Answer:
3,247,695
Step-by-step explanation:
We want the coefficient of the term with x^8
So Use Newton's Binomial Expansion formula
Formula is (x + y) ^n = Sum for i=0 to n (n choose i) x^(n-i)*y^i
here (x^2 + 3) ^ 12
( 12 choose i) * (x^2)^(12-i) * (3)^i
i needs to equal 8 for us to get x^8
(12 choose 8) * (x^2)^(12-8) * (3^8)
= (12 choose 8) * x^8 * (3^8)
so a = (12 choose 8) * 
a = (12! /(8! * 4!) ) *
a = ( 12*11*10*9/ 4*3*2*1) *
a = (11*5*9) *
a = 11*5*9 * 6561
a = 3,247,695
Answer:
184cm^2
Step-by-step explanation:
(5+5+6) * 10 = 160
6*4 = 24
160+24=184
there are 2 triangles so I am assuming they have the same dimensions
Answer:
For all the proofs you start with the given, and work you’re way down the problem.
1)
Statement Reasoning
LM=NO Given
∠LMO≅∠NOM. Given
OM=OM Reflexive Property of Equality
ΔLMO=ΔNOM SAS Congruence Postulate
2)
Statement Reasoning
∠A=∠D Given
CB bisects ∠ACD Given
CB=CB Reflexive Property of Equality
∠ACB=∠BCD Definition of Angle Bisector
∠ABC=∠CBD Definition of Angle Bisector
ΔABC=ΔDBC ASA Congruence Postulate
CA=CD Definition of Congruence
3)
Statement Reasoning
∠T=∠U Given
S is midpoint of TU Given
∠TSN=∠USH Vertical angles are congruent
TS=SU Definition of Midpoint
ΔTSN=ΔUSH ASA Congruence Postulate
SN=SH Definition of Congruent
Total marbles = 13
Number of yellow = 2
probability of getting yellow = 2/13
Answer:
Step-by-step explanation:
Given
See attachment for the grid coordinate
From the attachment, we have that:
Required
Determine the coordinates of the second truck
Represent the position with R'
From the question, we understand the position of R' is 6 above R
When a point (a,b) is moved n point above, the new point becomes (a, b + n)
So:
When moved 6 points above becomes:
<em>Hence, (-4,4) answers the question</em>
