You can put this solution on YOUR website!
If there is a pipe that has a diameter of 12 inches and is ten ft. long with each square inch weighing 4.75lbs how much does the pipe weigh all together?
.
area = length * circumference
circumference = (pi)d
.
area = length * circumference
weight = area * 4.75
weight = 120 * (pi) * 12 * 4.75
weight = 120 * 3.14 * 12 * 4.75
weight = 21477.6 lbs

You can put this solution on YOUR website!
(3x^10y^9)^3
(3)^3(x^10)^3(y^9)^3
27x^30y^27

You can put this solution on YOUR website!
A chemist is mixing a 40% salt solution with a 20% salt solution to make 50 L of a new solution that will contain 25% salt. How much of each of the original solutions should the chemist use?
.
Let x = amount (L) of 40%
then
50-x = amount(L) of 20%
.
.40x + .20(50-x) = .25(50)
.40x + 10 - .20x = 12.5
.20x + 10 = 12.5
.20x = 2.5
x = 12.5 L of 40% solution
.
20% solution:
50-x = 50-12.5 = 37.5 L of 20% solution

You can put this solution on YOUR website!
The way you would approach the problem depends on what was given to you.
Perhaps, it is best if you have a particular problem in mind.







If I have a problem that says find an equation of the perpendicular bisector of line AB..
.
First, determine the slope of line AB.
The slope of the perpendicular bisector is the reciprocal.
.
Next, apply the "mid-point" formula to get the (x,y) coordinates.
.
Now, you have the "slope" and one "point" plug it in to the "point-slope" formula:
y - y1 = m(x - x1)
.
Finally, you can manipulate the above until you get the form you're looking for -- either "slope-intercept form" or "standard form".
.

You can put this solution on YOUR website!
You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges a $130 fee plus $25 per hour. Quick Move charges a $55 fee plus $50 per hour.
.
Let h = hours needed for move
then
.
Cost of Heavy Lifters:
25h + 130
Cost of Quick Move:
50h + 55
.
For what values h (hours) does Quick Move offer the better deal?
"cost of Quick Move" < "cost of Heavy Lifters"
50h + 55 < 25h + 130
25h + 55 < 130
25h < 75
h < 3 hours (this is what they're looking for)

You can put this solution on YOUR website!
15 degrees 29 minutes - 3 degrees 45 minutes
.
First, you should know that 1 degree is equivalent to 60 minutes.
.
subtract minutes from minutes
and
subtract degrees from degrees
.
Since we are trying to subtract 45 minutes from 29 minutes, we need to borrow 1 degree:
14 degrees 89 minutes - 3 degrees 45 minutes
so, now we have:
(49-3) degrees (89-45) minutes
46 degrees 44 minutes

You can put this solution on YOUR website!
the length of a rectangle exceeds the width by 2 cm. If the diagonal is 10 cm long, find the width of the rectangle.
.
Let w = width
then
w+2 = length
.
applying Pythagorean theorem we have:
w^2 + (w+2)^2 = 10^2
w^2 + (w+2)(w+2) = 100
w^2 + (w^2+4w+4) = 100
2w^2+4w+4 = 100
w^2+2w+2 = 50
w^2+2w-48 = 0
(w+8)(w-6) = 0
w = {-8, 6}
throw out the negative solution leaving:
w = 6 cm

You can put this solution on YOUR website!
Since we are dealing with "base 10", if we rewrite:
log (10,000)
as
log (10^4)
this is equal to 4 (answer)

You can put this solution on YOUR website!
If a ball is traveling 74 MPH how long does it take it to travel forty feet.
.
First, convert 40 ft to miles:
40 ft * 1/5280 = 0.007576 miles
.
Then, apply distance formula:
d = rt
0.007576 = 74t
0.007576/74 = t
0.0001024 hours = t
converting to seconds:
0.0001024 * 60 * 60 = 0.369 seconds

You can put this solution on YOUR website!
I think your equation is:

if so:






.
.
OR, if your equation was:

if so:

You can put this solution on YOUR website!
You were correct in your approach...


