You can put this solution on YOUR website!
C=0.000015x^2 -0.03x+35
.
Since, the first coefficient (0.000015) is POSITIVE the equation is a parabola that opens upwards. This then says that finding the "vertex" will give you the minimum.
.
The vertex is then found by:
x = -b/2a
x = -(-0.03)/2(0.000015)
x = 0.03/2(0.000015)
x = 0.03/0.00003
x = 1000 (minimum number of tires)
.
The cost, plug it back into:
C=0.000015x^2 -0.03x+35
C=0.000015(1000)^2 -0.03(1000)+35
C=15 -30+35
C=15 +5
C= $20

You can put this solution on YOUR website!
if they gave you:
f(2) = -3, f(-2) =5
It's equivalent to giving you two points:
(2,-3), (-2,5)
.
Now, that you have two points:
m = (y2-y1)/(x2-x1)
m = (5-(-3))/(-2-2)
m = (5+3)/(-2-2)
m = 8/(-4)
m = -2 (slope)

You can put this solution on YOUR website!
what is one of the complementary angles is three more than two that twice the other? find the measure of each?
.
If two angles are complementary, the sum of the two angles equal 90 degrees.
.
Let x = one angle
then
2x+3 = other angle
.
x + 2x+3 = 90
3x+3 = 90
3x = 87
x = 29 degrees (one angle)
.
Other angle:
2x+3 = 2(29)+3 = 58+3 = 61 degrees

You can put this solution on YOUR website!
Isolate the unknown 'd' to one side of the equation.
13d-53=9d+19
Subtracting 9d from both sides:
4d - 53 = 19
Adding 53 to both sides:
4d = 72
Finally, divide both sides by 4:
d = 18

You can put this solution on YOUR website!
The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle?
.
Let x = length of shorter leg
then
4x+4 = length of longer leg
4x+5 = length of hypotenuse
.
x^2 + (4x+4)^2 = (4x+5)^2
x^2 + (4x+4)(4x+4) = (4x+5)(4x+5)
x^2 + 16x^2+32x+16 = 16x^2+40x+25
17x^2+32x+16 = 16x^2+40x+25
x^2+32x+16 = 40x+25
x^2-8x+16 = 25
x^2-8x-9 = 0
(x-9)(x+1) = 0
.
x = {9, -1}
We can toss out the negative solution leaving:
x = 9 cm (shorter leg)
.
Longer leg:
x+4 = 9+4 = 13 cm
.

You can put this solution on YOUR website!
A long distance telephone calling card charges $0.05 per minute, but adds on a $0.75 charge for each call dialed. Using 'C' for the number of calls made and 'I' for the time spent talking, create an expression that will keep track of the cost of using the card.
"cost of using card" = "total dialing charges" + "total minutes called"
"cost of using card" = .75C + .05I
.
Using the expression created calculate the remaining value on a $20.00 phone card after 5 calls that lasted a total of 26 minutes.
"remaining cost" = "current value" - "cost"
"remaining cost" = 20 - (.75C + .05I)
"remaining cost" = 20 - (.75(5) + .05(26))
"remaining cost" = 20 - (3.75 + .1.3)
"remaining cost" = 20 - 5.05
"remaining cost" = $14.95

You can put this solution on YOUR website!
Using "log rules":
ln (y^2-1)= ln(y-1) + ln5
ln (y^2-1)= ln(5(y-1))
ln (y^2-1)= ln(5y-5)
y^2-1= 5y-5
y^2-5y-1= -5
y^2-5y+4= 0
Factoring:
(y-4)(y-1)= 0
y = {1,4}
You have to toss out 1 as a possible solution since ln(0) is undefined.
.
Therefore:
y = 4

You can put this solution on YOUR website!
The "slope-intercept" form is:
y = mx + b
where
m is slope
b is y-intercept
.
-2x=2y+5
-2y-2x = 5
-2y = 2x + 5
y = (2/-2)x + (5/-2)
y = -x + (-5/2)

You can put this solution on YOUR website!
Express the area (A) of a rectangle with perimeter 100 feet as a function of the length (L) of one of its sides.
.
Normally, for a rectangle, if you had a "length" and "width" the perimeter would be:
"length" + "width" + "length" + "width"
or
2("length" + "width")
.
Area would be:
(length)(width)
.
So, if:
L = length
the
width = (100-2L)/2 = 50-L
.
Therefore, if A=Area then
A = L(50-L)
A = 50L-L^2
or
A = -L^2+50L

You can put this solution on YOUR website!
Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 mph faster than the other car, what was the average speed for each car for the 2-hour trip?
.
Let x = speed of one car
then because "one car traveled, on average, 8 mph faster than the other car"
x+8 = speed of second car
.
Applying "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
"distance traveled by car one" + "distance traveled by car two" = 208
2x + 2(x+8) = 208
2x + 2x + 16 = 208
4x + 16 = 208
4x = 192
x = 48 mph (speed of one car)
.
Second car:
x+8 = 48+8 = 56 mph (speed of second car)

