f(x) = (0.1 mm)*2x
where:
f(x) is the thickness of the paper after x folds
0.1 mm is the paper's thickness when unfolded (x=0)
x is the number of folds
f(0) = (0.1 mm)*20 = (0.1 mm)*1 = 0.1 mm
f(5) = (0.1 mm)*25 = (0.1 mm)*32 = 3.2 mm
f(10) = _____
f(20)...

Let x = the length of the shortest side.
The longest side of a triangle is 2 times the shortest side: = 2x
The third side is 5 more than the shortest side = x + 5
The perimeter of the triangle is the sum of the lengths of the sides and is equal to 65cm
...

Let x and y be the two unknown numbers. Since you have two unknowns, you need two equations to solve for them:
The difference between two numbers is 2: x-y = 2
The sum of their squares is 52: x2 + y2 = 52
Since x-y=2, then x = 2+y. Substitute...

Scores at or above 660:
660 and under 690 18
690 and under 720 11
720 and under 750 7
...

Using x to represent the number:
Five more than a number (x+5)
is less than 17 (< 17)
x+5 < 17

Let x = the hotel's cost before sales tax:
x + (0.045)x = $355.30
1.045x = $355.30
x = $355.30/1.045
x = $340
Yep,...

The equation of a line is y = mx + b where m is the slope and b is the y-intercept. So you need to find the slope (m) and y-intercept (b) of the tangent line. The slope is easy - it's just the derivative of f(x) at the given point, (0,1/2); that is, m = df(x)/dx at x = 0:
...

4x+8 27
L-------------M-------------------------N
<------------------ 6x -------------------->
LM = 4x+8
MN =...

P(AUB) = P(A) + P(B) - P(A∩B)
Hence:
P(A∩B) = P(A) + P(B) - P(AUB) = 0.41 + 0.37 - 0.5 = 0.28
p(A|B) = P(A∩B)/P(A) = 0.28/0.41 = 0.683

Let x = your age. Let's read the problem:
200
reduced by (-)
2 times my age (2x)
is (=) 18:
200 - 2x = 18
182 = 2x
Solve for x.

(-3x4)3(2x-2)/6x7
= (-3)3(x4)3*2/6x7*x2
= -54x12/6x9
= -9x3

Start with the formula for the gravitational force between two masses, m1 and m2, which you can look up in your book or on-line:
F = G*m1*m2/r2
Where:
G = Gravitational Constant = 6.674*10-11 Nm2/kg2
m1 = one mass = 58 kg
m2 =...

(708 lbs per year)/(365 days per year) = _____ lbs per day

distance = rate* time
Since Edward is driving at two different rates for two different times:
distance = rate1*time1 + rate2*time2
Where :
rate1 = 60 mph
time1 = 3 hours
rate2 = 50 mph
time2 = 3 hours
...

74 million = 74,000,000
There are six zeros, so that equates to 106. The first number must be one or greater and less than 10; so we change 74 to 7.4*10.
74 million = 7.4*10*106 = 7.4*107

f(x) = 3x + 1
g(x) = 3x - 2
(f/g)(x) = (3x+1)/(3x-2)
In math. division by zero is undefined. So any value of x that makes the denominator of a rational expression equal to zero will make the rational expression undefined. Such values of x are...

Let x and y be the two unknown numbers.
The sum of two numbers is 70: x + y = 70
The larger number (y) is 4 more than twice the smaller number (x): y = 2x + 4
Since x + y = 70, y = 70 -x. Substitute 70-x in place of y in the second equation:
...

distance = rate*time
distance/time = rate
The race course is 3 miles around and Jeff does it twice, so the distance he goes = 2*3 miles = 6 miles. He takes 20 minutes to go around once and 25 minutes to go around the second time, so the total time = 20 min +...

2x2 + 3x- 5
Use the ac method, where a = 2 , b = 3, and c = -5:
a*c = -10
We want two factors that multiply to -10 and add to 3. Answer = 5 and -2
5*(-2) = -10
5 + -2 = 3
Now factor by grouping:
2x2...

Let x be the unknown angle. Supplementary angles add to 180o, so the supplementary angle of x is 180o-x.
the measure of the angle (x)
is (=)
nine times greater than its supplement (9*(180o-x))
x = 9(180o-x)
x = 1620o - 9x
10x = 1620o
x = 162o
The...