Questions in mathematics

Questions in mathematics

📝 Answered - Homework Progress 61 / 95 Marks By rounding to 1 significant figure, estimate the answers to these questions: a) $875 \times 894$ b) $257 \times 789$ c) $887 \times 394$

📝 Answered - Evaluate the definite integrals: [tex]\( \int_{0}^{\pi} (1 + \sin t + \cos t) \, dt + \int_{\pi}^{2\pi} (1 + \sin t + \cos t) \, dt \)[/tex]

📝 Answered - Find the length of one of the sides of the rectangle (1) and square (2). 1. Rectangle with area A = 45 m² and one side 5 m. Find the other side. 2. Square with area A = 9 m². Find the side length.

📝 Answered - Solve for (x): [|5x-6|]

📝 Answered - The line [tex]l[/tex] has equation [tex]3 x-2 y=k[/tex] where [tex]k[/tex] is a real constant. Given that the line [tex]l[/tex] intersects the curve with equation [tex]y=2 x^2-5[/tex] at two distinct points, find the range of possible values for [tex]k[/tex].

📝 Answered - Which point is on the line that passes through point H and is perpendicular to line FG? (-6,10) (-2,-12) (0,-2) (4,2)

📝 Answered - Which statement best describes how to determine whether [tex]f(x)=9-4 x^2[/tex] is an odd function? A. Determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]9-4 x^2[/tex]. B. Determine whether [tex]9-4(-x^2)[/tex] is equivalent to [tex]9+4 x^2[/tex]. C. Determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-\left(9-4 x^2\right)[/tex]. D. Determine whether [tex]9-4(-x^2)[/tex] is equivalent to [tex]-\left(9+4 x^2\right)[/tex].

📝 Answered - Are the given lines parallel, perpendicular, or neither? [tex] \begin{array}{l} 3 x+12 y=9 \\ 2 x-8 y=4 \end{array} [/tex] A. The quotient of the slopes of the lines is 1, so the lines are parallel. B. The slopes of the lines are not the same, so they are perpendicular. C. The slopes of the lines are opposites, so they are neither parallel nor perpendicular. D. The product of the slopes of the lines is 1, so the lines are perpendicular.

📝 Answered - Using inequalities to determine the appearance of a graph and solution set: As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week but wants to make at least $200 per week. The inequalities [tex]$20 x+25 y \geq 200$[/tex] and [tex]$x+y < 10$[/tex] represent the situation. Which is true of the graph of the solution set? Check all that apply. A. The line [tex]$20 x+25 y \geq 200$[/tex] has a positive slope and a negative y-intercept. B. The line [tex]$x+y < 10$[/tex] has a negative slope and a positive y-intercept. C. The line representing [tex]$20 x+25 y \geq 200$[/tex] is solid, and the graph is shaded above the line. D. The line representing [tex]$x+y < 10$[/tex] is dashed, and the graph is shaded above the line. E. The overlapping region contains the point (4,5).

📝 Answered - On a number line, the directed line segment from [tex]$Q$[/tex] to [tex]$S$[/tex] has endpoints [tex]$Q$[/tex] at -8 and [tex]$S$[/tex] at 12. Point [tex]$R$[/tex] partitions the directed line segment from [tex]$Q$[/tex] to [tex]$S$[/tex] in a 4:1 ratio. Which expression correctly uses the formula [tex]$\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1$[/tex] to find the location of point R? A. [tex]$\left(\frac{1}{1+4}\right)(12-(-8))+(-8)$[/tex] B. [tex]$\left(\frac{4}{4+1}\right)(12-(-8))+(-8)$[/tex] C. [tex]$\left(\frac{4}{4+1}\right)(-8-12)+12$[/tex] D. [tex]$\left(\frac{4}{1+4}\right)(-8-12)+12$[/tex]