You can put this solution on YOUR website!
Since:
8*8 = 64
and
9*9 = 81
.
√78 is between 8 and 9

You can put this solution on YOUR website!
A 10-m ladder is leaning against a building. The bottom of the ladder is 5 m from the building. How high is the top of the ladder?
.
Apply Pythagorean's theorem:
Let H = height of top of ladder
.
H^2 + 5^2 = 10^2
H^2 + 25 = 100
H^2 = 75
H = sqrt(75)
H = 8.66 m

You can put this solution on YOUR website!
Let J = Jane's age
and B = Beth's age
.
From: "3 time's Jane's age, in years, is equal to 8 times Beth's age"
3J = 8B (equation 1)
.
From: "difference between their ages is 15 years"
J-B = 15 (equation 2)
.
Solving equation 2 for J:
J-B = 15
J = 15+B
.
Plug the above into equation 1 and solve for B:
3J = 8B
3(15+B) = 8B
45+3B = 8B
45 = 5B
9 = B (Beth's Age)
.
Plug the above into equation 2 and solve for J:
J-B = 15
J-9 = 15
J = 24 (Jane's Age)

You can put this solution on YOUR website!
logx(10-3x)=2
.
If you meant "log base x" then:
logx(10-3x)=2
10-3x=x^2
0 = x^2+3x-10
0 = (x+5)(x-2)
.
x = {-5, 2}

You can put this solution on YOUR website!
First order of business, put all the x's and y's to one side:
2x - 2y =3+x
x = 3y + 4
.
Rearranging then, we have:
x - 2y =3
x - 3y =4
.
Now, using the "elimination method", subtract the second equation from the first:
x - 2y = 3
-x + 3y = -4
---------------
y = -1
.
Now, use the above definition of 'y' and substitute it into equation 2:
x = 3y + 4
x = 3(-1) + 4
x = -3 + 4
x = 1
.
Solution:
(x,y) = (1, -1)

You can put this solution on YOUR website!
Let v = speed of paddleboat w/no current
.
Applying "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let t = time traveling upriver
then
2-t = time traveling downstream
.
We have two unknowns (v and t) so we'll need two equations:
t(v-4) = 1 (equation 1)
(2-t)(v+5) = 1 (equation 2)
.
Solving equation 1 for 't':
t(v-4) = 1
t = 1/(v-4)
.
Substitute the above into equation 2 and solve for v:
(2-(1/(v-4)))(v+5) = 1
multiply both sides by (v-4):
(2(v-4) - 1)(v+5) = 1
(2v-8 - 1)(v+5) = 1
(2v-9)(v+5) = 1
Applying FOIL:
2v^2 + 10v - 9v -45 = 1
2v^2 + v -45 = 1
2v^2 + v -46 = 0
.
Can't factor so use the quadratic formula. Doing so will yield:
v = {4.552, -5.052}
.
We can toss out the negative solution leaving us with:
v = 4.552 km/hr
.
Details of quadratic below:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=369 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.55234317807464, -5.05234317807464. Here's your graph:

You can put this solution on YOUR website!
odds = P(E)/(1-P(E))
.
Since P(E) = .30
odds = .30/(1-.30)
odds = .30/.70
odds = 1/2.33
odds = 1:2.33

You can put this solution on YOUR website!
Reviewing vertex formula:
http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php
.
Standard "vertex form":
y= a(x-h)^2+k
where
(h,k) is the vertex
.
The problem gives you:
(h,k) = (-1,5)
(x,y) = (2,7)
.
Plug the above into:
y= a(x-h)^2+k
7= a(2-(-1))^2+5
Solve for 'a':
7= a(2+1)^2+5
7= a(3)^2+5
7= 9a+5
2 = 9a
2/9 = a
.
Therefore:
y= a(x-h)^2+k
y= (2/9)(x-(-1))^2+5
y= (2/9)(x+1)^2+5
y= (2/9)(x^2+2x+1)+5
9y= 2(x^2+2x+1)+45
9y= 2x^2+4x+2+45
9y= 2x^2+4x+47
y = (2/9)x^2 + (4/9)x + (47/9)

You can put this solution on YOUR website!

