answer:To find the value of a+b+c+d, we first analyze the given function f. We can rewrite the given function fleft(frac{2x+5}{2x-5}right) as follows: begin{align*} fleft(frac{2x+5}{2x-5}right) &= frac{x+1}{2x+3} &= frac{1}{2}left(frac{2x + 2}{2x + 3}right) &= frac{1}{2}left[frac{(2x - 5) + 7}{(2x- 5) + 8}right] end{align*} From this, we can deduce that the function f has the form: begin{align*} f(u) &= frac{1}{2}left(frac{u+7}{u + 8}right) end{align*} where u = frac{2x+5}{2x-5}. Now, let's find fleft(-frac{5x-2}{5x+2}right). First, notice that -frac{5x-2}{5x+2} is the result of applying the matrix transformation begin{bmatrix}2&52&-5end{bmatrix} to the vector begin{bmatrix}x1end{bmatrix}, followed by a reflection through the line y = x: begin{align*} -frac{5x-2}{5x+2} &= left(-frac{5}{2}right)left(frac{2x+5}{2x-5}right) &= left(-frac{5}{2}right)cdot u end{align*} Substituting u into f(u) gives us: begin{align*} fleft(-frac{5x-2}{5x+2}right) &= fleft(-frac{5}{2}uright) &= frac{1}{2}left(frac{-frac{5}{2}u+7}{-frac{5}{2}u + 8}right) &= frac{1}{2}left(frac{-5u+14}{-5u + 16}right) &= frac{-u+2.8}{-u + 3.2} end{align*} Comparing this with frac{ax+b}{cx+d}, we have: begin{align*} frac{-u+2.8}{-u + 3.2} &= frac{ax+b}{cx+d} end{align*} Since f is a fractional linear transformation, we can represent it as a matrix multiplication. The matrix corresponding to f is begin{bmatrix}1/2 & 0 0 & 1/2end{bmatrix}, and the matrices representing the transformations from x to u and from u to -frac{5}{2}u are begin{bmatrix}2&52&-5end{bmatrix} and begin{bmatrix}-5/2&00&-5/2end{bmatrix}, respectively. By multiplying these matrices, we can find the matrix for fleft(-frac{5x-2}{5x+2}right). However, the question is flawed in that it asks for a single value for a+b+c+d, which is not possible due to the linear transformation nature of f. Instead, we have the transformation matrix for f and can represent the transformation as: begin{align*} begin{bmatrix}a&bc&dend{bmatrix} &= begin{bmatrix}1/2&00&1/2end{bmatrix}begin{bmatrix}-5/2&00&-5/2end{bmatrix}begin{bmatrix}2&52&-5end{bmatrix} &= begin{bmatrix}-5/4&00&-5/4end{bmatrix}begin{bmatrix}2&52&-5end{bmatrix} &= begin{bmatrix}-5/2&-25/4-5/2&15/4end{bmatrix} end{align*} Therefore, the coefficients a, b, c, and d do not sum up to a single value. However, if we assume they are integers, we can find a reduced form where they have no nontrivial common divisor. In this case, we can multiply the matrix by a constant to obtain integer coefficients: begin{align*} begin{bmatrix}a&bc&dend{bmatrix} &= 4cdotbegin{bmatrix}-5/2&-25/4-5/2&15/4end{bmatrix} &= begin{bmatrix}-10&-25-10&15end{bmatrix} end{align*} In this representation, a = -10, b = -25, c = -10, and d = 15. The sum of these coefficients is: begin{align*} a + b + c + d &= -10 - 25 - 10 + 15 &= -30 end{align*} However, this result is based on an assumption about the coefficients being integers, and the original question is flawed in its setup. The actual values of a, b, c, and d may not necessarily have a simple sum.

answer:The result of subtracting the second matrix from the first is: left( begin{array}{ccc} 1 & -9 & -4 4 & -6 & 2 end{array} right)

answer:When banks focus on lending to particular types of businesses, they may experience a decrease in operating costs due to economies of scale, such as implementing standardized lending processes for similar firms. However, this specialization simultaneously increases their credit risk, as their loan portfolio becomes less diversified. Consequently, if one borrower in that industry defaults, there is a higher probability that others will do the same, leading to a higher overall credit risk.

answer:To find the sum of the first 5 terms (S_5) in the arithmetic sequence, we can use the formula for the sum of the first n terms of an arithmetic series: [S_n = frac{n}{2}(2a_1 + (n - 1)d)] where n is the number of terms, a_1 is the first term, and d is the common difference. Given: n = 5, a_1 = frac{16}{85}, and d = -frac{28}{5} (since a_n = a_{n-1} - frac{28}{5}). Now, let's compute S_5: [S_5 = frac{5}{2}left(2 cdot frac{16}{85} + (5 - 1) cdot left(-frac{28}{5}right)right)] [S_5 = frac{5}{2}left(frac{32}{85} - frac{112}{5}right)] [S_5 = frac{5}{2}left(frac{32}{85} - frac{112 cdot 17}{5 cdot 17}right)] [S_5 = frac{5}{2}left(frac{32}{85} - frac{1848}{85}right)] [S_5 = frac{5}{2} cdot frac{-1816}{85}] [S_5 = frac{5 cdot -1816}{2 cdot 85}] [S_5 = frac{-9080}{170}] [S_5 = -frac{908}{17}] So, the sum of the first 5 terms is -frac{908}{17}.