3. Kate was given the following number pattern by her teacher. 22+1=5 42+1=17 62+1=37 102+1=101 14²+1=197 Kate made the following conjecture based solely on the number patterns shown. "When an even number is squared and one is added to it, the resulting number is a prime number". In the examples above 5, 17, 37, 101, and 197 are prime numbers because the only factors of these numbers are 1 and the number itself. a) Is Kate's conjecture True or False, based solely on the numbers shown? Use your understanding of even numbers and prime numbers to explain your answer. b) Determine a counterexample to the pattern above to show that Kate's conjecture is false.

(a) At a glance, determine the digit d so that 64,275,67d is divisible by 4. Is there more than one answer? (b) Can you choose the digit d so that 64,275,67d is divisible by 8 and not 16? O A. The digit d can be 6. Oc. The digit d can be 4 or 8. B. The digit d can be 0, 2, or 6. D. The digit d can be 8. O E. The digit d can be 2 or 6. OF. The digit d can be 0. O G. The digit d can be 2. O H. The digit d can be 4. O 1. The digit d can be 0, 2, 4, 6, or 8. O J. The digit d can be 0, 4, or 8.

Select the number line that shows that two opposite numbers have a sum of 0. A. B. C. D. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 6 4 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 2 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 3 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 SUBMIT