Using the hint provided:
Area of Triangle: A = base*height/2
.
From the problem it gave us:
base = 21
height = 15
.
Plugging it into:
A = base*height/2
A = 21*15/2
A = 315/2
A = 157.5 square inches
.
Since sunblock costs: $1.22 per square inch
1.22 * 157.5 = $192.15

You can put this solution on YOUR website!
Since the perimeter of any rectangle is:
width + width + length + length
2(width) + 2(length)
2(width + length)
.
Let w = width of rectangle
then because "length of a rectangle is three times its width"
3w = length of rectangle
.
2(width + length) <= 112
plugging in our variables above:
2(w + 3w) <= 112
2(4w) <= 112
8w <= 112
w <= 112/8
w <= 14 centimeters (width)
.
Solution: greatest possible width is 14 centimeters

You can put this solution on YOUR website!
Let x = time (in hours) it takes for train B to catch up to train A
Because of the difference in time the two trains passes a station we have:
x + (1/2) = time train A traveled
.
We use the "distance formula"
d = rt
where
d is distance traveled
r is rate or speed
t is time
.
For train B to catch up:
"distance traveled by train A" = "distance traveled by train B"
40(x + (1/2)) = 44x
multiplying both sides by 2:
40(2x + 1) = 88x
80x + 40 = 88x
40 = 8x
5 hours = x
.
But wait, the problem wanted "clock" time:
9:40 PM + 5 hours = 2:40 AM

You can put this solution on YOUR website!
find three consecutive odd integers such that the squar of the thid integer plus the product of the other two integers is 268.
.
Let x = first consecutive odd integer
then
x+2 = second consecutive odd integer
x+4 = third consecutive odd integer
.
From:"the square of the third integer plus the product of the other two integers is 268" we get:
(x+4)^2 + x(x+2) = 268
x^2+8x+16 + x^2+2x = 268
2x^2 + 10x + 16 = 268
x^2 + 5x + 8 = 134
x^2 + 5x - 126 = 0
(x-9)(x+14) = 0
.
x = {9, -14}
.
We can toss out the -14, leaving us with:
x=9
.
Solution:
9, 11, 13

You can put this solution on YOUR website!
.
Let x = time (in hours) it takes all three to eat one sheep
.
x/4 + x/5 + x/6 = 1
30x + 24x + 20x = 120
74x = 120
x = 120/74
x = 1.622 hours
or
1 hour 37 minutes and 18 seconds

You can put this solution on YOUR website!
A man will be 3 times as old as his son will be in 9 years. If he is 6 times as old as his son now, how old is the son?
.
Let x = son's age
then from "he is 6 times as old as his son now"
6x = man's age
.
From: "A man will be 3 times as old as his son will be in 9 years." we get our equation:
6x+9 = 3(x+9)
6x+9 = 3x+27
3x+9 = 27
3x = 18
x = 6 years old (son's age)

You can put this solution on YOUR website!
m^2 = 8m + 3
Move all the 'm' terms to one side:
m^2 - 8m = 3
Take half of b (-8) and square it (16). Add to both sides:
m^2 - 8m + 16 = 3 + 16
Factoring the left side:
(m-4)(m-4) = 19
(m-4)^2 = 19
Take the square root of both sides
m-4 = sqrt(19)
m = 4+sqrt(19)
or
m = {8.3589, -0.3589}

You can put this solution on YOUR website!
a circle has a radius of 10 inch. Find the increase in area that occurs when the radius is increased by 2 inches. Round to the nearest hundredths?
.
Area of a circle is (pi)r^2
.
"area of increased radius circle" - "area of original circle"
.
(pi)(10+2)^2 - (pi)(10)^2
(pi)(12)^2 - (pi)(10)^2
pi ((12)^2 - (10)^2)
pi (144 - 100)
pi (44)
(3.14)(44)
138.16 sq inches

You can put this solution on YOUR website!
That would be:
1.25 * 120 = $150.00

You can put this solution on YOUR website!

Factoring numerator and denominator:

Factor out a -1 from the denominator:

Now, we can cancel like-terms:

Distributing the -1:

You can put this solution on YOUR website!
Can you please help me? The problem is: The area of Lake Michigan is 9420 square miles less than the area of Lake Superior, which is about one-fifth the size of the Caspian Sea(about 150,000 sq mi.) Write and solve an equation to find the approximate area of Lake Michigan. Thanks!
.
Pull out information from the problem:
From: "Caspian Sea(about 150,000 sq mi.)":
Area of Caspian Sea = 150000 sq mi
.
From: "Lake Superior, which is about one-fifth the size of the Caspian Sea"
Area of Lake Superior = (1/5)(150000) sq mi
.
From: "Lake Michigan is 9420 square miles less than the area of Lake Superior"
Area of Lake Michigan = (1/5)(150000)-9420 (this is your equation)
.
To solve:
Area of Lake Michigan = (1/5)(150000)-9420
Area of Lake Michigan = 30000-9420
Area of Lake Michigan = 20580 sq mi

You can put this solution on YOUR website!
To cook the "stuffed turkey":
23.5 * 12 = 282 minutes
or 4 hours 42 minutes
.
"cooking time" + "cool down" + "carving" + "eating" = "total time"
282 + 10 + 15 + 60 = 367 minutes
.
or
6 hours 7 minutes
.
Subtracting the above from 4 PM:
Turkey should go in the oven at:
9:58 AM
.
Note: oven is assumed to be pre-heated

You can put this solution on YOUR website!
Are you saying:
Log base 18 of 68.3
.
If so:
log18(68.3)
= log(68.3)/log(18)
= 1.8344/1.2553
= 1.4614