Substituting y=6x+2 into equation 3y - 18x =12 looks like:
3(6x + 2) - 18x = 12
18x + 6 - 18x = 12 distributive property left side
6 = 12 simplifying the left side
We now see a contradiction: 6 does not equal 12 What this tells us is that there is no solutions to this equation. So choice 'C' ...
Answer:
4 and -7
Step-by-step explanation:
a coefficient is a number that is being multiplied with a variable (ex:5a) in this case the coefficients are 4 and -7
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:
B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that 
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then 
.
C) Consider 
. This set is orthogonal because 
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in 
. Then the columns of A form an orthonormal set. We have that 
. To see this, note than the component 
of the product 
is the dot product of the i-th row of 
and the jth row of 
. But the i-th row of is equal to the i-th column of . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then 
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set 
and suppose that there are coefficients a_i such that 
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then 
then 
.
Answer:
circumference of a circle
Step-by-step explanation:
Actually, the formula is C = 2πr. C stands for "circumference."
Answer: 672 cars will have defective engine mounds
Step-by-step explanation: 25% of 2,688 is 672
