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Here's a guess!
T, F, S, N, E. T, F, S, N, T,
What do they mean...my guess is they are the initial letters of the odd integers beginning with 3.
T = 3
F = 5
S = 7
N = 9
E = 11
T = 13
F = 15
S = 17
N = 19
T = 21

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This problem involves diophantine equations, where you have more unknowns than equations.
The solutions, however, are limited by the fact that the unknowns must be integers, i.e. whole cows, whole horses, etc.
We can set up two equations as follows: H = number of horses, C = number of cows, and ch = number of chicks.
From the problem description, we can write:
H+C+ch = 100 The total number of animals is 100.
($5)H+($3)C+($0.50)ch = $100 The total amount the farmer spends.
The two equations are:
1) H+C+ch = 100
2) 5H+3C+0.5ch = 100 Multiply this equation by 2 and subtract equation 1) from the result.
1) H+C+ch = 100
2a) 10H+6C+ch = 200
--------------------
3) 9H+5C = 100 Subtract 9H from both sides.
3a) 5C = 100-9H Now divide both sides by 5.
3b) C = 20-(9/5)H Now C can only be an integer if H is a multiple of 5. Let's try H = 5.
3c) C = 20-(9/5)(5)
C = 20 - 9
C = 11 This is one possibility. Now let's try H = 10
3d) C = 20 - (9/5)(10)
C = 20 - 18
C = 2 This is another possibility.
H cannot be greater than 10 otherwise you would end up with C being a non-integer or a negative number.
So, if C = 11 when H = 5, then ch = 100-11-5 = 84 - the number of chicks.
Let's check this solution.
H+C+ch = 100
5+11+84 = 100 and...
5($5) + 11($3) + 84($0.50) = $25 + $33 + $42 = $100 This is a valid solution!
Now if C = 2 when H = 10, then ch = 100-2-10 = 88 - the number of chicks.
Let's check this solution.
H+C+ch = 100
10+2+88 = 100 and...
10($5)+2($3)+88($0.50) = $50+$6+$44 = $100 This solution is also valid!
The two solutions are:
1) 5 horses, 11 cows, and 84 chicks.
2) 10 horses, 2 cows, and 88 chicks.

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To find the average score (A) of the first five tests, you'll add the scores and divide by 5.
where x is the score on the fifth test.
Now you need this average (A) to be at least 80 () but less than 90 ().
You can write the inequality thus:
To solve this, you'll simplify the numerator.
Now you'll multiply everything by 5.
Simplify.
Now you'll subtract 326 from everything.
Simplify.
Read this as: x is at least 74 but less than 124.
The range of scores needed to get a B average is at least 74 but less than 124.

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Let n be the required number. From the problem description, you can write:
Add the fractions, the LCD is 150.
Simplify.
Multiply both sides by 150.
Divide both sides by 43.

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1) Let x be the first odd integer, then x+2 will be the next consecutive odd integer.
From the problem description, you can write:
3x = 2(x+2)+5 Apply the distributive property to the right side.
3x = 2x+4+5 Simplify.
3x = 2x+9 Subtract 2x from both sides.
x = 9
The two integers are 9 and 11
Check:
3(9) = 2(11)+5
27 = 22+5
27 = 27
2) I don't know of an easy way to see if a similar problem to one you want help with has already been answered. You could try clicking on "Recent problems solved by all" and do a manual search but that could be quite time-consuming.

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Factor:
Do you recognise this as the sum of two cubes?
...but of course!
The sum of two cubes can be factored thus:

In your problem, A = x and B = 2, so...
and we're done!
Let's check the solution by multiplying the two factors, using FOIL.
Simplify by combining like-terms.

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From your equation, it appears that you assumed that the two segments were the same distance, but there is nothing in the problem to support this assumption.
So, back to basics:
and...

We know that:
and...

and we also know that:
So we can write:

aagh...to many variables! Let's replace with and replace with , so now we have:
and
Solve this for
...but, of course, , so...
Good, now we have one variable , so let's solve for it.


and...
hrs. Now we can find and


km and...


km
Check:
Total distance is = 90km

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Simplify:
When multiplying quantities with exponents, if the bases are the same (base is 2 in this case) then you add the exponents:
=

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Solve for h.
Isolate the variable term by subtracting 110 from both sides.
Divide both sides by 5 to further isolate the variable term.
Finally, add 60 to both sides to solve.
This can be simplified further to get:



If w = 135 pounds, then the height is:



inches.

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Let n be the number, and "at most 10" is written as "less-than-or-equal-to 10", so you can write:
To solve for n, multiply both sides by 2.

