answer:To solve this problem, we need to determine the value of x, which represents the scalar in the second vector. Let's break down the given equation: 3 begin{pmatrix} 2 -8 end{pmatrix} - X begin{pmatrix} 1 -7 end{pmatrix} = begin{pmatrix} -10 -10 end{pmatrix} Expanding the equation, we have: begin{pmatrix} 6 -24 end{pmatrix} - begin{pmatrix} X -7X end{pmatrix} = begin{pmatrix} -10 -10 end{pmatrix} Let's compare the components of the vectors: 6 - X = -10 -24 + 7X = -10 Simplifying the equations, we have: -X = -16 7X = 14 To solve for x, we divide both sides of the equation by -1 in the first equation and by 7 in the second equation: X = 16 X = 2 The value of x is 2. The answer is: 2

answer:If there are 6 white daisies, and there are nine times as many pink daisies as white daisies, then there are 6 x 9 = 54 pink daisies. If there are three less than four times as many red daisies as pink daisies, then there are (4 x 54) - 3 = 213 red daisies. The total number of daisies is 6 + 54 + 213 = 273 daisies. 273 The answer is: 273

answer:If Henry has 23 country CDs, and he has 3 more country CDs than rock CDs, then he has 23-3= 20 rock CDs. If he has twice as many rock CDs as classical CDs, then he has 20/2= 10 classical CDs. Therefore, Henry has 10 classical CDs in his collection. 10 The answer is: 10

answer:We want to find the length of the parametric curve described by [(x,y) = (2 sin t, 2 cos t)]from t = X to t = pi. To find the length of the curve, we can use the arc length formula for parametric curves: [L = int_{a}^{b} sqrt{left(frac{dx}{dt}right)^2 + left(frac{dy}{dt}right)^2} dt] In this case, we have: [frac{dx}{dt} = 2 cos t] [frac{dy}{dt} = -2 sin t] Substituting these values into the arc length formula, we have: [L = int_{X}^{pi} sqrt{(2 cos t)^2 + (-2 sin t)^2} dt] Simplifying the expression inside the square root, we get: [L = int_{X}^{pi} sqrt{4 (cos^2 t + sin^2 t)} dt] Since (cos^2 t + sin^2 t = 1), we can simplify further: [L = int_{X}^{pi} sqrt{4} dt] [L = int_{X}^{pi} 2 dt] Evaluating the integral, we have: [L = 2t Big|_{X}^{pi}] [L = 2pi - 2X] Given that the length of the curve is (2pi), we can set up the equation: [2pi = 2pi - 2X] Simplifying, we find: [0 = -2X] Dividing both sides by -2, we get: [X = 0] The value of X is 0. The answer is: 0