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Questions in mathematics

📝 Answered - Select whether the equation has a solution or not. [tex]$\sqrt{x-2}-\sqrt{2 x}=\sqrt{x+2}$[/tex] roots no roots

📝 Answered - Two cars raced at a race track. The faster car traveled 20 mph faster than the slower car. In the time that the slower car traveled 165 miles, the faster car traveled 225 miles. If the speeds of the cars remained constant, how fast did the slower car travel during the race? | | Distance (mi) | Rate (mph) | Time (h) | | :------------ | :------------ | :--------- | :---------- | | Slower Car | 165 | $r$ | $\frac{165}{r}$ | | Faster Car | 225 | $r+20$ | $\frac{225}{r+20}$ | A. 55 mph B. 60 mph C. 75 mph D. 130 mph

📝 Answered - Multiply: $\left(\sqrt{2 x^3}+\sqrt{12 x}\right)\left(2 \sqrt{10 x^5}+\sqrt{6 x^2}\right)$ where $x \geq 0$: A. $2 x^2 \sqrt{5}+2 x \sqrt{3 x}+2 x^3 \sqrt{30}+3 x \sqrt{2 x}$ B. $4 x^4 \sqrt{5}+2 x^2 \sqrt{3 x}+4 x^3 \sqrt{30}+6 x \sqrt{2 x}$ C. $x^4 \sqrt{20}+x^2 \sqrt{6 x}+x^3 \sqrt{120}+x \sqrt{12 x}$ D. $2 \sqrt{10 x^4}+2 \sqrt{3 x^3}+4 \sqrt{15 x^3}+6 \sqrt{2 x}$

📝 Answered - Solve the absolute value inequality: $|x+12|+5<27$ Isolate the absolute value by subtracting 5 from both sides. $|x+12|<22$

📝 Answered - A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. What is the approximate area of the path alone? Use 3.14 for [tex]$\pi$[/tex]. A. $172.70 ft ^2$ B. $178.98 ft ^2$ C. $200.96 ft ^2$ D. $379.94 ft ^2$

📝 Answered - The hypotenuse of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle measures $22 \sqrt{2}$ units. What is the length of one leg of the triangle? A. 11 units B. $11 \sqrt{2}$ units C. 22 units D. $22 \sqrt{2}$ units

📝 Answered - What is the solution of [tex]$\sqrt{x+12}=x$[/tex] A. [tex]$x=-3$[/tex] B. [tex]$x=4$[/tex] C. [tex]$x=-3$[/tex] or [tex]$x=4$[/tex] D. no solution

📝 Answered - 1. Fill in the blanks and write the name of the property in brackets used in the following: (i) [tex]\frac{8}{15} + 0 =[/tex] (ii) [tex]\frac{-17}{23} + \frac{13}{42} = \frac{13}{42} +[/tex] (iii) [tex]\frac{-18}{29} + \frac{18}{29} =[/tex] (iv) [tex]\frac{5}{6} + (\frac{-2}{9} + \frac{1}{4}) = (\_ + \_) + \frac{1}{4}[/tex]

📝 Answered - 9B = A 10a - 9B = B 9B² = 10a² - 9ab

📝 Answered - The successive discounts of 12%, 20%, and 25% are equivalent to a single discount of: 1. 52.2% 2. 49.5% 3. 47.2% 4. 57.0%