Answer: If order does not matter then we can use following formula to find different combinations of 6 numbers out of 46 numbers
Step-by-step explanation: Use following Combination formula
nCr = n! / r!(n-r)!
n=46
r=6
=46!/6!(46-6)!
=46!/[6!(40)!]
=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)
Cancel out 40!
=46*45*44*43*42*41/(6*5*4*3*2*1)
=6744109680/720
=9366819
Answer:
Given: The following system:
4x + y − 2z=18 ......[1]
2x-3y+3z = 21 ......[2]
x-3y=6 ......[3]
we can write equation [3] as;
3y = x-6 ......[4]
Multiply by 3 in equation [1] to both sides of an equation we get,
or
12x+3y-6z=54 ......[5]
Substituting the equation [4] in [2] and [5] we get;
2x-(x-6)+3z=21 or
2x-x+6+3z=21
Simplify:
x+3z=15 .....[6] [combine like terms]
12x+x-6-6z =54
Simplify:
13x-6z=60 ......[7] [Combine like terms]
On Solving equation [6] and [7] simultaneously,
x+3z=15
13x-6z=60
we get the value of x
i.e, x=6
Substitute the value of x in equation x+3z=15 we get
6+3z=15 or
3z=9
Simplify:
z=3
Also, substitute the value of x=6 in equation [3] we get the value of y;
x-3y=6
6-3y=6 or
-3y = 0
Simplify:
y = 0
Therefore, the solution to the system of three linear equation is, (6, 0 , 3)
The surface area of the triangular prism is 686.6 cm².
Step-by-step explanation:
Step 1:
The volume of a triangular prism can be determined by multiplying its area of the triangular base with the length of the prism.
The base triangle has a base length of 10 cm and assume it has a height of h m.
The volume of the prism
The height of the triangle is 8.66 cm.
Step 2:
The surface area of the triangle is obtained by adding all the areas of the shapes in the prism. There are 2 triangles and 3 rectangles in a triangular prism.
The triangles have a base length of 10 cm and a height of 8.66 cm. A triangles area is half the product of its base length and height.
The rectangles all have a length of 20 cm and a width of 10 cm. The area of a rectangle is the product of its length and width.
The area of the 2 triangles ![= 2 [\frac{1}{2} (10)(8.66)] = 86.6.](https://tex.z-dn.net/?f=%3D%202%20%5B%5Cfrac%7B1%7D%7B2%7D%20%2810%29%288.66%29%5D%20%3D%2086.6.)
The area of the 3 rectangle ![= 3[(20)(10)] = 600.](https://tex.z-dn.net/?f=%3D%203%5B%2820%29%2810%29%5D%20%3D%20600.)
Step 3:
The surface area of the triangular prism 
The surface area of the prism is 686.6 cm².
Answer:
4/8, 8/16, 2/4 any of those
Step-by-step explanation:
Surface area= 2(6x15)+2(7x15)+2(6x7)
=180+210+84
=474m
Volume=15x6x7
=630m^2