set each term (the "x" and the "x^2-5" to zero to get:
x^2-5 = 0
x^2 = 5
x = +-sqrt(5)
.
and, of course
x = 0
.
so, the solution set is:
x = {-sqrt(5), 0, sqrt(5)}

You can put this solution on YOUR website!
f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985)
a. According to this equation, what was the oil consumption in 1990?
1990 - 1985 = 5
set x = 5 and solve f(5)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(5)^2 + 2(5) + 58
f(5)=-0.1(25) + 10 + 58
f(5)= 65.5 million barrels
.
b. Using this equation, the maximum oil consumption will occur in what year?
It would be the vertex.
x = -b/(2a)
x = -2/(2(-0.1))
x = -2/(-0.2)
x = 10
year:
1985 + 10 = 1995
.
c. What is the maximum oil consumption?
set x = 10 solve for f(x)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(10)^2 + 2(10) + 58
f(5)=-0.1(100) + 20 + 58
f(5)= 68 million barrels
.
d. Does this equation realistically describe oil in 2030? why or why not?
2030-1985 = 45
set x = 45 solve for f(x)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(45)^2 + 2(45) + 58
f(5)=-0.1(2025) + 90 + 58
f(5)=-54.5 million barrels
answer: NO, because the result is negative
.

You can put this solution on YOUR website!
The base of a 17-ft ladder is 7 feet away from the wall. How far above the floor is the top of the ladder? Give your answer to the nearest thousandth.
.
Applying the Pythagorean theorem:
Let x = length above the floor
then
x^2 + 7^2 = 17^2
x^2 + 49 = 289
x^2 = 240
x = 15.492 feet

You can put this solution on YOUR website!
x^2-2/3x=0
take half of b, square it, and add to both sides (2/6)^2 = (1/3)^2 = 1/9:
x^2-2/3x+1/9 = 1/9
(x-1/3)^2 = 1/9
x-1/3 = sqrt(1/9)
x = sqrt(1/9) + 1/3
x = +-1/3 + 1/3
x = {0, 2/3}

You can put this solution on YOUR website!
A triangular garden has an area of 90 sq feet. It's height is 8 feet more than its base. Find the measure of the base.
.
Since:
A = (1/2)bh
where
A is area
b is base
h is height
.
90 = (1/2)b(b+8)
180 = b(b+8)
180 = b^2+8b
0 = b^2+8b-180
0 = (b+18)(b-10)
b = {-18, 10}
throw out the negative solution leaving:
b = 10 feet (length of base)

You can put this solution on YOUR website!
To find the area of a triangle you need the "base" and the "height":
Area = (1/2)bh

You can put this solution on YOUR website!
if you were charged $762 in taxes on a 2,540 purchase, what percent tax were you charged?
.
Let x = tax rate
then
2540x = 762
x = 762/2540
x = 0.30
or
x = 30% (that is an awfully high tax rate!)

You can put this solution on YOUR website!
Giving just the volume is not enough information.
You need to provide the width, length and height of the storage area.
.
9'11" (L) x 6'4" (W) x 6'2" (H)
But, these dimensions does NOT equate to a 10 cubic foot volume (as stated earlier).
.
The longest part would be the diagonal:
Let d = length of diagonal
then
d^2 = 9.917^2 + 6.333^2
d^2 = 138.454
d = 11.76 feet
.
No, the ladder will NOT fit.

You can put this solution on YOUR website!
A cyclist travel 27 km in 2 hours.How far would he travel in 7 hours?
.
distance formula:
d = rt
d = (27/2)(7)
d = (189/2)
d = 94.5 km

You can put this solution on YOUR website!
You forgot the x-term:
I'm assuming instead of:
x^2+4+1=0
you meant:
x^2+4x+1=0
x^2+4x=-1
half b then double -- add to both sides:
x^2+4x+4=-1+4
(x+2)^2 = 3
x+2 = sqrt(3)
x = +-sqrt(3) - 2
x = {-3.732, -0.268}
.
.
x^2+x-1=0
x^2+x = 1
x^2+x+ 1/4 = 1 + 1/4
(x+ 1/2)^2 = 1.25
(x+.5)^2 = 1.25
x+.5 = sqrt(1.25)
x = +-sqrt(1.25) - .5
x = {-1.618, 0.618}