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Let x = the year of birth of the youngest, then x+1 will be the year of birth of the next oldest and x+2 will be the year of birth of the eldest friend.
So we need to find x.
x+(x+1)+(x+2) = 5961
3x+3 = 5961 Subtract 3 from both sides.
3x = 5958 Divide both sides by 3.
x = 1986
x+1 = 1987
x+2 = 1988
Check:
1986+1987+1988 = 5961

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You are taking the right approach! Let's see how it goes:
and...
We are given that:


or
and we have to find:
and but we also know that:
or
Let's put in some values.
or

Now, since we can write:
Solve this for


substitute
Solve this for


hours.


hours.
Check:
The total trip distance.
= 575

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Let x = the number of ml of the 5% solution required, then 20-x = the number of ml of the 50% solution needed. The sum of these will equal 20 ml of 30% solution.
From these facts, we can write the necessary equation to find x, after converting the percentages to their decimal equivalents.
x(0.05)+(20-x)(0.5) = 20(0.3) Simplify and solve for x.
0.05x+10-0.5x = 6
-0.45x+10 = 6
-0.45x = -4
x = 8.89
So you would need 8.89 ml of the 5% solution and 20-x = 11.11 ml of the 50% solution to obtain 20 ml of 30% solution.

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1) I think that you will have to find your own answer to this question but one example might be:
When I hit a baseball into the air, the height, in feet, it reaches can be expressed by the polynomial:

2) FOIL stands for:
F = First terms.
O = Outer terms.
I = Inner terms.
L = Last terms.
The purpose of FOIL is a mnemonic (memory aid) which reminds you of the order in which to multiply the terms of two binomials.
For example, to multiply the binomials:
you would multiply the first term (F) of each binomial ((2x)(3x)), then the two outer terms ((2x)(4)), then the two inner terms ((3)(3x)), and finally the two last terms ((3)(4)), so it looks like this:
then you would simplify this by combining like-terms to get: as the answer.
3) The inner and outer products of the product of the sum and difference will add up to zero:
and when you combine like-terms, the +ab and -ab add up to zero so you are left with:

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If 1 = 2n, then n must be the multiplicative inverse of 2!

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This is a case of a geometrical progression and can be repesented as...
+...+
The sum of this progression is cents
So, at the end of the year (52 weeks) you would have a total of:
$45,035,996,273,704.95
On the 52nd week, you would get:
cents, which amounts to $22,517,998,136,852.48

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First, I would calculate the flat-rate cost (C) and the cost per mile (x). This can be done as follows:
Write the equation for the cost of the brother's move of $52.90 for a 20-mile move...
1) ...and the sister's move.
2)
Now you have two equations with two unknowns (C and x).
Rewrite these as:
1a) and...
2a)
But the flat rate, C, is the same in both cases, so equation 1a) is equal to 2a).
Simplify and solve for x, the cost per mile.
Add 60x to both sides.
Now subtract $52.90 from both sides.
Finally, divide both sides by 40 to get x.
So the cost per mile is 72 cents. Now that we have that, we can go back to either equation 1a) or 2a) to find the value of C, the flat-rate cost. Let's use equation 1a) and we;ll substitute x = $0.72:
Simplify.

...and this ($38.50) is the flat-rate cost.
Now we can work out the cost for a one-day move of 85 miles by using 1) but substituting C = $38.50 and x = $0.72 per mile..
=
The cost of a one-day move of 85 miles is $99.70

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Solve for y:
Add the two fractions on the left side. The LCD is
Multiply both sides by and simplify.

Add 45 to both sides.
Divide both sides by -7.

Check: Substitute y = -8 in original equation.
Evaluate.



OK!

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I have worked your problem two different ways and find that the answer that you give (x = 7) is just not possible.
In the first place, to remove any ambiguity on the problem statement, please use parentheses! Why? Because...
3/7x can be interpreted to mean either: or
Whereas, (3/7)x can be interpreted only as
In the second place, the only way that I can get the answer that you give, (x = 7) is if the problem starts with , so...
Multiply through by the LCD of 7.
Simplify.
Add 3x to both sides.
Add 35 to both sides.
Finally, divide both sides by 7.
or
Please check the original problem for a possible missing negative sign!

