Answer:
A
Step-by-step explanation:
This is a linear function whose slope is -3 and whose y-intercept is (0, 2). Answer A is correct.
Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,

or in matrix form,

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

and this is what we wanted to prove. QED
Do each equation individually and compare if they are the same end answer in each question. which ever one is unequal than that is the answer
Given:
Minni is arranging 3 different music CDs in a row on a shelf.
To find:
The sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R).
Solution:
We know that the total number of ways to arrange n items is n!.
Minni is arranging 3 different music CDs in a row on a shelf. So, the total number of ways is:


The sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R) is:
{JPR, JRP, PJR, PRJ, RJP, RPJ}
Therefore, the required sample space is {JPR, JRP, PJR, PRJ, RJP, RPJ}.
So the best way to do these is concentration1 (%) × volume1 = concentration2 × volume2
Or C1V1 + C2V2 = C3V3, where C1 = 100% (bc ALL pecans), V1 = 6 lbs, C2 = 70%, C3 = 82%:
100%×6 + 70%×v2 = 82%×(6+v2)
100%=1.00, 70%=.7, 82%=.82
note: if none is poured out then v3 = v1+v2
6 + .7v2 = .82 (6+v2)
6 + .7v2 = 4.92 + .82v2
6 + .7v2 -.7v2 = 4.92 + .82v2 -.7v2
6 = 4.92 + .12v2
6-4.92 = 4.92-4.92 + .12v2
1.08 = .12v2
.12v2/.12 = 1.08/.12
v2 = 9 lbs
that's only v2!!!
For the final poundage, we need v3:
v3 = 6 + v2 = 6 + 9 = 15 lbs