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Does the system of equations have no solution, one solution, or infinitely many solutions?
y = 5x – 4
y = 5x – 5
1 solutions
Answer 353219 by nerdybill(7008)   on 2011-11-29 17:54:31 (Show Source):
You can put this solution on YOUR website!Does the system of equations have no solution, one solution, or infinitely many solutions?
y = 5x – 4
y = 5x – 5
.
Since slope (5) is the same for both but the y-intercepts are diffferent
we conclude that
there is "no solution"
.
See the site below, it describes the three cases:
http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php
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Linear-equations/538398: find the x and y intercepts of: y = -2x - 6
1 solutions
Answer 353163 by nerdybill(7008) on 2011-11-29 09:59:44 (Show Source):
You can put this solution on YOUR website!find the x and y intercepts of: y = -2x - 6
.
to find the x-intercepts, set y=0 solve for x:
y = -2x - 6
0 = -2x - 6
6 = -2x
-3 = x
so, x-intercept is at (-3,0)
.
to find the y-intercepts, set x=0 solve for y:
y = -2x - 6
y = -2(0) - 6
y = -6
so, y-intercept is at (0,-6)
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Percentage-and-ratio-word-problems/537209: From the top of the building in the illustration, a ball is thrown straight up with an initial velocity of 40 feet per second. The equation s = -16t2 + 40t + 48 gives the height s of the ball t seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. (Round your answer to one decimal place.)
Thank you in advance!
1 solutions
Answer 352762 by nerdybill(7008) on 2011-11-27 14:59:05 (Show Source):
You can put this solution on YOUR website!From the top of the building in the illustration, a ball is thrown straight up with an initial velocity of 40 feet per second. The equation s = -16t2 + 40t + 48 gives the height s of the ball t seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. (Round your answer to one decimal place.)
s = -16t2 + 40t + 48
The "vertex" defines the max height.
It reaches this height when
t = -b/(2a)
t = -40/(2(-16))
t = -40/(-32)
t = 1.25 seconds
.
Max height:
s = -16(1.25)^2 + 40(1.25) + 48
s = 73.0 feet
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Percentage-and-ratio-word-problems/537211: The height (in feet) of the water level in a reservoir over a 1 year period is modeled by the function H(t) = 2.4(t - 10)2 + 15, where t = 1 represents January, t = 2 represents February, and so on. How low did the water level get that year, and when did it reach the low mark?
Thank you in advance!
1 solutions
Answer 352761 by nerdybill(7008) on 2011-11-27 14:54:26 (Show Source):
You can put this solution on YOUR website!The height (in feet) of the water level in a reservoir over a 1 year period is modeled by the function H(t) = 2.4(t - 10)2 + 15, where t = 1 represents January, t = 2 represents February, and so on. How low did the water level get that year, and when did it reach the low mark?
The vertex of H(t) = 2.4(t - 10)2 + 15 gives you the low point:
equation given is in the "vertex" form:
y= a(x-h)^2+k
vertex is at (10,15)
when did it reach the low mark?
t = 10 (October)
How low did the water level get:
h(t) = 15 feet
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Linear-equations/537074: How do you change 4x-2y=10 into slope-intercept form? I have no idea what to do. Thanks for your time.
1 solutions
Answer 352718 by nerdybill(7008) on 2011-11-27 10:57:15 (Show Source):
You can put this solution on YOUR website!How do you change 4x-2y=10 into slope-intercept form?
.
The "slope-intercept" form of a line is:
y = mx + b
all you need to do, is to rearrange the terms of the given equation to make it look like the form above...
You started with:
4x-2y=10
begin by subtracting 4x from both sides:
-4x+4x-2y = -4x+10
-2y = -4x+10
multiply both sides by -1:
2y = 4x-10
divide both sides by 2:
y = 2x-5 (this is what they're looking for)
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Length-and-distance/537067: A 18-foot ladder leans against a wall at a 74 degree angle of elevation. Find the distance from the ladder's base to the wall.
1 solutions
Answer 352713 by nerdybill(7008) on 2011-11-27 10:05:15 (Show Source):
You can put this solution on YOUR website!A 18-foot ladder leans against a wall at a 74 degree angle of elevation. Find the distance from the ladder's base to the wall.
.
Let x = distance (base to wall)
.
