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Find the inverse of the function: y =
Swap x and y and solve for y
x =
multiply both sides by 12
12x = 3y + 9
12x - 9 = 3y
divide all terms by 3
4x - 3 = y
:
y = 4x - 3 is the inverse

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(3x+3y)^2*(2x+3y)
First FOIL
(3x + 3y)* (3x + 3y) = 9x^2 + 9xy + 9xy + 9y^2
Combine like terms and you have
9x^2 + 18xy + 9y^2
:
Multiply this by (2x+3y), but do it this way, long multiplication
9x^2 + 18xy + 9y^2
. . . . . . . . . 2x + 3y
------------------
:
You should get: 18x^3 + 63x^y + 72xy^2 + 27y^3
Corrected to: 18x^3

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Justin drove to his parents 175 miles away.
On his way there his speed averaged 24 times faster than on his way back.
He drove a total of 5 hours.
What was his speed on the way there and on the way back?
:
Let s = his speed back
then
24s = his speed there
:
Write time equation: time = dist/speed
:
There time + return time = 5 hrs
+ = 5
Multiply by 24s, results
175 + 24(175) = 24s(5)
175 + 4200 = 120s
4375 = 120s
s =
s = 36.46 mph on the way back
then
24(36.46) = 875 mph on the way there, must have used an F-16 Jet

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how can i do a 3-D figure with a length of 5 a width of 4 and a height of 3
:
Get a rectangular piece of cardboard, the dimensions: 11" by 10"
Cut 3" squares from each corner, bend up the sides to form an open rectangular box.
If you need a cover just add a piece, 5" by 4" for the top

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A skateboard ram inclines at an angle of 20 degrees.
If the ramp has a run of 4 meters, what is the length of the ramp?
:
You solve this using the cosine of 20 degrees, let r = the length of the ramp
cos(20) =
r =
r = 4.2567 meters

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On a 42km go-kart course, A drives 0.4km/hr faster than S, but has engine trouble and stops for 30min.
A arrives at the finish line 15min after S.
How fast did each drive and how long did each take to finish the course?
:
Let s = S's speed
then
(s+.4) = A's speed
:
Change 30 min to .5 hrs
Change 15 min to .25 hrs
:
Write a time equation, time = dist/speed
:
A's time = S's time + .25 hr
+ .5 = + .25
= + .25 -.5
= - .25
:
multiply by s(s+.4), results:
42s = 42(s+.4) - .25s(s+.4)
42s = 42s + 16.8 - .25s^2 - .1s
:
Combine like terms on the left
.25s^2 + .1s + 42s - 42s - 16.8 = 0
.25s^2 + .1s - 16.8 = 0
;
Get rid of those decimals, multiply by 100
25s^2 + 10s - 1680 = 0
:
simplify, divide by 5
5s^2 + 2s - 336 = 0
:
you can use the quadratic formula to solve, but this will factor to:
(5s+42)(s-8) = 0
:
Positive solution is what we want here
s = 8 km/hr is S's speed
then, obviously,
8.4 km/h is A's speed
:
:
:
See if that work out
+ .5 = + .25
5 + .5 = 5.25 + .25
5.5 = 5.5; confirms our solutions

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if the base of a right angle triangle is 90 inches and the height is 46 inches, what are the other two angles?
:
Find the other two angles, A & B
=
A = 62.928 degrees
and
=
B = 27.072 degrees
:
:
Check this by finding the sum of the three angles
90 + 62.928 + 27.072 = 180

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Pat has $3.80 in nickels and dimes.
Let's do this equation in cents
5n + 10d = 380
:
If there are 51 coins in all,
n + d = 51
Multiply by 10, subtract the 1st equation
10n + 10d = 510
5n + 10d = 380
----------------Subtraction eliminates d, find n;
5n = 130
n = 130/5
n = 26 nickels
then
51 - 26 = 25 dimes
;
:
Check solutions by finding the actual value:
.05(26) + .10(25) =
1.30 + 2.50 = 3.80

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No

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Factor to reveal perfect squares

