Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 8 −2 −4 1 (a) the characteristic equation (λ−9)λ=0 (b) the eigenvalues (enter your answers from smallest to largest.) (λ1, λ2) = 0,9 the corresponding eigenvectors x1 = 2,1 x2 = 1,−4

Katie wants to collect over 100 seashells. she already has 34 seashells in her collection. each day, she finds 12 more seashells on the beach. katie can use fractions of days to find seashells. write an inequality to determine the number of days, dd, it will take katie to collect over 100 seashells.

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?

The table shows values for functions f(x) and g(x) . x f(x)=−4x−3 g(x)=−3x+1+2 −3 9 179 −2 5 53 −1 1 1 0 −3 −1 1 −7 −7 2 −11 −25 3 −15 −79 what is the solution to f(x)=g(x) ? select each correct answer.