The 4C matrix is obtained when all elements of matrix C are multiplied by 4. It <span>has all the same elements as C, only multiplied by 4.
Let's analyze all matrices
A. Not all elements of A can be divided by 4 (3 can not be divided by 4, the solution is not a whole number).
B. All elements of matrix B can be divided by 4, which means that B is a $C matrix (there is a matrix C which multiplied by 4 gives the matrix B).
C. Not all elements of C can be divided by 4.
D. Not all elements of D can be divided by 4.
Solution: B
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The partial fraction expansion takes the form
-6<em>x</em>/((<em>x</em> + 2) (<em>x</em> + 8)) = <em>a</em>/(<em>x</em> + 2) + <em>b</em>/(<em>x</em> + 8)
Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.
Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:
-6<em>x</em> = <em>a</em> (<em>x</em> + 8) + <em>b</em> (<em>x</em> + 2)
Expand the right side and collect terms by powers of <em>x</em> :
-6<em>x</em> = (<em>a</em> + <em>b</em>) <em>x</em> + (8<em>a</em> + 2<em>b</em>)
It follows that
<em>a</em> + <em>b</em> = -6 and 8<em>a</em> + 2<em>b</em> = 0
==> <em>a</em> = -2 and <em>b</em> = 8
So we end up with
-6<em>x</em>/((<em>x</em> + 2) (<em>x</em> + 8)) = -2/(<em>x</em> + 2) + 8/(<em>x</em> + 8)
Answer:
-1 1/3
Step-by-step explanation:
Convert any mixed numbers to fractions. New equation:
5/2 ÷ −15/8
Fraction division formula:
5x8/2x-15 = 40/-30
Convert:
-1 1/3