Extract the square root of these squares

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The first three problems are all "shared work" problems and can be done in the same way.
I will complete the 1st one, and give the equation for the other two for you to do yourself.
:
:
1.)Euclid works 2 times as fast as his sitter.
Together they cleaned the house in 4 hours.
How long would it take each of them to clean the house?
:
let t = time for E to do the job
then
2t = time for his sitter to do the job
let the completed job = 1
+ = 1
multiply by 2t to get rid of the denominators
2t* + 2t* = 2t(1)
cancel the denominators, resulting in:
2(4) + 4 = 2t
8 + 4 = 2t
12 = 2t
t = 12/2
t = 6 hrs for E to do the job alone
then
2(6) = 12 hrs for his sitter to do it
:
Check these solutions ensuring that the two fractions add up to 1
+ =
+ = 1
:
:
2.)A small pipe and a large pipe both carry water to storage tank.
The large pipe fills the tank twice as fast as the small pipe.
When both pipes are used, the tank is filled in 8 hrs.
:
let t = time for the large pipe to fill the tank
then
2t = time required by the smaller pipe
let the completed job = 1 (full tank)
+ = 1
:
:
3.)Working alone a man can mow a lawn in 3hours.
His friend can complete the same job in 2hours.
How long would it take them working together?
;
let t = time required when working together
+ = 1
:
:
4.)A rope that is 20 feet long is cut into 2 pieces.The ratio of the smaller piece to the larger piece is 3/5.
Find the length of the shorter piece.
:
let x = the multiplier
3x + 5x = 20
8x = 20
x =
x = 2.5 is the multiplier
the shorter rope (3x); 3*2.5 = 7.5 ft
:
:
5.)If 561 is divided by a certain number,the quotient is 29 and the remainder is 10.
Find the number.
:
Let n = "that certain number"
= 29 +
multiply thru by n, results:
561 = 29n + 10
561 - 10 = 29n
551 = 29n
n =
n = 19 is the number
:
:
Let me know how you do on these. C

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multiply and simplify
4x^2/5x^2-20x+20 * 5x-10/2x
type exponential notation with positive exponents
:
*
Factor
*
Factor again
*
You can cancel out 5, (x-2), 2x, leaving just

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two lines, AB and CD, intersect at point E.
find the values of x and y given that:
the measure of angle AED equals (10x+9y), the measure of angle AEC equals (xy), and the measure of angle CEB equals (15x).
:
We know AED = CEB, therefore
10x + 9y = 15x
9y = 15x - 10x
9y = 5x
:
We know AEC + CEB = 180 degrees, therefore
xy + 15x = 180
xy = 180 - 15x
divide by x
y = - 15
replace y with this in the 1st equation
9( - 15) = 5x
- 135 = 5x
simplify, divide by 5
- 27 = x
multiply both sides by x, results
324 - 27x = x^2
Arrange as a quadratic equation on the right
0 = x^2 + 27x - 324
You can use the quadratic formula but this will factor to:
(x+36)(x-9) = 0
positive solution
x = 9
Find y
9y = 5x
9y = 5(9)
9y = 45
y = 45/9
y = 5
:
You can use x=9, y=5 to find the measure of the angles, and confirm that the angle conform the rules of intersecting lines

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If Judy runs the 100 yard track and Mary runs the 75 yard track, how many times
will they each have to run to complete the same number of yards.
:
The least common multiple of 100 and 75
Prime factor
100: 2*2*5*5
75: 3*5*5
LCM; 2*2*3*5*5 = 300 yds,
Judy: 300/100 = 3 laps
Mary: 300/75 = 4 laps

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Molly wanted to make an offer on a new car with a sticker price of $12,305.
If the dealer’s margin of profit was 16% and Molly wanted to offer $500 more than the base price, calculate the amount of her offer to the nearest dollar.
:
Find the cost (c) of the car to the dealer
:
c + .16c = 12305
1.16c = 12305
c =
c = 10607.76, the cost to the dealer
then
10607.76 + 500 ~ $11,108, the amt of the offer

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Each one of these problems can be solved by finding the hypotenuse of a right triangle:
:
1.) Andre rode in a bike trek from his home due north for 10 miles and then due east for 3 miles.
How far, to the nearest tenth, is he from home after his first day?

h = 10.4 mi
:
2.) He continues north for another 12 miles and then turned west and rode for 15 miles.
At the end of the second day, how far was he from the first night's stop?

