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Let A = angle
Let (90 - A) = the complement of the angle
A = 2(90 - A)
Can you take it from here?

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Let L = liters
0.40L + 10(0.80) = 0.60(L + 10)
The above equation is all you need to find the answer.

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I know that this is a geometry question but it can be solved using trigonometry.
We use the law of sines.
The sum of the angles of a triangle is 180 degrees.
To find the missing angle, add 51 + 75 and then subtract the sum from 180.
This will give you 54 degrees.
We now use the law of sines.
Let x = the missing side we want to find
sin51/x = sin75/25
x(sin75) = sin51(25)
x(sin75) = 19.42864904
x = 19.42864904/sin75
x = 20.11401756
The side opposite the smallest angle is 20 inches.

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Equilateral means all sides are the same.
The bottom side can be divided into two parts of equal length: 10cm = 5cm + 5cm.
Let h = height
Use the Pythagorean Theorem to find h.
h^2 + 5^2 = 10^2
Can you take it from here?

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3x/4 + 82 = x
4*(3x/4) + 4*84 = 4*x
3x + 328 = 4x
328 = 4x - 3x
328 = x
Now, 3/4 * 328 = 246

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Let c = number of cashews
Let p = number of peanuts
c + p = 0.5
6.25c + 2.00p = 1.70
This is your system of equations in two variables.
Can you take it from here?
If not, write back.

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You want the other six numbers to be as small as possible. The smallest the first six might be is 1,2,3,4,5,6 and the sum of these is 21. The total of all the numbers is 7x7=49 so the largest number would be 49-21=28.

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7(b-3)= -28
7b - 21 = -28
7b = -28 + 21
7b = -7
b = -7/7
b = -1

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To evaluate a function, we insert a given x value, a number in the domain, and see what number we get, which is a number in a range.
SAMPLE:
f(x) = x + 2
Pick a number for x. Any number will do.
Say, x = 3.
f(3) = 3 + 2
f(3) = 5
Here, 3 is the number in the domain of the function and 5 is the range of the function.
Understand?

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The domain is all values that x can take on. The only problem I have with this function is that I cannot have a negative inside the square root. So I'll set the insides greater-than-or-equal-to zero, and solve. The result will be my domain:
4 - x ≥ 0
- x ≥ 0 - 4
-x ≥ -4
x ≤ -4/-1
x ≤ 4
The values for x must be less than or equal to 4. Anything else will make the square root function undefined.

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Use the sum of cubes formula.
A^3 + B^3 = (A + B)(A^2 - AB + B^2)
x^3 + 1 = x^3 + 1^3
Let A = x
Let B = 1
x^3 + 1 = (x + 1)(x^2 - (x)(1) + 1^2)
x^3 + 1 = (x + 1)(x^2 - x + 1)
The other factor is (x^2 - x + 1).

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The lngth of tv sets are given by the diagonal measure.
The height is the side measure (from top to bottom).
The width is the bottom measure (from left to right).
The diagonla is 20. Th width is 16 inches.
Use the Pythagorean Theorem to find the height.
Let h = height
16^2 + h^2 = 20^2
256 + h^2 = 400
h^2 = 400 - 256
h^2 = 144
=
h = 12
The height is 12 inches.

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9P3 = 9!/(9 - 3)!
9P3 = 362880/6!
9P3 = 362880/720
9P3 = 504 batting line ups.
I hope this helps. If not, write back.

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Each die has numbers 1 to 6.
There are 3 prime numbers per die. The prime numbers are 2, 3 and 5 for each die. This means there are 6 prime numbers in total from a list of 12 possibilities.
Let P = probability
P(rolling a prime) = (what we want)/(total number of possible outcomes)
P(rolling a prime) = 6/12 or 1/2

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Celcius? You mean degrees, right? Angles are measured in degrees and radians.
But in your case, we are dealing with degrees since this is not a trigonometry question.
115 + x + x = 180
115 + 2x = 180
Can you take it from here?

