answer:[ begin{align*} &text{Solve for }x: &sqrt{3x - 14} + sqrt{14x - 7} = 12 end{align*} ] Square both sides to eliminate the square roots: [ begin{align*} &(sqrt{3x - 14} + sqrt{14x - 7})^2 = 12^2 &3x - 14 + 14x - 7 + 2sqrt{(3x - 14)(14x - 7)} = 144 &2sqrt{(3x - 14)(14x - 7)} = 165 - 17x end{align*} ] Square again to get rid of the square root: [ begin{align*} &4(3x - 14)(14x - 7) = (165 - 17x)^2 &168x^2 - 868x + 392 = 289x^2 - 5610x + 27225 end{align*} ] Move all terms to one side: [ begin{align*} &168x^2 - 868x + 392 - 289x^2 + 5610x - 27225 = 0 &-121x^2 + 4742x - 26833 = 0 end{align*} ] Divide by the coefficient of ( x^2 ): [ begin{align*} &x^2 - frac{4742x}{121} + frac{26833}{121} = 0 end{align*} ] Complete the square: [ begin{align*} &left(x - frac{2371}{121}right)^2 = frac{2371^2 - 4 cdot 121 cdot 26833}{121^2} &left(x - frac{2371}{121}right)^2 = frac{5621641 - 11004928}{14641} &left(x - frac{2371}{121}right)^2 = frac{-5342787}{14641} &left(x - frac{2371}{121}right)^2 = -frac{4123 cdot 13001}{14641} end{align*} ] The equation now represents a non-real solution since the square of a real number cannot be negative. Therefore, there is no real solution for ( x ) that satisfies the original equation. The final answer is: [ text{No real solution exists.} ]

answer:To find the derivatives, first determine the value of (t) corresponding to the point ((-1, 0)). From (x = t^2 - 2), we have: (-1 = t^2 - 2) (1 = t^2) (t = pm 1) Since both (t = 1) and (t = -1) satisfy (y = t^2 - 1), we have: (y = 0) for both (t = 1) and (t = -1). Next, find (displaystyle frac{dy}{dt}): (displaystyle frac{dy}{dt} = frac{d}{dt}(t^2 - 1) = 2t) Evaluate (displaystyle frac{dy}{dt}) at (t = pm 1): (displaystyle frac{dy}{dt} = 2(pm 1) = pm 2) Now, find (displaystyle frac{dx}{dt}): (displaystyle frac{dx}{dt} = frac{d}{dt}(t^2 - 2) = 2t) Evaluate (displaystyle frac{dx}{dt}) at (t = pm 1): (displaystyle frac{dx}{dt} = 2(pm 1) = pm 2) Finally, find (displaystyle frac{dy}{dx}): (displaystyle frac{dy}{dx} = frac{frac{dy}{dt}}{frac{dx}{dt}} = frac{2t}{2t} = 1) Therefore, the derivatives at the point ((-1, 0)) are (displaystyle frac{dy}{dt} = pm 2), (displaystyle frac{dx}{dt} = pm 2), and (displaystyle frac{dy}{dx} = 1).

answer:A chart of accounts that categorizes financial transactions into relevant categories, such as revenue, expenses, assets, and liabilities.

answer:In both New Zealand and Australia, the legislative branches are known as the Parliament.