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oberobic answered: 2303 problems
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Pythagorean-theorem/525402: the diagonal of a square is the square root of 15. what is the perimeter of the square?
1 solutions
Answer 348090 by oberobic(2304)   on 2011-11-02 21:23:51 (Show Source):
You can put this solution on YOUR website!The diagonal of a square is the hypotenuse of a right triangle.
Applying the Pythagorean formula...
.
15 = a^2 + b^2
.
Since it is a square, we know that a=b
.
15 = 2a^2
a^2 = 7.5
a = sqrt(7.5)
a = 2.738612787525831
.
So the sides are 2.738612787525831.
.
The perimeter = 4*2.738612787525831 = 10.95445115010332
.
Done.
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Travel_Word_Problems/525385: If a driver is travelling at the speed of 80km/hr how long will it take the driver to travel 210 km ?
1 solutions
Answer 348084 by oberobic(2304) on 2011-11-02 21:04:32 (Show Source):
You can put this solution on YOUR website!The units of measure will help you understand what to do.
You want an answer in terms of time, specifically in terms of hours.
You know the vehicle is traveling at 80 km/hr.
You know the vehicle travels 210 km.
So, to end up with answer in hrs, you need to divide 210 km by 80 km/hr.
.
You also could apply the fundamental distance equation:
d = r*t
t = d/r
.
210/80 = 21/8 = 2 5/8 hr
.
5/8 hr * 60 min/hr = 300/8 min = 37.5 min
.
t = 2 hr 37.5 min
.
Done.
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Rectangles/525377: Could you please answer the following. "A rectangle has a perimeter of 38 feet and an area of 48 square feet. What are the dimensions of the rectangle"?
1 solutions
Answer 348079 by oberobic(2304) on 2011-11-02 20:54:08 (Show Source):
You can put this solution on YOUR website!2(L+W) = 38
L*W = 48
so
W = 48/L
.
substitute
.
2(L+48/L) = 38
2L +96/L = 38
.
multiply both sides by L to eliminate the fraction
.
2L^2 +96 = 38L
.
2L^2 -38L +96 = 0
.
divide by 2
.
L^2 -19L +48 = 0
.
factor
.
(L-3)(L-16) = 0
.
L = 3 or L=16
so
W = 16 or 3, respectively
.
Done.
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Problems-with-consecutive-odd-even-integers/525369: Four times the first of three consecutive even integers is sixteen more than three times the second. Find the integers
1 solutions
Answer 348072 by oberobic(2304) on 2011-11-02 20:43:27 (Show Source):
You can put this solution on YOUR website!There are three consecutive even integers. Define these as:
x
x+2
x+4
.
4x - 16 = 3*(x+2)
4x -16 = 3x + 6
x = 22
.
x+2 = 24
.
x+4 = 26
.
Check the answer.
4x = 4*22 = 88
88 -16 = 72
3*24 = 72
Correct.
.
Answer: The three consecutive even integers are: 22, 24, and 26.
.
Done.
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Geometry_Word_Problems/525360: what will it cost to to carpet a rectangular floor measuring 15 feet by 21 feet if the carpet costs 20.97 per square yard
1 solutions
Answer 348070 by oberobic(2304) on 2011-11-02 20:39:54 (Show Source):
You can put this solution on YOUR website!area = 15 ft * 21 ft = 315 sq ft
but you need this in yards
1 sq yd = 3 ft * 3 ft = 9 sq ft
.
315 sq ft / 9 sq ft/yd = 35 sq yd
.
35 sq yd * $20.97 / sq yd = $733.9499999999999 or about $733.95
.
Done.
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Linear-equations/525262: Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2 Please show all of your work.
1 solutions
Answer 348056 by oberobic(2304) on 2011-11-02 20:19:04 (Show Source):
You can put this solution on YOUR website!The line perpendicular to -7x +9y = -2 has the inverse reciprocal slope.
First get the line into slope-intercept form.
-7x +9y = -2
9y = 7x -2
y = (7/9)x - 2/9
.
m = slope = 7/9
.
So, the perpendicular line would have a slope of -9/7.
.
y = -(9/7)*x + b
.
Use the point (-7,6) to find 'b'.
.
6 = -(9/7)*(-7) + b
6 = 9 + b
b = -3
.
y = -(9/7)x -3
.
In the following graph:
the red line is y = (7/9)x - 2/9
the green line is y = -(9/7)x -3
.
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test/525277: Mariam uses a pottery wheel to make three bowls in 2 hours. Duane makes five bowls in 3 hours. Who makes bowls faster Mariam or Duane?
1 solutions
Answer 348052 by oberobic(2304) on 2011-11-02 20:02:07 (Show Source):
You can put this solution on YOUR website!Mariam's bowl-making speed = 1/M bowls/hr
1/M * 2hr = 3 bowls
.
Duane's bowl-making speed = 1/D bowls/hr
1/D * 3 hr = 5 bowls
.
1/M *2 = 3
2/M = 3
2 = 3M
3M = 2
M = 2/3 bowls/hr
.
1/D *3 = 5
3/D = 5
3 = 5D
5D = 3
D = 3/5 bowls/hr
.