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Here is another method:
Let n = number of balls purchased
Let p = price per ball
Therefore:
n * p = 24
(n + 1)(p - 0.5) = 24
Therefore:
p = 24/n
(n + 1)((24/n) - 0.5) = 24
24 - 0.5n + (24/n) - 0.5 = 24
-0.5n + (24/n) - 0.5 = 0
Multiply through by -2n:
n^2 + n - 48 = 0
n = (-1 +/- sqrt(1^2 - 4(1)(-48))) / (2*1)
n = (-1 +/- sqrt(1 + 192)) / 2
n = (-1 +/- sqrt(193)) / 2
n = -0.5 +/- sqrt(48.25)
n =~ 6.47 or -7.47
Suppose she bought 6 balls, so they each cost $4. If they had cost $3.50, then $24 would still not be enough to buy 7 balls. So that doesn't work.
Suppose she bought 7 balls, so they each cost about $3.43. If they had cost $2.93, she could have bought 8 balls for $24 (and received $0.56 in change).
Suppose she bought 8 balls, so they each cost $3. If they had cost $2.50, she could have bought 9 balls for $24 (and received $1.50 in change).
Suppose she bought 9 balls, so they each cost about $2.67. If they had cost $2.17, she could have bought at least 11 balls for $24. So that doesn't work.
So the answer must be 7 (or 8).

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Length = 6
diagnoal = 10
side = x
We need to find x using the Pythagorean Theorem.
x^2 + 6^2 = 10^2
x^2 + 36 = 100
x^2 = 100 - 36
x^2 = 64
=
x = 8
The width is 8.
Area = length times width
Area = length times width
Area = 6 times 8
Area = 48 square feet
Done!

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You need the formula: P(A or B) = P(A) + P(B) - P(A and B),
where is P = probability.
Let A = selecting a teaching assistance
Let B = selecting a female
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = (28/49) + (28/49) - (28/49*28/49)
P(A or B) = (4/7) + (4/7) - (4/7*4/7)
P(A or B) = (8/7) - (16/49)
P(A or B) = 40/49

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-5 < 9x + 8 -8x
Treat it like a regular equation disregarding the inequality sign.
On the right side, combine like terms. We can combine 9x and -8x because they both share an x. After that, subtract 8 from both sides.
-5 < 9x - 8x + 8
-5 < x + 8
-5 - 8 < x
-13 < x
Done!
But, what does the answer mean?
It means that any value you choose for x must be bigger than -13 to make the original inequality question a true statement.
Let me ask you some questions.
Can x be -15?
No, because -15 is smaller than -13.
Can x be -100?
No, because -100 is smaller than -13.
It must be bigger than -13. Any number to the right of -13,
(not including -13), on the real number can be used to replace x with. The question, however, is not asking you to replace x with a number. The correct answer is -13 < x. I just wanted to break down the answer a bit more in detail.
Understand?

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Let n = total of city commissioners
Let r = how many candidate are taken from the total
This is a combination question from probability math.
The formula you need is given by: nCr = n!/[(n - r)! * r!]
The exclamation point (!) means factorial.
What is a factorial anyway?
A factorial is the product of all the positive integers from 1 to a given number.
For example, 6 factorial, written 6!, means 6 x 5 x 4 x 3 x 2 x 1 = 720.
What would 4! be? It is 4 x 3 x 2 x 1 = 24.
Understand?
============================================
Back to your question.
Let n = 12
Let r = 6
Replace every n! with 12 and every r! with 6 and then do the math.
nCr = 12!/[(12 - 6)!*6!]
nCr = 479001600/(720)(720)
nCr = 479001600/518400
nCr = 924
There are 924 ways or combinations to select 6 city commissioners from a group of 12 candidates.

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Let p = perimeter
Let x = lengths and sides
The perimeter of a rectangle formula is given by P = 2L + 2W.
38 = 2(2x) + 2(2x)
Can you take it from here?

