The volume of a prism = area of the base * height
substitute:
640 = A * 8
base area=80 sq ft<span />
29440 divided by 2 equals 14,720
3(n - 5) = 24
Distributive property
3*n = 3n
3*5 = 15
3n - 15 = 24
+ 15 +15
3n = 39
3n/3 = 39/3
x = 39/3
x = 13
Answer: x = 13
Answer:
The coach can choose a lineup of 11 players in 6,047,981,701,347 different ways.
Step-by-step explanation:
Since the varsity soccer team has 20 players, and three of the players are trained to be goalies while the remaining 17 can play any position, and only 11 players can be on the field at once, and the coach wants to make sure there is exactly one goalie on the field, to determine how many ways can the coach choose a lineup of 11 players if exactly 1 player must be a goalie the following calculation has to be made:
3 x 17 ^ 10 = X
3 x 2,015,993,900,449 = X
6,047,981,701,347 = X
Therefore, the coach can choose a lineup of 11 players in 6,047,981,701,347 different ways.
Hello from MrBillDoesMath!
Answer: (1/7) * ( 4 +\- sqrt(5) i)
where i = sqrt(-1)
Discussion:
The solutions of the quadratic equation ax^2 + bx + c = 0 are given by
x = ( -b +\- sqrt(b^2 - 4ac) )/2a.
The equation 7 x^2 + 3 = 8x can be rewritten as
7x^2 - 8x + 3 = 0.
Using a = 7, b = -8 and c = 3 in the quadratic formula gives:
x = (8 +\- sqrt ( (-8)^2 - 4*7*3) ) / (2*7)
= ( 8 +\- sqrt( 64 - 84)) /(2*7)
= ( 8 +\- sqrt( -20) ) / (2*7)
= ( 8 +\- sqrt( -20) ) / 14
= 8/14 +\- sqrt(5 *4 * -1) /14
= 4/7 +\- 2 sqrt(5) *i /14
As 2/14 = 1/7 in the second term
= 4/7 +\- sqrt(5) *i /7
Factor 1/7 from each term.
= (1/7) * ( 4 +\- sqrt(5) i)
Thank you,
MrB
