mph faster than on the first 10 miles of the trip. If the entire trip took them 1 1/2 hours, what was their average speed on the first half of the ride?
-------------------------------
d = distance one way = 10 miles
r = rate going without tailwind
d/r + d/(r+3) = 1.5
10/r + 10/(r+3) = 1.5
10(r+3) + 10r = 1.5r(r+3)

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=1681 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 12, -1.66666666666667. Here's your graph:

---------------
Ignore the negative solution
r = 12 mph (1st half)

 Equations/305480: Find the equation of the line through the points (4, -1) and (2, -7). write in standard form using integers only. debsyzach@yahoo.com1 solutions Answer 218718 by Alan3354(31532)   on 2010-05-17 15:29:16 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at Moral Loophole@aol.com
 Expressions-with-variables/305382: Good Morning Algebra.com, I have a question for you again and would appreciate your help Post a fifty word response to the following o How do you know when an equation has infinitely many solutions? o How do you know when an equation has no solution? Again Thank you for you help! The needy one :)1 solutions Answer 218634 by Alan3354(31532)   on 2010-05-17 10:34:34 (Show Source): You can put this solution on YOUR website!If the number of variables is more than the number of equations, there are an infinite number of solutions. x = 6 has one solution. x+y = 6 has an infinite number of solutions. ------------------ You asked about "an equation", I think you meant a system of equations. -------------- x + y = 2 x - 2y = 10 has one solution. -------------- x + y = 2 2x + 2y = 4 has an infinite number, the 2nd eqn is 2x the 1st --> dependent. ------------- x + y = 2 x + y = 3 has no solution --> inconsistent. ------------------ x + y + z = 3 x + y - z = 1 has an infinite number, only 2 eqns with 3 variables. -------------
Geometry_Word_Problems/305289: Write the equation and then solve.
a) One leg of a right triangle is four less than twice the other.
The hypotenuse is 10. Find the length of each leg.

1 solutions

Answer 218628 by Alan3354(31532)   on 2010-05-17 10:15:27 (Show Source):
You can put this solution on YOUR website!
Write the equation and then solve.
a) One leg of a right triangle is four less than twice the other.
The hypotenuse is 10. Find the length of each leg.
-------------------
1st side = x
2nd side = 2x-4

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=1936 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6, -2.8. Here's your graph:

-----------------
Ignore the negative solution
x = 6
2x - 4 = 8
--> 6, 8 & 10 triangle

 Bodies-in-space/305336: Find the volume of a sphere with a radius of 3 in.1 solutions Answer 218605 by Alan3354(31532)   on 2010-05-17 08:54:48 (Show Source):

1 solutions

Answer 218563 by Alan3354(31532)   on 2010-05-16 22:34:54 (Show Source):
You can put this solution on YOUR website!

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=32 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.82842712474619, -0.82842712474619. Here's your graph:

------------------
= 2 ± 2sqrt(2)

 Human-and-algebraic-language/305256: what is 53/20 times number of additional cans collected plus 2.65 translated? 1 solutions Answer 218562 by Alan3354(31532)   on 2010-05-16 22:31:36 (Show Source): You can put this solution on YOUR website!That makes no sense.
Quadratic_Equations/305172: solve the equation in the complex number system
117x^2+1=18x
1 solutions

Answer 218560 by Alan3354(31532)   on 2010-05-16 22:21:43 (Show Source):
You can put this solution on YOUR website!

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -144 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -144 is + or - . The solution is , or Here's your graph:

