answer:We are given two equations involving the matrix mathbf{M} and two different vectors. We want to find the value of X in the given situation. The equation mathbf{M} begin{pmatrix} 1 2 end{pmatrix} = begin{pmatrix} -4 4 end{pmatrix} tells us that when we multiply matrix mathbf{M} by the vector begin{pmatrix} 1 2 end{pmatrix}, we get the vector begin{pmatrix} -4 4 end{pmatrix}. Similarly, the equation mathbf{M} begin{pmatrix} -3 1 end{pmatrix} = begin{pmatrix} -23 2 end{pmatrix} tells us that when we multiply matrix mathbf{M} by the vector begin{pmatrix} -3 1 end{pmatrix}, we get the vector begin{pmatrix} -23 2 end{pmatrix}. To find the matrix mathbf{M}, we can write these equations as a system of linear equations. Let's denote the elements of matrix mathbf{M} as a, b, c, and d. Then we have: a(1) + b(2) = -4 c(1) + d(2) = 4 a(-3) + b(1) = -23 c(-3) + d(1) = 2 Simplifying these equations, we get: a + 2b = -4 c + 2d = 4 -3a + b = -23 -3c + d = 2 We can solve this system of linear equations to find the values of a, b, c, and d. From the first equation, we can isolate a in terms of b: a = -4 - 2b Substituting this into the third equation, we have: -3(-4 - 2b) + b = -23 Simplifying, we get: 12 + 6b + b = -23 7b = -35 b = -5 Substituting the value of b back into the first equation, we have: a + 2(-5) = -4 a - 10 = -4 a = 6 Similarly, we can find the values of c and d. From the second equation, we can isolate c in terms of d: c = 4 - 2d Substituting this into the fourth equation, we have: -3(4 - 2d) + d = 2 Simplifying, we get: -12 + 6d + d = 2 7d = 14 d = 2 Substituting the value of d back into the second equation, we have: c + 2(2) = 4 c + 4 = 4 c = 0 Therefore, the matrix mathbf{M} is: begin{pmatrix} 6 & -5 0 & 2 end{pmatrix} Given that the matrix mathbf{M} is begin{pmatrix} 6 & -5 0 & 2 end{pmatrix}, we can conclude that the value of X is begin{pmatrix} 6 & -5 0 & 2 end{pmatrix}. The answer is: 2

answer:First, we need to convert the length of the fence from yards to feet. Since 1 yard is equal to 3 feet, the length of the fence is 25 yards x 3 feet/yard = 75 feet. Next, we need to calculate how many trees Holly will need to plant along the fence. Since each tree measures 1.5 feet wide and the fence is 75 feet long, Holly will need 75 feet / 1.5 feet/tree = 50 trees. Now, we can calculate the total cost of planting the trees. Since each tree is on sale for 8.00, the total cost will be 50 trees x 8.00/tree = 400.00. Therefore, the total cost for Holly to plant the trees along the entire length of her fence will be 400.00. 400 The answer is: 400

answer:We can divide 7.50 by 0.85 to find the maximum number of cards she can buy. Using long division, we get begin{array}{c|cccc} multicolumn{2}{r}{} & & 8 & cline{2-5} 0.85 & 7.50 & Big) multicolumn{2}{r}{6.80} & Big) cline{2-3} multicolumn{2}{r}{} & 7.00 & Big) multicolumn{2}{r}{} & 6.80 & Big) cline{3-4} multicolumn{2}{r}{} & & 0.20 & Big) end{array} Since she can't afford another card with 0.20, she can buy at most boxed{8} cards. The answer is: 8

answer:Darnell has 1000 square feet of fabric. He has already used 16 square flags, which means he used 16 * (4 * 4) = 256 square feet of fabric for square flags. He has also used 20 wide flags, which means he used 20 * (5 * x) = 100x square feet of fabric for wide flags. He has used 10 tall flags, which means he used 10 * (3 * 5) = 150 square feet of fabric for tall flags. The total amount of fabric he has used is 256 + 100x + 150 = 406 + 100x square feet. To find the amount of fabric he has left, we subtract the amount he has used from the total amount he had: 1000 - (406 + 100x) = 594 - 100x square feet. We are given that the amount of fabric he has left is 294 square feet, so we can write: 594 - 100x = 294. Solving for x, we get: x = 3. The value of x is 3. 3 The answer is: 3