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here is our original equation
(i)
step 1 - subtract 5 to get
(ii)
step 2 - take out the gcf to get
(iii)
step 3 - divide by a-3 to get
(iv)
restrictions: a cannot = 3

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we simplify the fraction as (-4/3)
and then use the division rule, subtract exponents, to get x^(2/3)
together the answer is

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We will rewrite this as

or

now the derivative is

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step 1 - we take a derivative of both sides and get

step 2 - solve for dy/dx

step 3 - put your coordinates in and get

---
so, the slope is
dy/dx = m = 5/12
---
step 4 - using slope and our coordinate as well as y = mx + b, we get

and then

solving for b, we get

---
step 5 - final equation is

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The perimeter is expressed as
(i)
or
(ii)
dividing by 2 we get
(iii)
solve for y as
(iv)
---
area formula is
(v)
substituting (iv) into (v) we get
(vi)

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Line them up like this
endpoint: (3,2)
midpoint: (8,0)
endpoint:
to find the endpoint coordinates,
look at the x's. 3 to 8 means add 5. add 5 more and we get 13
look at the y's. 2 to 0 means subtract 2. subtract 2 more and we get -2.
The other endpoint is
(13,-2)

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draw a right triangle and place 25 degrees at a bottom vertex
in this case we have the opposite side and want the hypotenuse. This means we need sine theta.
sin 25 = 6/r
r = 6/sin(25) ~ 14.2 feet

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here s the original question
solve the following formula: F=(GMm)/d2
for d2
----
step 1 cross multiply to get

step 2 - divide by F to get

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1.What is the surface area that has a diameter of 3 inches and height of 5 inches?

the diameter = 3, so radius = 1.5

so

or

---
2.What is the total square feet of a rectangle that is 12 ft x 8ft x11ft?

we get

then

or
---
3.A rectangular swimming pool has a length of 18 ft, width of 10 ft, and a depth of 4ft. What is the volume of water the pool can hold?

or

which is
cu. ft.

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We use implicit differentiation here. On the left, it is regular derivatives, but on the right we need to the product rule. we get
(i)
step 1 - subtract 1 (dy/dx) from both sides and then subtract y from both sides to get
(ii)
step 2 - factor out the dy/dx to get
(iii)
step 3 - divide by x-1 to get
(iv)

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First our license plate must be in the form of
# - L - L,
or,
number - letter - letter.
we have 2 choices for the numbers, 3 or 7
we have 3 choices for the letters c - a - r.
repetition is allowed: So there is a second 3 choices for letters c - a - r
---
1. Use the counting principle to determine the number of points in the sample space.
ANSWER: The counting principal is all about multiplying the number of ways one event occurs x the number of ways a second event occurs x the number of ways a third event occurs and so on. In our case we have 2 number choices and 3 letter choices, but two times.
2 x 3 x 3 = 18.
---
2. Construct a tree diagram to represent this situation.
ANSWER:
step 1 - write a 3 and below it with a little space write a 7
step 2 - from the 3 draw 3 arrows and next to the end of these write c, a, r
step 3 - next to each of the letters draw another 3 arrows and write the letters again for c, a, r
step 4 - from the 7 draw 3 arrows and next to the end of these write c, a, r
step 5 - next to each of the letters draw another 3 arrows and write the letters again for c, a, r
---
3. List the sample space.
ANSWER: this is pretty straight forward from the tree diagram. we get
3aa, 3ab, 3ac, 3ba, 3bb, 3bc, 3ca, 3cb, 3cc,
7aa, 7ab, 7ac, 7ba, 7bb, 7bc, 7ca, 7cb, 7cc.
3ab plate is different from 3ba plate
---
4. Determine the EXACT probability of creating a mini license plate with a C. Give the solution in reduced fraction form.
ANSWER: 3ac, 3bc, 3cc, 3ca, 3cb, 7ac, 7bc, 7cc, 7ca, 7cb
"with a C" means to me one or two C"s in any order.
P(C) = 10/18 = 5/9.

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lets start with
(i)
we know v = 50, so we get
(ii)
If we solve for h, we get
(iii)
now we look at surface area as
(iv)
substitute (iii) into (iv) to get
(v)
now everything is in terms of r.
getting a common denominator as pir^2, we get
(vi)
now, factoring, we get
(vii)
reducing we get
(viii)
It turns out that r is minimum at 2.
This means that h = 50/4pi or h ~ 3.97887
This gives us a minimum sa at
sa = 75.1326

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You are good at

next subtract 24 to get

subtract 6y to get

divide to get

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divide both sides by 0.8 to get
x < -50

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here is the problem
(i)
step 1 - distribute the (-) to get
(ii)
step 2 -combine like terms to get
(iii)
step 3 - add 4 to get
(iv)
divide by 5 to get
(v)

