Let A be a matrix with linearly independent columns. Select the best statement. A. The equation Ax=0 has nontrivial solutions precisely when it has more columns than rows. B. The equation Ax=0 has nontrivial solutions precisely when it has more rows than columns. C. The equation Ax=0 has nontrivial solutions precisely when it is a square matrix. D. The equation Ax=0 never has nontrivial solutions. E. There is no easy way to tell if such an equation has nontrivial solutions. F. The equation Ax=0 always has nontrivial solutions. G. none of the above

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

The length of a rectangle is x times the square root of 100. the width is one-half y more than three-halves x. given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y? a) 5xy − 15x = 125 b) 5xy + 15x = 125 c) 15x2 − 5xy = 125 d) 15x2 + 5xy = 125

Which letters from the table represent like terms? a and b b and c a and d b and d