You can put this solution on YOUR website!
16+ 12x- x^3 when x=3
.
just substitute the x with a 3 and solve:
16+ 12(3)- 3^3
16+ 36 - 27
16+ 36 - 27
52 - 27
25

You can put this solution on YOUR website!
r^2 + 10r+25
(r+5)(r+5)
or
(r+5)^2

You can put this solution on YOUR website!
Angela takes 40 minutes to dust and clean her home while her sister rani takes an hour (6o min) to do same work. One day their mother joins the two sisters and together the three of them dust and clean their house in just 15 min. How long would their mother take if she did the job alone.
.
Let x = time (min) for mother to do it alone
then
15(1/40 + 1/60 + 1/x) = 1
multiplying both sides by 2400x:
15(60x + 40x + 2400) = 2400x
15(100x + 2400) = 2400x
1500x + 36000 = 2400x
36000 = 900x
40 mins = x

You can put this solution on YOUR website!
Each cycle of a screen saver program generates and then erases numbers of little animated figures called froobies. The formula P=-2x^2+106x-674 models the population, P, of froobies after x minutes within a cycle. How many minutes into a cycle will the froobie population reach 118?
.
Given:
P=-2x^2+106x-674
Set P to 118 and solve for x:
118=-2x^2+106x-674
0 = -2x^2+106x-792
0 = 2x^2-106x+792
0 = x^2-53x+396
factoring we have:
0 = (x-9)(x-44)
x = {9, 44} minutes

You can put this solution on YOUR website!
The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height.
.
Draw a diagram, it'll help you see the solution.
.
Begin by find the length of the diagonal on the bottom:
Let d = diagonal
then
d^2 = 8^2 + 12^2
d^2 = 64 + 144
d^2 = 208
d = sqrt(208)
d = 14.222 cm
.
Now, we can find the inner height:
Let h = inner height
then
h^2 + 14.222^2 = 17^2
h^2 + 208 = 289
h^2 = 81
h = 9 cm

You can put this solution on YOUR website!
What is the solution to the equation x(x-1)=0?
.
Set each term on the left to zero and solve:
(x)(x-1)=0
.
So:
x = 0
or
x-1 = 0
x = 1
.
solution: x = {0,1}

You can put this solution on YOUR website!
You have to apply FOIL
.
f(x)=x^2+1 find for f(x+2)
.
f(x+2)=(x+2)^2+1
f(x+2)=(x+2)(x+2)+1
f(x+2)=(x^2+2x+2x+4)+1
f(x+2)=(x^2+4x+4)+1
f(x+2)= x^2+4x+5

You can put this solution on YOUR website!
A manufacturing company makes ladies purses receiving $120 for each purse sold. If x represents the number of purses made, the income received is determined by the revenue function R(x) = 120x. The company has a fixed cost of $12,000 per month and variable costs of $57.50 for each purse made. The cost function is C(x) = 57.5x + 12000. How many purses must the company sell for revenue to equal cost?
120x = 57.5x + 12000
62.5x = 12000
x = 192 purses

You can put this solution on YOUR website!
Assume that a company has total annual fixed costs of $480,000 and that variable costs is $6 per unit. If each unit sells for $10, then each unit exceeds the specific variable costs by $4.
a. What is the cost function?
C(x) = 6x + 480000
b. What is the revenue function?
R(x) = 10x
c. How many units must be sold in order for the company to break-even?
set
R(x) = C(x)
10x = 6x + 480000
4x = 480000
x = 120,000 units

You can put this solution on YOUR website!
Break-even means:
"Revenue" = "Costs"

You can put this solution on YOUR website!
two complementary angles are (a+20*) and (a+30*).what is the value of a?
.
I'm assuming the * indicates degrees.
.
When two angles ar complementary, the sum is 90 degrees giving us our equation:
(a+20) + (a+30) = 90
2a + 50 = 90
2a = 40
a = 20 degrees