Algebra 2 need a lil help
2 answers:
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Answer:
b)
Step-by-step explanation:
A is invertible if and only if det(A)≠0. Let's compute the determinant of A and find the values k for which it is nonzero.
Using Sarrus's rule, we obtain that
Note that the determinant is a quadratic equation on k, which can be factored as above.
Now the determinant is only zero if k=5 or k=2 (the zeroes of the quadratic polynomial). Therefore, if k≠2,5 the determinant is nonzero so A is invertible.
Let the Width be x cm
Then the length which is 5cm more than width must be (x+5) cm
Using the formula for the area = length* width
x(x+5) =50
(Distribute x on the parenthesis )
(subtract 50 )
(Factor)
we get
(Not x=-10 because negative side length not possible)
Width = 5 cm
Length = 5+5= 10 cm
Perimeter = 2(Length + width)
So
Perimeter = 2(10+5)
Perimeter = 2*15=30 cm