Show that each statement is false by providing a counterexample. (a) If the length of AC is 46 and point B lies on AC, then A B = 34 and
BC = 12.
Counterexample:
AB = BC = 0
(b) If the perimeter of a rectangle is 32, then the length is 8 and the
width is 8.
Counterexample:
length
width
(c) If _ 1 and 2 are complementary angles, then one of them must have
a measure less than 45.
Counterexample:
m1 =
1 m 2 =
(d) If the measures of R, S, and I sum to 180 , then one of the
angles must be obtuse.
Counterexample:
m z R = 0°, m 2 S = O", m
°, m_T =
Х

Factor completely. x^8 - 1/81 a) (x^4 + 1/9)(x^2 + 1/3)(x^2 - 1/3) b) (x^4 - 1/9)(x^2 + 1/3)(x^2 - 1/3) c) (x^4 + 1/9)(x^2 - 1/3)2

On a piece of paper, graph . then determine which answer choice matches the graph you drew

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