answer:we can multiply the given matrix mathbf{M} by the given matrix begin{pmatrix} -3 & 4 & 0 5 & -7 & 0 0 & 0 & X end{pmatrix} and set it equal to the identity matrix mathbf{I}. [mathbf{M} begin{pmatrix} -3 & 4 & 0 5 & -7 & 0 0 & 0 & X end{pmatrix} = mathbf{I}] Multiplying the matrices, we get: [begin{pmatrix}-7&-4&0-5&-3&00&0&1end{pmatrix} begin{pmatrix} -3 & 4 & 0 5 & -7 & 0 0 & 0 & X end{pmatrix} = mathbf{I}] Simplifying the multiplication, we have: [begin{pmatrix} (-7)(-3) + (-4)(5) + (0)(0) & (-7)(4) + (-4)(-7) + (0)(0) & (-7)(0) + (-4)(0) + (0)(X) (-5)(-3) + (-3)(5) + (0)(0) & (-5)(4) + (-3)(-7) + (0)(0) & (-5)(0) + (-3)(0) + (0)(X) (0)(-3) + (0)(5) + (1)(0) & (0)(4) + (0)(-7) + (1)(0) & (0)(0) + (0)(0) + (1)(X) end{pmatrix} = mathbf{I}] Simplifying further, we get: [begin{pmatrix} 21 & 0 & 0 -10 & 23 & 0 0 & 0 & X end{pmatrix} = mathbf{I}] Comparing the elements of the matrices, we can see that X = 1. The value of the unknown variable X is 1. The answer is: 1

answer:We know that Alfred has 100.00 left over from last year's holiday, which means he needs to save a total of x - 100.00 over 12 months. To find out how much money Alfred needs to save each month, we can divide the total amount he needs to save by the number of months: (x - 100.00) / 12. We are given that Alfred needs to save 75.00 each month, so we can write: (x - 100.00) / 12 = 75.00. Multiplying both sides by 12, we get: x - 100.00 = 900.00. Adding 100.00 to both sides, we get: x = 1000.00. The value of x is 1000.00. 1000 The answer is: 1000

answer:To solve this problem, we need to determine the value of x, which represents the fraction of the remaining money that John spent on necessities. Let's break down the information given: Initial amount of money: 20 Amount spent on snacks: 1/5 * 20 Remaining money: 20 - (1/5 * 20) Amount spent on necessities: x * (Remaining money) Money left: 4 We can set up the equation as follows: Remaining money - (x * Remaining money) = Money left 20 - (1/5 * 20) - (x * (20 - (1/5 * 20))) = 4 Let's simplify and solve for x: 20 - (1/5 * 20) - (x * 16) = 4 20 - 4 - (x * 16) = 4 16 - (x * 16) = 4 To isolate x, we divide both sides of the equation by 16: 16 / 16 - (x * 16) / 16 = 4 / 16 1 - x = 1/4 To solve for x, we subtract 1 from both sides of the equation: 1 - 1 - x = 1/4 - 1 -x = -3/4 Finally, we multiply both sides of the equation by -1 to solve for x: x = 3/4 The value of x is 3/4. 3 The answer is: 3

answer:To solve this problem, we need to determine the value of x, which represents the number of cows Mr. Bodhi has. Let's break down the information given: Number of cows: x Number of foxes: 15 Number of zebras: 3 * 15 = 45 Number of sheep: 20 Total number of animals: 100 We can set up the equation as follows: Number of cows + Number of foxes + Number of zebras + Number of sheep = Total number of animals x + 15 + 45 + 20 = 100 Let's simplify and solve for x: x + 80 = 100 To isolate x, we subtract 80 from both sides of the equation: x + 80 - 80 = 100 - 80 x = 20 The value of x is 20. 20 The answer is: 20