answer:Given equation can be written as, frac{log (x+12)}{log (3)}+frac{log (11 x+8)}{log (3)}=frac{log (16 x+10)}{log (3)} Rightarrow log _{3}(x+12)+log _{3}(11 x+8)=log _{3}(16 x+10) Rightarrow log _{3}[(x+12)(11 x+8)]=log _{3}(16 x+10) Rightarrow (x+12)(11 x+8)=16 x+10 Rightarrow 11 x^{2}+96 x+96=16 x+10 Rightarrow 11 x^{2}+80 x+86=0 Rightarrow (11 x+86)(x-1)=0 Rightarrow x=frac{-86}{11} text { or } x=1 Since log (x+12) and log (11 x+8) are defined only when x+12>0 and 11 x+8>0 respectively, we have x>-12 and x>-frac{8}{11}. Therefore, the only real solution is x=frac{-86}{11}. The answer is left{xto frac{1}{11} left(-62-3 sqrt{322}right)right}

answer:To complete the square for the given quadratic expression, follow these steps: 1. Factor out the coefficient of x^2, which is 7 sqrt{2}, from the first two terms: 7 sqrt{2} (x^2 + frac{2}{7} x) - 3 sqrt{2} 2. Add and subtract the square of half the coefficient of x inside the parentheses: 7 sqrt{2} left(x^2 + frac{2}{7} x + frac{1}{49} - frac{1}{49}right) - 3 sqrt{2} 3. Notice that (frac{1}{7})^2 = frac{1}{49}, so the expression inside the parentheses becomes a perfect square: 7 sqrt{2} left(left(x + frac{1}{7}right)^2 - frac{1}{49}right) - 3 sqrt{2} 4. Distribute the 7 sqrt{2} to both terms inside the parentheses: 7 sqrt{2} left(x + frac{1}{7}right)^2 - frac{7 sqrt{2}}{49} - 3 sqrt{2} 5. Combine the constants: 7 sqrt{2} left(x + frac{1}{7}right)^2 - frac{22 sqrt{2}}{7} So the completed square form of the quadratic expression is 7 sqrt{2} left(x + frac{1}{7}right)^2 - frac{22 sqrt{2}}{7}.

answer:In the sentence "The funny cat sat on the mat", the word "funny" is an adjective that modifies the noun "cat". An adjective is a word that describes a noun or pronoun. In this case, the adjective "funny" describes the cat as being amusing or comical. The answer is "funny".

answer:0.0864 The probability is calculated as follows: {eq}begin{align*} &= text{Sum of probabilities when X is greater than 2} [0.3 cm] &= 0.0768 + 0.0077 + 0.0019 [0.3 cm] &= 0.0864 end{align*} {/eq}