Let A be an mtimesn matrix. Explain why the equation Upper A Bold x equals Bold b has a solution for all b in set of real numbers R Superscript m if and only if the equation Upper A Superscript Upper T Baseline Bold x equals Bold 0 has only the trivial solution.

Based on the diagram, match the trigonometric ratios with the corresponding ratios of the sides of the triangle. tiles : cosb sinb tanb sincposs matches: c/b b/a b/c c/a

The elmina wilson company produces spaghetti sauce that is used in restaurants. the fixed costs total $1,329,050. the selling price per 64 oz. can of sauce is $12.40. the variable cost per can is $4.80. what is the break-even point in number of cans?

N=1,2,3,4,5 a n= 9,18,36,72,144 a recursive rule for the sequence is: f(1)= and f(n)= for n≥2. an explicit rule for the sequence is: f(n)= find a recursive rule and an explicit for the geometric sequence. 768,192,48,12,3,… a recursive rule for the sequence is: f(1)= and f(n)= for n≥2. an explicit rule for the sequence is: f(n)=∙ -1. concept 3: deriving the general forms of geometric sequence rules your turn use the geometric sequence to find a recursive rule and an explicit rule for any geometric sequence. 4,8,16,32,64,… recursive rule for the geometric sequence: f(1)= and f(n)=f(n-1)∙ for n≥2. recursive rule for any geometric sequence: given f(1),f(n)=f(n-1)∙ for n≥2. explicit rule for the geometric sequence: f(n)=∙-1. explicit rule for any geometric sequence: f(n)=∙-1 concept 4: constructing a geometric sequence given two terms your turn find an explicit rule for the sequence using subscript notation. the third term of a geometric sequence is 1/48 and the fifth term of the sequence is 1/432. all the terms of the sequence are positive. the explicit rule for the geometric sequence is