Either
2(2d - 40) + (d + 20) = 180 simplify
4d - 80 + d + 20 = 180
5d - 60 = 180
5d = 240
d = 240/5 = 48°
Or
2(d + 20) + (2d - 40) = 180
2d + 40 + 2d - 40 = 180
4d = 180
d = 180/4 = 45°
The numerator is defined for all x
The x values that make the denominator = 0 will not be defined
x^2 -20x + 100 = 0 factor
(x - 10) ( x - 10) = 0
Setting either factor to 0 and solving for x
x - 10 = 0
x = 10 = the value of x that makes the rational function undefined
19, 19, 20, 20, 21, 21, 22, 24, 25, 25, 26, 27, 28, 28, 30, 30, 30, 31, 32, 32, 34, 34, 35, 38, 39, 45, 48
Mean = 29 = x
Median = 28 = y
Mode = 30 = z
x ( y - z) = 29 ( 28 - 30) = 29 (-2) = -58
ab + a + b = 95
ab + a = 95 - b
a ( b + 1) = 95 - b
a = (95 - b) / ( b + 1)
When b = 7 a = 11 relatively prime
When b = 15 a = 5 not relatively prime
a + b = 20
See the following :
Let C =(-10,20) C = (0,0)
The slope of this line = -2
And the eqation of this line is y = -2x (1)
The equation of the circle with its ceenter at A is ( x+10)^2 + ( y - 10)^2 = 100 (2)
Sub (1) into (2) and we have that
(x + 10)^2 + ( -2x - 10)^2 = 100
x^2 + 20x + 100 + 4x^2 + 40x + 100 = 100
5x^2 + 60x + 100 = 0
x^2 + 12x + 20 = 0 factor as
( x + 10) ( x + 2) = 0
The second factor set to 0 and solved for x gives x = -2 = x coordinate of F
And the y coordinate is -2 (-2) = 4 = HF = side of the square
The height of the larger equilateral triangle is sqrt ( 3)
So....the height of the smaller equilateral triangle formed by the chord is sqrt (3)/ 2 = (1/2)sqrt (3)
The radius of the cirlcle can be found as
2^2 = 2R^2 - 2R^2 cos 120°
4 = 2R^2 + R^2
4 = 3R^2
R^2 = 4/3
R = 2/sqrt (3) = (2/3)sqrt (3)
So the distance from the center of the circle to the chord is (2/3)sqrt (3) -(1/2) sqrt(3) = (1/6)sqrt (3)= sqrt (3)/6
Using the Pythagorean Theorem, 1/2 the chord length can be found as
sqrt [ ( 4/3) - ( sqrt (3)/6 )^2 ] = sqrt [ 48/36 - 3/36 ] = (1/6) sqrt (45) = (1/6) sqrt (9 * 5) =
(3/6) sqrt (5) = sqrt ( 5)/2
So....the chord length is twice this = sqrt (5)
We need the cost of one gallon of gas to solve this......
Sum > Product
1 2 3 4 5
1 > > > > >
2 > = < < <
3 > < < < <
4 > < < < <
5 > < < < <
P (sum < = product) = 16/25
THX, JoLink
Here's a slightly easier way
[ (1)(14) + (2)(5) + (3)(9) + (4)(7) + (5)(7) + (6)(8) ]
_____________________________________________ =
14 + 5 + 9 + 7 + 7 + 8
[ 14 + 10 + 27 + 28 + 35 + 48 ]
_______________________________ =
50
162 / 50 ≈ 3.24.......corrected !!!!
m/n + n/m =
[ m^2 + n^2 ] / mn
Now just fill in what we know
[ 8 ] / [ 4 ] = 2 = m + n