----------------
= (27 ± 2i)/39

 Probability-and-statistics/305237: Given a standard deck of playing cards, fin the probability of being dealt a flush. (A flush is a 5 card hand in which all the cards are the same suit.) (State answer as a fraction.)1 solutions Answer 218559 by Alan3354(31532)   on 2010-05-16 22:17:31 (Show Source): You can put this solution on YOUR website!Given a standard deck of playing cards, fin the probability of being dealt a flush. ------------- The 1st card can be any suit. The 2nd card is 12 of 51 remaining of the same suit. The 3rd card is 11 of 50. The 4th is 10/49 The 5th is 9/48 12/51 x 11/50 x 10/49 x 9/48 = 11880/5880000 = 99/49000 ~ 1 in 500
 Problems-with-consecutive-odd-even-integers/305180: Find two consecutive even integers whose product is 624.1 solutions Answer 218513 by Alan3354(31532)   on 2010-05-16 20:07:16 (Show Source): You can put this solution on YOUR website!sqrt(624) = ~25 --> 24*26 = 624
 Trigonometry-basics/305188: how do i find the exact value of cos 810 degrees?1 solutions Answer 218504 by Alan3354(31532)   on 2010-05-16 19:46:32 (Show Source): You can put this solution on YOUR website!Subtract 360º repeatedly until the angle is less than 360 810 - 360 = 450 450 - 360 = 90 cos(90) = 0 ----------------
 Miscellaneous_Word_Problems/305147: A cyclist is traveling 85 miles in 5 hours against the wind. He travels 174 miles in 6 hours with the wind. What is the rate of the still air and the rate of the wind.1 solutions Answer 218500 by Alan3354(31532)   on 2010-05-16 19:41:21 (Show Source): You can put this solution on YOUR website!What does the wind have to do with the speed of a bicycle? Have you ever ridden a bicycle in the wind? ------------- The best answer is, "We don't know."
 Linear-systems/305127: how can i solve this substitution methods: 3x-2y=-7 y=2x+61 solutions Answer 218471 by Alan3354(31532)   on 2010-05-16 17:34:25 (Show Source): You can put this solution on YOUR website!Sub for y in the 1st equation y = 2x +6
 Polygons/305124: a regular hexagon has a side 12 in. long, its area is? The formula is P - 1/2 ap. I am stuck 1 solutions Answer 218470 by Alan3354(31532)   on 2010-05-16 17:33:42 (Show Source): You can put this solution on YOUR website!A regular hexagon is 6 regular trianles.
 Numbers_Word_Problems/305083: The sum of the angles of any four sided polygon is 360. If the measures the angles of a four sided polygon are four consecutive odd integers, find the measure of each angle.1 solutions Answer 218469 by Alan3354(31532)   on 2010-05-16 17:11:38 (Show Source): You can put this solution on YOUR website!360/4 = 90, the center of the 4 numbers --> 87, 89, 91, 93
 Finance/305013: I am having a hard time with something, could someone help please? How much money is 1.6 million dollars? I can't figure out if it should be \$1,500,000 or \$1,750,000, or something else altogether. I'm supposed to be working on line-item, performance, and program budgets and I can't get past this, great huh? I'd really appreciate some help, thanks a lot. 1 solutions Answer 218440 by Alan3354(31532)   on 2010-05-16 11:47:58 (Show Source): You can put this solution on YOUR website!\$1,600,000
 Triangles/305008: Which list could not be the measures of lengths of the three sides of a given triangle? 2 ft, 6 ft, 5 ft 12 yd, 35 yd, 20 yd 5 cm, 12 cm, 15 cm 11 mi, 4 mi, 12 mi ??1 solutions Answer 218434 by Alan3354(31532)   on 2010-05-16 11:21:15 (Show Source): You can put this solution on YOUR website!Which list could not be the measures of lengths of the three sides of a given triangle? 2 ft, 6 ft, 5 ft 12 yd, 35 yd, 20 yd 5 cm, 12 cm, 15 cm 11 mi, 4 mi, 12 mi ------------------------ 12 yd, 35 yd, 20 yd This one won't work.
 Bodies-in-space/305011: My friend and i have been working on this math problem and we can't seem to figure it out. We were wondering if someone could help us? Please and Thank You!! We would deeply apprecaite it!! Spheres About two cans of paint are needed to cover the hemispherical dome of the silo. Approximatley how many cans are needed to paint the rest of the silo's exterior? the height is 20m from the bottom to the top of the cylinder and the base is 10m1 solutions Answer 218431 by Alan3354(31532)   on 2010-05-16 10:57:51 (Show Source): You can put this solution on YOUR website!About two cans of paint are needed to cover the hemispherical dome of the silo. Approximatley how many cans are needed to paint the rest of the silo's exterior? the height is 20m from the bottom to the top of the cylinder and the base is 10m diameter -------------------- The surface area of a sphere of radius 5 meters is Half of that is 50 pi square meters -------------------------------- The lateral area of the silo is r = 5, h = 20 Area = 200 pi That's 4 times the hemisphere, so it's ~8 cans of paint.
 Circles/305000: I have been working on this math problem and i can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I deeply appreciate it!! A regular square pyramid with base edge 4 cm is inscribed in a cone with height 6 cm. What is the volume of the cone?1 solutions Answer 218422 by Alan3354(31532)   on 2010-05-16 09:49:30 (Show Source): You can put this solution on YOUR website!The diameter of the base of the cone is 4sqrt(2) --> r = 2sqrt(2) Vol of cone = cc
