Questions in mathematics

Questions in mathematics

📝 Answered - $-\frac{6}{7}+\left(-\frac{4}{7}\right)$

📝 Answered - Multiply. Write your answer in simplest form. $\frac{7}{11} \times \frac{1}{4}$

📝 Answered - Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. [tex]\frac{x-1}{x-2} \leq 0[/tex] Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is [tex](-\infty, 1) \cup(2, \infty)[/tex]. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set.

📝 Answered - \frac{a x-a y+b x-b y}{x^2-y^2} \times \frac{x^2 y+x y^2}{a b^2+a^2 b}

📝 Answered - The speed that a tsunami can travel is modeled by the equation [tex]$S=356 \sqrt{d}$[/tex], where [tex]$S$[/tex] is the speed in kilometers per hour and [tex]$d$[/tex] is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour? A. 0.32 km B. 0.75 km C. 1.12 km D. 3.17 km

📝 Answered - The length of one push pin is 24.3 mm. Find the length of 35 push pins when arranged together (in centimetres).

📝 Answered - What is the equation of the line that is perpendicular to the given line and passes through the point $(5,3)$? $4 x-5 y=5$ $5 x+4 y=37$ $4 x+5 y=5$ $5 x-4 y=8$

📝 Answered - Find the value of the expression: [tex]$27 a^0 c^3 \text { for } a=\frac{2}{3}, c=-\frac{1}{3}$[/tex]

📝 Answered - You took a loan to buy a new car. After agreeing to pay $60,000 in interest in 410 days at 8.25% ordinary interest, how much was your loan?

📝 Answered - Solve the system. If the system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, whether the system is inconsistent, or the equations are dependent. [tex] \begin{array}{rrl} -3 x-4 y & +4 z & =-3 \\ 2 y-z & =1 \\ -3 x & +2 z & =-1 \end{array} [/tex] The system has one solution. The solution set is {([ ])} The system has no solution. The system is inconsistent. The equations are dependent. The system has infinitely many solutions. The system is inconsistent. The equations are dependent.