h = 19.2 mi
:
3.) The third day he headed north and rode for 17 miles and west for 10 miles.
How far is he from his seconds nights stop?

h = 19.7 mi
:
How many miles south must he ride to be able to turn east and ride straight home?
Add up the total miles traveled north, to find the required miles south.
10 + 12 + 17 = 39 miles south then turn east

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I think you mean
The half-life of 234U, uranium-234, is 2.52(10^5) yrs.
:
If 98.2% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
:
The half-life formula: A = Ao*2(-t/h)
where:
A = resulting amt after t yrs
Ao = initial amt
h = half-life of substance
t = time of decay
:
Let initial amt; Ao = 100
A = 98.2, resulting amt
h = 2.52(10^5) yrs
find t
:
100*2^(-t/(2.52(10^5)) = 98.2
:
2^ =
:
2^ = .982
:
*ln(2) = ln(.982)
:
=
:
= -.0262
:

t = 6,603.68 yrs

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A stationary cyclist is passed by another cyclist riding with a constant speed of 3.4 m/s.
Immediately as the other bike passes the stationary bicyclist hops on his bike and accelerates at 2.4m/s2 until he catches up.
(a) How much time does it take to catch up and how far has he traveled in this time?
:
Let t = time required for him to catch up
then
3.4t = distance (in meters) traveled by both bikes when this happens
:
2.4t = cyclist speed after t seconds
= av velocity of cyclist over this distance, (from 0 to 2.4t m/s^2)
:
*t = = 1.2t^2 distance traveled over t time
It is equal to the other rider's dist
1.2t^2 = 3.4t
1.2t^2 - 3.4t = 0
Divide both sides by 1.2t
1.2t(t - 2.83) = 0
t = 0, start time
and
t = 2.83 seconds to catch up
dist = 2.83 * 3.4 = 9.622 meters

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The shape of the gateway arch in st. Louis, Missouri, is a catenary curve, which closely resemble a parabola. The function models the shape of the arch, where y is the height in feet and x is the horizontal distance from the base of the left side of the arch in feet.
:
Convert the coefficient of x^2 to a decimal = -.00635
:
a)Find the vertex
Find the axis of symmetry
x =
x = 315 ft, from the left side of the base
Find y (the height)

y = -630 + 1260
y = 630 ft high
vertex, 315, 630
:
b) Describe a reasonable domain and range for the function. Explain.
domain 0 to 630; range 0 to 630 (only positive values here)
:
c) According to the model, what is the maximum height of the arch
630 ft
d) What is the width of the arch at the base?
2(315) = 630 ft
:
A graph of this equation illustrates this well

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just write an equation for what it says
:
When one-fourth of a number is added to one-eighth of the number,
the sum is 100 more than the number.
n + n = n + 100
clear the denominators, mult by 8, results:
2n + n = 8n + 8(100)
3n = 8n + 800
-800 = 8n - 3n
-800 = 5n
n =
n = -160
:
:
See if that works in the original equation
(-160) + (-160) = -160 + 100
-40 + (-20) = -60; confirms our solution of n = -160

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an airplane takes off at a 12 degree angle and travels at a rate of 240ft/sec. how long does it take for the plane to reach an altitude of 10000 ft?
:
We can solve this as a right triangle, the path of the plane is the hypotenuse (p)
the height is the side opposite the angle of 12 degrees, use the sine
Sine(12) =
.2079p = 10000
p =
p = 48,097.34 ft
Find the the time to travel this distance at 240 ft/sec
t =
t = 200.4 seconds, 3 min 20.4 sec to reach an altitude of 10000 ft

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A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour.
Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 22 miles per hour.
What is the amount of time that the cyclist travels before overtaking the runner?
:
let t = travel time of the bike
then
(t+2) = running time of the runner
:
When the bike overtakes the runner, they will have traveled the same distance
Write a distance equation; dist = speed * time
:
6(t+2) = 22t
6t + 12 = 22t
12 = 22t - 6t
12 = 16t
t =
t = .75 hrs, or 45 min for the bike to overtake the ground-pounder
:
:
Check by finding the actual dist of each, they should be equal
22(.75) = 16.5 mi
6(2.75) = 16.5 mi

