Answer:
see explanation
Step-by-step explanation:
The perimeter is the sum of the 3 sides of the triangle , that is
3x + 2x + 6 + 6x - 3 ( simplify by collecting like terms )
= 11x + 3
Given the perimeter = 36 units , then
11x + 3 = 36 ( subtract 3 from both sides )
11x = 33 ( divide both sides by 11 )
x = 3
Then
base = 2x + 6 = 2(3) + 6 = 6 + 6 = 12 units
height = 3x = 3(3) = 9 units
hypotenuse = 6x - 3 = 6(3) - 3 = 18 - 3 = 15 units
<span>If two events are independent, the occurrence of one event does not affect the other.
That is if two events are independent, then P(Aâ©B)=P(A)P(B)
Let A be the even getting a sum of 6 in a single roll of two dice.
Sample space of A ={(1,5)(5,1)(2,4)(4,2)(3,3)}
n(A)=5; n(S)=36
Therefore P(A) =n(A)/n(S) =5/36 ---------(1)
Let B be the event of rolling doubles.
Sample space for B ={(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)}
n(B)=6;n(S)=36
P(B) = n(B)/n(S) = 6/36 --------------(2)
Aâ©B is the event of getting a sum of 6 and rolling doubles.
Therefore n(Aâ©B)=1
P(Aâ©B)=1/36 ------(3)
Multiplying equation (1) and (2)
(5/36)*(6/36)=5/216
but P(Aâ©B)=1/36
P(Aâ©B) ≠P(A)P(B)
Therefore, the events are not independent.</span>
Answer:
{x,y} = {67/16,-15/4}
Step-by-step explanation:
// Solve equation [2] for the variable y
[2] 2y = -8x + 26
[2] y = -4x + 13
// Plug this in for variable y in equation [1]
[1] 4x + 5•(-4x+13) = -2
[1] -16x = -67
// Solve equation [1] for the variable x
[1] 16x = 67
[1] x = 67/16
// By now we know this much :
x = 67/16
y = -4x+13
// Use the x value to solve for y
y = -4(67/16)+13 = -15/4
" the quotient " means divide
9 more then the quotient of -36 and -4...
(-36/-4) + 9 =
9 + 9 =
18
