answer:Let's call the certain number "x". We can write the operations as an equation: ((x - 50) / 4) * 3 + 28 = 73 Now, let's solve for x step by step: 1. Subtract 28 from both sides to isolate the multiplication and division on the left side: ((x - 50) / 4) * 3 = 73 - 28 ((x - 50) / 4) * 3 = 45 2. Divide both sides by 3 to isolate the division: (x - 50) / 4 = 45 / 3 (x - 50) / 4 = 15 3. Multiply both sides by 4 to isolate x - 50: x - 50 = 15 * 4 x - 50 = 60 4. Add 50 to both sides to solve for x: x = 60 + 50 x = 110 The certain number is boxed{110} .

answer:To determine the value of a+b for which 4x^{a+b}-3y^{3a+2b-4}=2 is a linear equation in x and y, we analyze the powers of x and y. For the equation to be linear, the exponents of x and y must be equal to 1. Given that the equation is linear, we have two conditions based on the exponents of x and y: 1. The exponent of x, which is a+b, must equal 1. 2. The exponent of y, which is 3a+2b-4, must also equal 1. Therefore, we set up the following system of equations: [ left{begin{array}{l} a+b=1 3a+2b-4=1 end{array}right. ] Solving this system of equations, we start with the first equation: [ a+b=1 ] For the second equation, we simplify it to: [ 3a+2b=5 ] To solve this system, we can use substitution or elimination. Here, we proceed directly to the solution as given: [ left{begin{array}{l} a=3 b=-2 end{array}right. ] Substituting a=3 and b=-2 into the expression for a+b, we find: [ a+b = 3 + (-2) = 1 ] Therefore, the value of a+b that makes the given equation linear in x and y is 1. Thus, the correct answer is boxed{text{D}}.

answer:Let's start solving the given expression: 2(3+1)(3^2+1)(3^4+1)(3^8+1), = (3-1)(3+1)(3^2+1)(3^4+1)(3^8+1), = (3^2-1)(3^2+1)(3^4+1)(3^8+1), = (3^4-1)(3^4+1)(3^8+1), = (3^8-1)(3^8+1), = 3^{16}-1. Thus, the final answer is boxed{3^{16}-1}.

answer:The volume V of a cone is given by the formula: [ V = frac{1}{3}pi r^2 h ] Where: - V is the volume, - r is the radius of the base, - h is the height, - π is Pi. Given: - V = 24pi cubic centimeters, - h = 6 cm. Plug these values into the formula to find r: [ 24pi = frac{1}{3}pi r^2 cdot 6 ] [ 24pi = 2pi r^2 ] [ 12 = r^2 ] [ r = sqrt{12} = 2sqrt{3} text{ cm} ] Now, calculate the circumference C of the base: [ C = 2pi r = 2pi times 2sqrt{3} = 4sqrt{3}pi ] Thus, the circumference of the base of the cone is boxed{4sqrt{3}pi}.