Applying trigonometry:
cos x = adjacent/hypotenuse
cos(74) = x/18
18*cos(74) = x
4.96 feet = x
or approximately:
5 feet = x
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Travel_Word_Problems/537068: Janet can shovel snow in her driveway in 65 minutes, Tom can do the same job in 45 mins. How long will it take if they work together?
1 solutions
Answer 352711 by nerdybill(7008) on 2011-11-27 10:01:57 (Show Source):
You can put this solution on YOUR website!Janet can shovel snow in her driveway in 65 minutes, Tom can do the same job in 45 mins. How long will it take if they work together?
.
Let x = time (mins) it takes for both
then
x(1/65 + 1/45) = 1
multiply both sides by (65)(45):
x(45 + 65) = (65)(45)
x(110) = 2925
x = 26.6 minutes
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Linear-equations/536741: Good Saturday morning Tutors.
I need help to write the slope-intercept equation for the line that passes through (-5,10) and (-4,3).
1 solutions
Answer 352566 by nerdybill(7008) on 2011-11-26 11:04:01 (Show Source):
You can put this solution on YOUR website!write the slope-intercept equation for the line that passes through (-5,10) and (-4,3)
.
Begin by finding the slope between (-5,10) and (-4,3)
m = (y2-y1)/(x2-x1)
m = (3-10)/(-4-(-5))
m = (-7)/(-4+5)
m = (-7)/(1)
m = -7
.
Use the slope (-7) and either one of the provided points (-4,3), plug into the "point-slope" form:
y - y1 = m(x - x1)
y - 3 = -7(x - (-4))
y - 3 = -7(x + 4)
y - 3 = -7x - 28
y = -7x - 25 (this is what they're looking for)
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Number-Line/536725: use all four integers -6, -4, 3, and 8, along with any operation signs to complete the equation.
_ _ _ _ = -2
1 solutions
Answer 352565 by nerdybill(7008) on 2011-11-26 10:49:18 (Show Source):
You can put this solution on YOUR website!use all four integers -6, -4, 3, and 8, along with any operation signs to complete the equation.
_ _ _ _ = -2
.
((-4) - (-6)) * 3 - 8 = -2
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Geometry_Word_Problems/536709: please help me solve this, find the area of a rectangle whose side is 5 feet and whose diagonal is  , thankyou
1 solutions
Answer 352546 by nerdybill(7008) on 2011-11-26 08:33:55 (Show Source):
You can put this solution on YOUR website!find the area of a rectangle whose side is 5 feet and whose diagonal is
.
Apply Pythagorean theorem to find the length of the other side:
Let x = length of other side of rectangle
then
 feet
.
Area then is:
5*7 = 35 square feet
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Quadratic_Equations/536074: How can i complete the square with :
2k^2 + 4k-10=0
my answer was 5, it's obviously wrong... help plz! thank you
1 solutions
Answer 352115 by nerdybill(7008) on 2011-11-23 10:37:28 (Show Source):
You can put this solution on YOUR website!2k^2 + 4k-10=0
divide through by 2:
k^2 + 2k-5=0
k^2 + 2k = 5
take 1/2 'b', square it and add to both sides:
k^2 + 2k + 1 = 5 + 1
k^2 + 2k + 1 = 6
(k+1)(k+1) = 6
(k+1)^2 = 6
k+1 = sqrt(6)
k = +-sqrt(6) - 1
k = {-sqrt(6)-1, sqrt(6)-1}
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Linear-equations/536042: write equation of a perpendicular line in slope intercept form if y=2/5x-4 (-1,2)
1 solutions
Answer 352109 by nerdybill(7008) on 2011-11-23 09:41:14 (Show Source):
You can put this solution on YOUR website!write equation of a perpendicular line in slope intercept form if y=2/5x-4 (-1,2)
.
Slope of:
y=2/5x-4
is 2/5
.
A line perpendicular must have a slope that is the negative reciprocal:
(2/5)m = -1
m = -5/2 (this is the slope of the new line)
.
Plug slope (-5/2) and (1,2) into "point-slope" form:
y - y1 = m(x - x1)
y - 2 = (-5/2)(x - 1)
y - 2 = (-5/2)x + 5/2
y = (-5/2)x + 5/2 + 2
y = (-5/2)x + 5/2 + 4/2
y = (-5/2)x + 9/2 (this is what they're looking for)
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logarithm/536046: Solve:
log(36,10x-11)+log(36,X)=1/2
i get to this point here: log(36,10x^2-11x)=1/2
but then im lost after
thanks
Angela
1 solutions
Answer 352107 by nerdybill(7008) on 2011-11-23 09:26:22 (Show Source):
You can put this solution on YOUR website!Solve:
log(36,10x-11)+log(36,X)=1/2
.
i get to this point here:
log(36,10x^2-11x)=1/2 (so far, so good)
.
