Questions in mathematics

Questions in mathematics

📝 Answered - What is equal to the value of $9-(-5)$?

📝 Answered - Factor: [tex]2 r^2+11 r+5[/tex]

📝 Answered - Perform the division. $\frac{-30 x^6+100 x^7}{25 x^7}= \square$ (Simplify your answer.)

📝 Answered - Ann is planning a trip to Australia. The table below shows the cities she hopes to visit while she is there, as well as the amount of money she estimates that she will spend in each place as a result of lodging, eating, transport, and similar expenses. All costs are given in Australian dollars ($). | City | Cost ($) | | -------------- | -------- | | Toowoomba | 161 | | Sunshine Coast | 264 | | Newcastle | 198 | | Perth | 130 | | Sydney | 224 | | Hobart | 301 | | Bendigo | 277 | Ann has $1,265 budgeted for this portion of her trip. Which of the following possibilities represents the smallest portion she can cut out of her plans to stay under budget? A. Toowoomba and Perth B. Hobart

📝 Answered - (a) f(x) = x - 3 → f(-2) (b) g(x) = x² - 3x + 5 → g(1) (c) h(x) = √(x³ + x + 6) → h(3) (d) p(x) = (x² + 1) / (x - 4) → p(5)

📝 Answered - A number ending in '7' will have the unit's place of its square as: (1) 4 (2) 9 (3) 1 (4) 6

📝 Answered - 8. [tex]x^2y - x^2 + 2xy - 2x + 3 = 0[/tex] 9. [tex]x^3 - x^2y - xy^2 + y^3 + 2x^2 - 4y^2 + 2xy + x + y + 1 = 0[/tex] 10. [tex]x^3 + 2x^2y - xy^2 - 2y^3 + xy - y^2 - 10 = 0[/tex] 11. [tex]x^3 + 2x^2y - xy^2 - 2y^3 + 3xy - 3y^2 + 4x + 7 = 0[/tex] 12. [tex]6x^3 - 11x^2y + 6xy^2 - y^3 + 2x + 3y + 7 = 0[/tex] 13. [tex]4x^3 - x^2y - 4xy^2 + y^3 + 3x^2 + 2xy - y^2 + x + y + 7 = 0[/tex] 14. [tex]x^3 + x^2y - xy^2 - y^3 - 3x + 5 = 0[/tex] 15. [tex]x^3 + x^2y - xy^2 - y^3 + x^2 - y^2 + 5 = 0[/tex] 16. [tex]x^3 + y^3 - 3ax^2 = 0[/tex] 17. [tex](x - y + 1)(x - y - 2)(x + y) = 8x - 1[/tex] 18. Show that the eight points of intersection of the curve [tex]xy(x^2 - y^2) + x^2 + y^2 = a^2[/tex] and its asymptotes lie on a circle whose centre is at the origin. 19. Find the equation to the cubic which has the same asymptotes as the curve [tex]x^3 - 6x^2y + 11xy^2 - 6y^2 - x + y + 1 = 0[/tex] and which passes through the points [tex](0, 0), (1, 1)[/tex] and [tex](0, 1)[/tex]. 20. Find the asymptotes of the curve [tex](y - x)(y - 2x)^2 + (y + 3x)(y - 2x) + 2x + 2y - 1 = 0[/tex] and show that their points of intersection with the curve lie on a straight line. 21. Find the asymptotes of the curves. (i) [tex]r \cos \theta = a \sin \theta[/tex] (ii) [tex]r = a \log \theta[/tex] (iii) [tex]r \sin \theta = a \cos 2\theta[/tex] (iv) [tex]r \cos \theta = a \sin^2 \theta[/tex] (v) [tex]r \theta = ae^{\theta}[/tex] (vi) [tex]r \sin \theta = e^{\theta}[/tex] (vii) [tex]r = a \sec \theta[/tex]

📝 Answered - Calculate the total cost for attending a conference if registration is $400, and the employee needs hotel, rental car, per diem, parking, and coverage for 4 days. | Expense | Cost per day | | ----------- | ----------- | | Hotel | $230 | | Rental Car | $110 | | Per Diem | $55 | | Parking | $40 | | Coverage | $400 | $[?]

📝 Answered - Find the $x$-intercept. $\begin{array}{c} y=\frac{3 x+30}{x-10} \ ([?], 0) \end{array}$

📝 Answered - Assume that you have a square. What can you conclude from applying the law of detachment to this conditional? If you have a square, then you have a rectangle. A. You have a quadrilateral. B. You have a rectangle. C. Squares and rectangles are the same. D. All sides are the same length.