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Let a = his present age
:
"in 2 years they will be twice as old as they were 5years ago,"
a + 2 = 2(a-5)
a + 2 = 2a - 10
a - 2a = -10 - 2
-a = -12
a = 12 yrs is his present age
:
:
Check this in the given statement:
"in 2 years they will be twice as old as they were 5 yrs ago,"
12+2 = 2(12-5)
14 = 2(7)

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or those people with highly sensitive skin, an ultra-violet, or UV, rating of 6 will cause sunburn after 10 min.
Given that the number of minutes it takes to burn t varies inversely as the UV rating u, how long will it take a highly sensitive person to burn on a day with a UV rating of 4?
:
let t = time to burn on a 4UV day
;
Varies inversely so we can write it
=
Cross multiply
4t = 60
t =
t = 15 min

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a traveler takes a bus ride at 10 miles an hour to a certain point and then walks back 2 miles an hour.
If he returns 3 hours after he left, how far did he walk?
:
Let d = the distance walked (and rode by bus)
:
Write a time equation, time = dist/speed
:
bus time + walk time = 3 hrs
+ = 3
multiply by 10
10* + 10* = 10(3)
cancel out the denominators
d + 5d = 30
6d = 30
d = 30/6
d = 5 miles walked
;
:
Check solution of d=5 by finding the times
5/10 = .5 hrs
5/2 = 2.5 hrs
--------------
total: 3 hrs

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i have 87 grams , 43 grams, and 35 grams. I am trying to recalculate each of those numbers into a percentage to total 100 percent.
:
43 + 35 = 78 grams, assuming that's what mean:
:
* 100 = 55.1%
* 100 = 44.9%
----------------------------
check, find total: 100%

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"A charter flight club charges its members $400 per year.
But, for each new member in excess of 60, the charge for every member is reduced by $5.
What number of members leads to a maximum revenue?"
:
Let x = no. of $5 decrease for each member
and
Let x = increase in membership
:
f(x) = (400-5x)(60+x)
FOIL
f(x) = 24000 + 400x - 300x - 5x^2
A quadratic equation
f(x) = -5x^2 + 100x + 24000
Max revenue will occur at the axis to symmetry, x = -b/(2a)
a = -5, b = 100
x =
x = +10
A decrease of 5(10) = $50 giving us $350 per member
An increase of 10 people giving us 70 members for max revenue

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The three digits: a, b, c, d
:
"The sum of the digits is 12."
a + b + c + d = 12
:
"The digit in the thousandths place is 3 times the digit in the tens place."
a = 3c
"The digit in the tenths place is one more than the digit in the hundredths place."
c = b + 1
or
b = (c-1)
:
a + b + c + d = 12
Replace a and b
3c + (c-1) + c + d = 12
5c + d = 12 + 1
5c + d = 13
Assume that c has to equal 2, therefore
5(2) + d = 13
10 + d = 13
d = 13 - 10
d = 3
find the rest of the digits
a = 3(2) = 6
b = 2-1 = 1
c = 2
d = 3
then
6123 is the number
:
Assume that c has to equal 1, therefore
5(1) + d = 13
5 + d = 13
d = 13 - 5
d = 8
find the rest of the digits
a = 3(1) = 3
b = 1-1 = 0
c = 1
d = 8
then
3018 is the number
:
"To the nearest ten, the number rounds to 30." Not sure what bearing this has on this problem.

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The cost of a new car included a 4.5% sales tax.
If c represents the cost before tax, write an expressions for the total cost, including the sales tax.
:
total cost = c + .045c

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The greatest of three Consecutive whole numbers is X. Find the sum of X times the smallest number twice the middle number and three times the greatest.
:
The three numbers: x, (x-1), (x-2)
:
Punctuation helps make sense of this
"Find the sum of X times: the smallest number, twice the middle number, and three times the greatest."
:
x((x-2) + 2(x-1) + 3x)
x(x - 2 + 2x - 2 + 3x)
x(6x - 4)
or
6x^2 - 4x

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let n = no. of nickels
let q = no. of quarters
:
Write an equation for each statement
:
"Maria has a collection of coins; the value of the collections is $7.50."
.05n + .25q = 7.50
:
" There are six more quarters than nickels."
q = (n+6)
:
Replace q in the 1st equation with (n+6), find n
.05n + .25(n+6) = 7.50
:
I think you can do this now.