36^log(36,10x^2-11x) = 36^(1/2)
10x^2-11x = 36^(1/2)
10x^2-11x = 6
.
10x^2-11x = 6
10x^2-11x - 6= 0
10x^2 -15x+4x - 6= 0
(10x^2-15x) + (4x-6) = 0
5x(2x-3) + 2(2x-3) = 0
(2x-3)(5x+2) = 0
x = {3/2, -2/5}
throw out the negative solution (extraneous) leaving:
x = 3/2
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Rate-of-work-word-problems/535304: an older machine can do a job in 104 minuets, it takes only 40 minuets when a newer machine works simultaneously. how long would it take the newer machine to do the job working alone?
1 solutions
Answer 351846 by nerdybill(7008) on 2011-11-21 18:15:12 (Show Source):
You can put this solution on YOUR website!an older machine can do a job in 104 minuets, it takes only 40 minuets when a newer machine works simultaneously. how long would it take the newer machine to do the job working alone?
.
Let x = time (minutes) it takes for newer machine alone
then
40(1/104 + 1/x) = 1
multiplyb both sides 104x:
40(x + 104) = 104x
40x + 4160 = 104x
4160 = 64x
65 minutes = x
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Linear-equations/534869: Parallel, perpendicular pr neither?
Y=-4x-91
Y=-121-5x
1 solutions
Answer 351666 by nerdybill(7008) on 2011-11-20 22:04:57 (Show Source):
You can put this solution on YOUR website!Parallel, perpendicular pr neither?
Y=-4x-91
Y=-121-5x
.
Examine the slope of each line:
-4 and -5
since they're not the same, they're not parallel
since they don't multiply to give you -1 they're not perpendicular
therefore
answer: Neither
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Triangles/534861: One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides?
1 solutions
Answer 351664 by nerdybill(7008) on 2011-11-20 22:02:22 (Show Source):
You can put this solution on YOUR website!One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45 inches. What is the length of all sides?
.
Let x = length of "other leg"
then
x-9 = 2nd leg
.
applying Pythagorean theorem:
x^2 + (x-9)^2 = 45^2
x^2 + (x-9)(x-9) = 45^2
x^2 + x^2-18x+81 = 2025
2x^2-18x+81 = 2025
2x^2-18x-1944 = 0
x^2-9x-972 = 0
(X+27)(x-36) = 0
x = {-27, 36}
throw out the negative answer leaving:
x = 36 inches
.
Answer: the three sides are:
36, 27, and 45 inches
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Percentage-and-ratio-word-problems/534200: The cost to produce one DVD player is $85 plus a one-time fixed cost of $150,000. The revenue received from selling one DVD player is $225.
(a) Write a formula that gives the cost C of producing x DVD players
1 solutions
Answer 351385 by nerdybill(7008) on 2011-11-19 11:09:44 (Show Source):
You can put this solution on YOUR website!The cost to produce one DVD player is $85 plus a one-time fixed cost of $150,000. The revenue received from selling one DVD player is $225.
(a) Write a formula that gives the cost C of producing x DVD players
.
Let x = number of DVD players
then
C = 85x + 150000
where "C" is cost
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Evaluation_Word_Problems/534070: Billy drops an egg off the roof of a buliding 80 ft above ground. Using the model . How long did it take for the egg to hit the ground? using the equation h=-16t^2+h
1 solutions
Answer 351265 by nerdybill(7008) on 2011-11-18 21:58:11 (Show Source):
You can put this solution on YOUR website!Billy drops an egg off the roof of a buliding 80 ft above ground. Using the model . How long did it take for the egg to hit the ground? using the equation h(t)=-16t^2+h
.
Set h to 80 (represents initial height)
and
set h(t) to zero (represents ground level)
solve for t:
h(t)=-16t^2+h
0=-16t^2+80
16t^2 = 80
t^2 = 5
t = sqrt(5)
t = 2.24 seconds
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Rational-functions/533853: Find the x and y intercept for 5y-x=10 I need help
1 solutions
Answer 351180 by nerdybill(7008) on 2011-11-18 10:14:50 (Show Source):
You can put this solution on YOUR website!Find the x and y intercept for 5y-x=10
.