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Let f = full-price ticket
Let s = student ticket
f + s = 496
6.00f + 4.25s = 2498.25
This is a system of linear equations in two variables. The two variables are f and s. I selected f and s but you can use any other two letters.
You now have the two equations above. Use the substitution method to find the value of s. I assume that you know how to solve this type of problem.
Can you take it from here?

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This is addition of cubes.
Use the following formula:
a^3 + b^3 = (a + b)(a^2 – ab + b^2)
Write 8 as 2^3 and 64 as 4^3 to get the same exponent of 3.
(2x)^3 + 4^3 = (2x + 4)((2x)^2 - (2x)(4) + 4^2)
(2x)^3 + 4^3 = (2x + 4)(4x^2 - 8x + 16)
So, 8x^3 + 64 in factored form looks like this: (2x + 4)(4x^2 - 8x + 16)

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Your graph will have points in the form (t,c).
STEPS:
1-select about 3 values for t (I chose t = 0...see below)
2-simplify the right side of the equation for each value selected in terms of t
3-When you find the value of t and c, plot each point (t,c) on the coordinate plane
4-Connect each point with a line
==================================
Let's say that t = 0
c = 20t + 30
c = 20(0) + 30
c = 0 + 30
c = 30
Your first point to plot is (0,30).
Can you find two more points and then follow the above steps?
Your function is a straight line. Can you do it now?

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Since 4 boys can shovel a driveway in 2 hours, 1 boy can do it in 4 x 2 hours = 8 hours. Thus, 5 boys can do it in 8/5 hours. Now, each hour is 60 minutes, so 5 boys can do it in 8/5 * 60 = 60 + 36 = 96 minutes.
How about now?

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Let x be the speed for the first part of the trip. So that part takes 54/x hours.
So the speed for the second part of the trip is x - 5, so that part takes 8/(x-5).
Therefore:
(54/x) + (8/(x-5)) = 3
54(x - 5) + 8x = 3x(x - 5)
54x - 270 + 8x = 3x^2 - 15x
62x - 270 = 3x^2 - 15x
3x^2 - 15x - 62x + 270 = 0
3x^2 - 77x + 270 = 0
x = (-(-77) +/- sqrt((-77)^2 - 4(3)(270))) / (2*3)
x = (77 +/- sqrt(5929 - 3240)) / 6
x = (77 +/- sqrt(2689)) / 6
x =~ 21.4759 or 4.19
If x =~ 4.19, then the speed for the first part of the trip is 4.19, and the speed for the second part of the trip is -0.81. But a negative number makes sense, so we'll discount that solution.
Therefore, x =~ 21.4759, so the speed for the first part of the trip is about 21.4759, so the speed for the second part of the trip is about 16.4759.

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Is this what you wanted to type: = 125?
If so, write back.

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Let n = the number
10 times (n - 5), which be written 10(n - 5).
We now apply the distributive rule to remove the parentheses.
10(n - 5) = 10n - 50.

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To Change from Standard Form to Scientific Notation:
(1) Place the decimal point such that there is one non-zero digit to the left of the decimal point.


(2) Count the number of decimal places the decimal has "moved" from the original number. This will be the exponent of the 10.


(3) If the original number was less than 1, the exponent is negative; if the original number was greater than 1, the exponent is positive.
762.20 = 7.62 x 10^2

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To Change from Scientific Notation to Standard Form:
(1) Move the decimal point to the right for positive exponents of 10. The exponent tells you how many places to move.


(2) Move the decimal point to the left for negative exponents of 10. Again, the exponent tells you how many places to move.

6.20 x 10^-2 = 0.0620

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The statement "two less than a number y is seven times y" can be written in the following way: y - 2 = 7y.
You need to solve for y.
y - 2 = 7y
y - 7y = 2
-6y = 2
y = 2/-6
y = -2/6
y = -1/3
Done!