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Let v = video and d = dvd
---
from the given we get
(i)
(ii)
step 1 - multiply (ii) by -4 to get
(iii)
step 2 - add (ii) and (iii) to get
(iv)
divide by -26 to get
(v)
and then
(vi)

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Let the height = h.
base = h + 10
area = 28
---
The area of a triangle has the formula

---
from the given information, we get

multiply both sides by 2 to get

distribute to get

set = 0 to get

factor to get

solving we get
h = -14
and
h = 4
we can't use the -14, so our only answer is
h = 4 cm

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We can solve this by polynomial or synthetic division. Synthetic is faster. First, set 6x + 4 = 0 and solve for x as x = -2/3. Now divide as
(-2/3) // . . . . . . . . 18 . . . . . . -36. . . . . . -38 . . . . . . . -4
. . . . . . . . . . . . . . . . . . . . . . . . -12 . . . . . . 32 . . . . . . . . 4
. . . . . . . . . . . . . . . .18. . . . . . . -48. . . . . . .-6. . . . . . . . .0
---
we know one root is x = (-2/3)
we have
18x^2 - 48x - 6 = 0
divide by 6 to get
3x^2 - 8x - 1 = 0
using the quadratic, we get
x ~ 2.786
and
x ~ -0.1196
so, our 3 roots are
{-2/3, -.1196, and 2.786}

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The solution is (15, 40)
Here is the graph

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The solution should be (-20,0)
Here is the graph

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this is a mixture problem. Here is a table based on the given information
solutions . . . . . . . % . . . . . . . . ounces . . . . . . . . . .%ounces
salt . . . . . . . . . . .4 . . . . . . . . .32 . . . . . . . . . . . . . . .128
water . . . . . . . . .0 . . . . . . . . . x . . . . . . . . . . . . . . . .0
mixture. . . . . . . 6 . . . . . . . . . x + 12. . . . . . . . . . . . 6x + 72
looking at the third column, we have

subtract 72 to get

dividing, we get

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---
the only answer is 5.
---
In general, we have

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This is a RTD problem. Here is a table based on given information
paddle . . . . . . . . .rate . . . . . . . . . time . . . . . . . . . distance
up stream . . . . . .r - c . . . . . . . . . . .10 . . . . . . . . . . 10r - 10c =15
down stream . . . .r + c . . . . . . . . . . .5 . . . . . . . . . . .5r + 5c = 22.5
totals . . . . . . . . .
Looking at column 3 we get
(i) 10r - 10c = 15
(ii) 5r + 5c = 22.5
multiply (ii) by 2 to get
(iii) 10r + 10c = 45
add (i) and (iii) to get
(iv) 15r = 60
divide to get
(v) r = 4
This means that the current is
c = 2.5

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Here is the original equation
(i)
to find the inverse switch the x and y parts.
(ii)
cross multiply to get
(iii)
add 2 and then subtract xy to get
(iv)
factor out the y to get
(v)
divide by 1-x to get
(vi)
this is the inverse
----
a). domain of f(x) is all reals except x = -3
The range of f^(-1)(x) is all reals except y = -3
b). The range of f(x) is all reals except y = 1
the domain of f^(-1)(x) is all reals except x = 1

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we are given
(i)
step 1 - multiply by the conjugate of (2-i) which is (2+i) to get
(ii)
and simplified, we get
(iii)
we then separate our real and imaginary parts to get
(iv) +
---
at this point there is no equal sign, so we can't solve for x and y, just rewrite using x and y in the real and imaginary parts.

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WE need the circumference formula which is

we know r = 6.5, so we have
{{C = 2*pi*6.5}}}
or
feet

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here is the original equation
(i)
step 1 - distribute the 13 and the -3 to get
(ii)
step 2- combine like terms to get
(iii)
step 3 - solve for x to get
(iv)

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Commutative property is expressed as
a + b = b+ a
OR
a x b = b x a
The idea is that we are reversing our information.
----
Associative property is expressed as
(a + b) + c = a + (b + c)
OR
(a x b) x c = a x (b x c)
The order is the same, only parenthesis have shifted.
-----
that is the main difference.

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Here is the original equation
(i)
step 1 - multiply both sides by (6/a) to get
(ii)

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The volume of a cone is
(i)
where B = area of base (circle) and h = height.
from (i) we could say
(ii)
Now from above, we get
(iii)
or
(iv)

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here is the original system:
(i)
(ii)
since we must use substitution, we can solve (i) for n and get
(iii)
substitute (iii) into (ii) to get
(iv)
distribute and simplify to get
(v)
combine like terms to get
(vi)
add 138 to get
(vii)
divide by 37 to get
(viii)
now,

So, we get
(4,-1)