Rearrange the given equation into the "point-slope" form:
y = mx + b
where
m is the slope
b is the y-intercept at (0,b)
.
5y-x=10
5y=x+10
y = (1/5)x + 2
From inspection, then we have
slope is 1/5
y-intercept is at (0,2)
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Linear-systems/533861: Solve the system of equations using substitution.
y = 4x + 10
y = 3x + 7
Please Explain how you go the answer! Thank You!!
1 solutions
Answer 351178 by nerdybill(7008) on 2011-11-18 10:12:42 (Show Source):
You can put this solution on YOUR website!y = 4x + 10 (equation 1)
y = 3x + 7 (equation 2)
.
Plug definition of y from equation 2 into equation 1 and solve for x:
3x + 7 = 4x + 10
7 = x + 10
-3 = x
.
Plug definition of x above into equation 2 to find y:
y = 3x + 7
y = 3(-3) + 7
y = -9 + 7
y = -2
.
Answer:
x = -3
y = -2
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Linear-equations/532886: i forgot how to do slope intercept form because point slope confused me this week. My question is how do you write an equation in slope intercept with an equation like (3,1); slope=2
1 solutions
Answer 350921 by nerdybill(7008) on 2011-11-16 18:05:34 (Show Source):
You can put this solution on YOUR website!Plug the given info:
(3,1); slope=2
.
into the "point-slope" form of
y - y1 = m(x - x1)
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5 (this is what they're looking for)
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Rate-of-work-word-problems/531348: A pipe can fill a tank in 30minutes and another pipe can make empty the tank in
45 minutes. How much time it takes to empty the tank if both are working together.
1 solutions
Answer 350423 by nerdybill(7008) on 2011-11-14 13:46:52 (Show Source):
You can put this solution on YOUR website!A pipe can fill a tank in 30minutes and another pipe can make empty the tank in
45 minutes. How much time it takes to empty the tank if both are working together.
assuming the tank was completely filled at the start then:
Let x = time (minutes) to empty tank
then
x(1/30 - 1/45) = 1
multiplying both sides by 90:
x(3 - 2) = 90
x(1) = 90
x = 90 minutes
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Inverses/530998: 1/x + 1/y = 5, can you solve for x without ending up with an xy
1 solutions
Answer 350288 by nerdybill(7008) on 2011-11-13 19:06:11 (Show Source):
You can put this solution on YOUR website!Not sure what you mean but here's how to solve for x:
1/x + 1/y = 5
multiply both sides by xy:
(xy)(1/x + 1/y) = 5xy
distribute on the left:
y + x = 5xy
y = 5xy - x
factor the right:
y = x(5y - 1)
y/(5y-1) = x
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Linear_Equations_And_Systems_Word_Problems/530973: the average american uses 100 gallons of water each day.
a.write an equation that gives the gallons of water that a person uses the t days.
b.graph the equation for t greater than or equal to 0.
c.how many days does it take for the average american to uses 5000 gallons of water?
1 solutions
Answer 350284 by nerdybill(7008) on 2011-11-13 18:58:06 (Show Source):
You can put this solution on YOUR website!the average american uses 100 gallons of water each day.
a.write an equation that gives the gallons of water that a person uses the t days.
f(t) = 100t
b.graph the equation for t greater than or equal to 0.
you do this part
c.how many days does it take for the average american to uses 5000 gallons of water?
set f(t) to 5000 and solve for t:
f(t) = 100t
5000 = 100t
50 days = t
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Angles/530983: The base angles of an isosceles triangle are congruent. If the measure of each of the base angles is twice the measure of the third angle, find the measure of all three angles.
1 solutions
Answer 350282 by nerdybill(7008) on 2011-11-13 18:51:45 (Show Source):
You can put this solution on YOUR website! The base angles of an isosceles triangle are congruent. If the measure of each of the base angles is twice the measure of the third angle, find the measure of all three angles.
Let x = measure of third angle
then
2x = measure of base angle
.
2x + 2x + x = 180
5x = 180
x = 36 degrees (third angle)
.
base angle:
2x = 2(36) = 72 degrees
.
the three angles are:
72, 36 and 72 degrees
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