 Functions/304970: Please help me to solve this function so I will understand g(x)=(sin5x)^2x+31 solutions Answer 218420 by Alan3354(31532)   on 2010-05-16 09:44:17 (Show Source): You can put this solution on YOUR website!Solve it for what?
 Equations/304984: Solva for Z: |6z-3| + 5 I go z as equal to 0 and 11 solutions Answer 218417 by Alan3354(31532)   on 2010-05-16 09:27:25 (Show Source): You can put this solution on YOUR website!Solva for Z: |6z-3| + 5 I go z as equal to 0 and 1 ----------------- |6z-3| + 5 <= 8 |6z+3| <= 3 ---------- Case 1: 6z + 3 <= 3 6z <= 0 z <= 0 -------- Case 2: -6z-3 <= 3 -6z <= 6 z >= -1 --------- The solution can't be "equal", it's not an equation. z can be any value between -1 and zero, inclusive {z| -1 =< z =< 0}
 Mixture_Word_Problems/304988: A boy can pedel his bicycle 3/4 miles in 6 minutes. What is his rate in mph?? Sat prep. Question. Ans. 15/2 mph1 solutions Answer 218416 by Alan3354(31532)   on 2010-05-16 09:11:26 (Show Source): You can put this solution on YOUR website!0.75 mi/0.1 hr = 7.5 mph
 Pythagorean-theorem/304996: The legs of a right triangle are 6 and 10 centimeters long, respectively. What is the length of the hypotenuse?1 solutions Answer 218415 by Alan3354(31532)   on 2010-05-16 09:10:20 (Show Source): You can put this solution on YOUR website! c =~ 11.6619 cm
 Linear-equations/304971: Write the equation of the line (in slope-intercept form) that passes through (3,7) and has a slope of 1/31 solutions Answer 218414 by Alan3354(31532)   on 2010-05-16 09:08:00 (Show Source): You can put this solution on YOUR website!A line and a point example. Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2) ----------------- Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y. 9x+3y = 36 3y= - 9x + 36 y = -3x + 12 The slope, m = -3 ------------------ The slope of lines parallel is the same. The slope of lines perpendicular is the negative inverse, m = +1/3 ---------------- Use y = mx + b and the point (1,2) to find b. 2 = (1/3)*1 + b b = 5/3 The equation is y = (1/3)x + 5/3 (slope-intercept form) x - 3y = -5 (standard form) ------------------------ For further assistance, or to check your work, email me via the thank you note, or at Moral Loophole@aol.com
 Mixture_Word_Problems/304990: A plane travel x miles during the first 2 hours of a trip and y miles during the last 3 hours of the trip. What is the average rate of the entire trip? Sat prep. Question. Ans. x+y/51 solutions Answer 218413 by Alan3354(31532)   on 2010-05-16 09:05:43 (Show Source): You can put this solution on YOUR website!Why do you post these if you know the answers?
 Problems-with-consecutive-odd-even-integers/304974: If a and b are both even numbers, which of the following COULD be and odd integer? A) (a + b)^2 B) a2 + b2 C) (a + 1)^2 + (b + 1)^2 D) (a + 1)*(b + 1) - 1 E) (a + 1) / (b + 1) 1 solutions Answer 218405 by Alan3354(31532)   on 2010-05-16 07:33:28 (Show Source):
 Equations/304891: if it takes three days to travel to the moon(which is 240,000 mi away), how long will it take to reach Venus(which is 26,000,000 mi away)?1 solutions Answer 218367 by Alan3354(31532)   on 2010-05-15 22:31:05 (Show Source): You can put this solution on YOUR website!if it takes three days to travel to the moon(which is 240,000 mi away), how long will it take to reach Venus(which is 26,000,000 mi away)? ------------------------ 240000 miles/3 days = 26000000 miles/ d days 26000000/d = 80000 d = 26000000/80000 d = 325 days Pack a big lunch
 Length-and-distance/304925: Write the equation of a circle with a diameter having endpoints at (-2,6) and (8,4).1 solutions Answer 218361 by Alan3354(31532)   on 2010-05-15 22:22:48 (Show Source): You can put this solution on YOUR website!Write the equation of a circle with a diameter having endpoints at (-2,6) and (8,4). ---------------- The center is the midpoint (3,5) The radius is the distance from (3,5) to (8,4) = sqrt(26)
 Length-and-distance/304924: Line segment CD is tangent to circle Z at (1,7). If Z has coordinates (5,2), find the slope of line segment CD.1 solutions Answer 218360 by Alan3354(31532)   on 2010-05-15 22:20:10 (Show Source): You can put this solution on YOUR website!Is (5,2) the center? Or a point on the circle?
 Linear-equations/304904: I need to graph the following lines with the given point and slope (1,-1);m=3/4 (-2,4); m=1/3 (-2,-1); m=2/5 (5,3);m=4 X-intercept=-2;m= - 4/3 ;1 solutions Answer 218355 by Alan3354(31532)   on 2010-05-15 21:34:05 (Show Source): You can put this solution on YOUR website!I need to graph the following lines with the given point and slope (1,-1);m=3/4 Plot the point (1,-1) Count 3 squares up and 4 squares to the right and plot that point. Draw a straight line thru them. -------------------------- (-2,4); m=1/3 Do it like the one above, 1 square up and 3 to the right. ------------------------- (-2,-1); m=2/5 Same as above ---------------- (5,3);m=4 Same again, 4 up and 1 right ------------------------- X-intercept=-2;m= - 4/3 Plot (-2,0) Count 4 down and 3 right or (4 up and 3 left)
 Surface-area/304910: What happens to a cubes surface area if it is tripled?1 solutions Answer 218353 by Alan3354(31532)   on 2010-05-15 21:11:36 (Show Source): You can put this solution on YOUR website!If the surface area is tripled, it's 3 times as much.