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Solve for x:
-3(x+1) = 2(x-8)+3 First, apply the "distributive property" to both sides of the equation.
-3x-3 = 2x-16+3 Simplify.
-3x-3 = 2x-13 Add 3x to both sides.
-3 = 5x-13 Add 13 to both sides.
10 = 5x Finally, divide both sides by 5.
2 = x or x = 2
Check: Substitute x = 2 in the original equation.
-3(2+1) = 2(2-8)+3 Simplify.
-6-3 = 4-16+3 Evaluate.
-9 = 7-16
-9 = -9 It checks!

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Ok, you can start by recalling that the "domain" of a function is the set of all possible values of the independent variable.
In your function x is the independent variable (y is the dependent variable).
So you can answer the problem by assigning to x in your function, each of the given values of the domain, then solve for the corresponding value of y.
Let x = -2 The first of the given values in the domain.



This is the value of y that corresponds to the domain value of -2.
Now you repeat this process for each of the remaining given values of the domain.
Let x = -1 The second value in the set.




Let x = 1 The third value.



You proceed in this fashion until you have used all five values of the given set.
Let x = 3.



You should be able to finish these.

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First, let's concentrate on the amount of copper (Cu) in the starting alloy and the resulting alloy.
The amount of copper in the starting alloy is: 60% of 50 kg or (0.6)(50). To this we want to add x kg of Cu to make (50+x) kg of an alloy, 75% of which is Cu. So we set up the equation:
(0.6)(50) + x = (0.75)(50+x) Simplify and solve for x.
30+x = 37.5+0.75x Subtract 0.75x from both sides.
30+0.25x = 37.5 Subtract 30 from both sides.
0.25x = 7.5 Finally, divide both sides by 0.25
x = 30
You would need to add 30kg of Cu to the 50kg of the starting alloy to obtain 80kg (50kg + 30kg) of the resulting alloy containing 75% Cu.
Check:
50(0.6)+30 = (50+30)(0.75)
30+30 = (80)(0.75)
60 = 60

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Factor:
Notice that , so now you can write:
The difference of two squares can be factored: Applying this to your problem:
but again, we have the difference of two squares in the second factor, so...
we would normally stop here, because the factors of involve the imaginary number
If you are interested though:
but don't use this if you have not yet come to imaginary numbers.

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The volume of a right circular cone is given by:
where r = 10ft. and h = 18ft. If you use as an approximation, you get:




cu.ft.

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Here's where "a picture is worth a thousand word" n'est-ce pas?
Anyway, I get the picture! (lol)

You are correct for rows 1, 2, and 4. The third row is shown below:
: Base = 2 Exponent = 5
: Base = 3 Exponent = 4
: Base = 5 Exponent = 3
: Base = r Exponent = 8

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Subtract:
= =

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Graph y = 2x-3 on a coordinate plane.
This is quite easy to do on your own coordinate graph paper. This is a linear equation (you can tell this because the highest power of the independent variable, x, is 1) and since you need only two points to define a straight line, you would just assign a value to x and solve for the corresponding value of y to give you one point (x, y) then do this again with a different value of x to get the second point.
Plot these two points on your graph paper and draw the straight through them.
Let's pick x = 0 for the first point. Plugging this into your equation, we can solve for the corresponding value of y, the dependent variable.
For x = 0
y = 2(0)-3
y = -3
The coordinates of the first point are (0, -3) and...
For x = 3
y = 2(3)-3
y = 6-3
y = 3
The coordinates of the second point are (3, 3)
The graph appears below:

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Find the x-intercept:

The x-intercept is where the graph of this linear equation intersects (crosses) the x-axis. At this point, y is zero, so by setting y = 0 in the equation and solving for x, you will get the value of x where the line crosses the x-axis, also known as the x-intercept. So we'll set y = 0.

Divide both sides by 2.
This is the x-intercept! This is clear from the graph of the linear equation.

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Simplify? We don't like to see radicals in the denominator, so...
Multiply the numerator and the denominator by conjugate of the denominator which is ().
Simplify the denominator.
Simplify some more.

Cancel a 2 in the top & bottom.

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Rewrite as a function of x:
First, solve this for y.
Divide both sides by 10.
or
Now, to write this as a function of x in function form, just replace the y with f(x)

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A. Complete the square to find the centre and the radius.
Add 3 to both sides.
Group the like-terms together on the left side.
Now complete the squares in the x- and y-terms. To do this, you add the square of half the x-coefficient and the square of half the y-coefficient to both sides of the equation.
For the x's this would be and for the y's this would be , so we get:
Factor the trinomials and simplify.
Now compare this with the standard form for a circle with centre at (h, k) and radius r.
and you can see that the centre (h, k) is at (-3, 2) while the radius is = 4.
Follow this approach on the second problem and see how you do.
If you still have problems, please re-post.