2/3 = .67
3/5 = .60
.
So, Mariam makes bowls faster than Duane.
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Graphs/525306: Write the slope-intercept equation for the line that passes through (-4, 6) and (2, -6)
1 solutions
Answer 348047 by oberobic(2304) on 2011-11-02 19:50:37 (Show Source):
You can put this solution on YOUR website!m = (y-y 1)/(x-x 1)
.
m = 6-(-6) / -4-2
m = 12 / -6
m = -2
.
y = -2x + b
.
use one of the points to find 'b'
.
6 = -2*-4 + b
6 = 8 +b
b = -2
.
y = -2x -2
.
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Problems-with-consecutive-odd-even-integers/525298: What are four consecutive even integers such that the sum of the first and the third is six less than the largest?
1 solutions
Answer 348045 by oberobic(2304) on 2011-11-02 19:46:07 (Show Source):
You can put this solution on YOUR website!Four consecutive even integers could be defined as w, x, y, and z.
But then you would have 4 unknowns, so you would need 4 equations to solve the problem.
However, we're told they're consecutive even integers, so you can define them as
x, x+2, x+4, and x+6. Now you have only one unknown.
.
x + x+4 + 6 = x+6
.
2x = -4
x = -2
.
So the numbers are -2, 0, 2, and 4
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Mixture_Word_Problems/525282: keil is going to mke 10 pounds of mixed nuts for a party. If Keil can spend $47.50 on nuts and peanuts cost $2.00 per pound and fancey nuts cost 7.50 per pound, how many pounds of each should he buy?
1 solutions
Answer 348038 by oberobic(2304) on 2011-11-02 19:24:29 (Show Source):
You can put this solution on YOUR website!p = lb of peanuts
200p = cost of peanuts in cents
f = lb of fancy nuts
750f = cost of fancy nuts in cents
.
4750 cents is the budget
.
200p + 750f = 4750
.
p + f = 10
so
p = 10-f
.
Substitute
.
200(10-f) + 750f = 4750
2000 -200f +750f = 4750
550f = 2750
f = 5
.
p = 10-f
p = 10-5
p = 5
.
Check the budget.
200p = 200*5 = 1000
750f = 750*5 = 3750
1000 + 3750 = 4750
Correct.
.
Answer: 5 lb of peanuts and 5 lb of fancy nuts will make 10 lb of mix at a cost of $47.50.
.
Done.
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Reduction-of-unit-multipliers/525280: Use two unit multipliers to convert 4.4 square meters to square centimeters.
Ive tried to do it several ways and I cannot figure out how to go from meters squared to centimeters squared?
1 solutions
Answer 348036 by oberobic(2304) on 2011-11-02 19:18:39 (Show Source):
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Age_Word_Problems/524758: Tom is 10 years older than Pat. In 6 years. Tom will be 1.5 times as old as Pat will be then. Find their present ages.
1 solutions
Answer 347900 by oberobic(2304) on 2011-11-01 22:32:11 (Show Source):
You can put this solution on YOUR website!T = P + 10
.
In 6 years,
T+6
P+6
.
T+6 = 1.5(P+6)
.
Substitute for T
.
(P+10) + 6 = 1.5P + 9
P +16 = 1.5P + 9
-.5P = -7
P = 14 = Pat's age
.
T = P+10 = Tom's age
T = 24
.
Check the values in 6 years.
.
30 = 1.5(20) ?
Yes
.
Answer: Pat is 14 and Tom is 24.
.
Done.
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Equations/524755: Can you please help me with this problem? I have to write the equation of a line in slope-intercept form that has an x-intercept of 1/2 and a y-intercept 2/3
1 solutions
Answer 347898 by oberobic(2304) on 2011-11-01 22:23:44 (Show Source):
You can put this solution on YOUR website!The y-intercept is 2/3, which is also the point (0,b)
So, b = 2/3
.
The x-intercept is when y = 0, so the point is (1/2,0).
.
0 = mx + b
0 = m(1/2) + 2/3
-(1/2)m = 2/3
m = (2/3)/(-(1/2))
m = (2/3)*-(2/1)
m = -4/3
.
check
-4/3*1/2 = -4/6 = -2/3
correct
.
so, the slope is
m = -4/3
.
which means the equation is
y = -4/3 + 2/3
.
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Miscellaneous_Word_Problems/524744: Kate makes a batch of salsa in a large cylindrical pot. The inside of the pot is 9 inches in diameter, and it is filled with 4 inches of salsa. Kate plans to store the salsa in small cylindrical glass jars that are 3 inches in diameter and 4 inches high. How many jars will Kate need for all the salsa/ (use 3.14 to approximate.)
1 solutions
Answer 347895 by oberobic(2304) on 2011-11-01 22:11:38 (Show Source):
You can put this solution on YOUR website!Pot volume:
p = pi*r^2*h
p = 3.14*(4.5^2)*4
p = 254.34 cubic inches of salsa
.
Jar volume
j = pi*r^2*h
j = 3.14*(1.5^2)*4
j = 28.26
.
Number of jars needed to hold the salsa:
254.34/28.26 = 9
.
Done.
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