Prove or disprove each of the following statements:
(a) there exists a prime number x such that x + 16 and x + 32 are also prime numbers.
(b) ∀a, b, c, m∈z+, if a≡b(mod m), then c^a≡c^b(mod m)
(c) for any positive odd integer n, 3|n or n^2≡1 (mod 12).
(d) there exist 100 consecutive composite integers

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 3 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30∘c on monday, but decreased at a constant rate in the next 3 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.

For the word below, click on the drop-down arrows to select the root and its meaning. version

Given right triangle a w/a hypotenuse length of x+4 and a leg of x, and right triangle b, w/ a hypotense length of 3y and a leg length of y+4 for what values of x and y are the triangles congruent by hl?