| Topic | Problem | Solution |
|---|---|---|
| None | For the piecewise linear function, find $(a) f(-3… | We need to find the value of the function at x = -3. Since -3 is less than or equal to -1, we will … |
| None | Decide whether the following relation defines a f… | Decide whether the following relation defines a function: \(\{(3,5),(1,5),(5,4)\}\) |
| None | Use the properties of logarithms to evaluate each… | Use the properties of logarithms to evaluate each of the following expressions. |
| None | In the space below, algebraically solve the equat… | Find the angles whose cosine is 0.5: \(\cos^{-1}(0.5) = 60^\circ, 300^\circ\) |
| None | LINEAR SYSTEMS Solving a word problem involving a… | Set up the equations: \(x + y = 51\) and \(y = x - 15\) |
| None | The $n^{\text {th }}$ term of a sequence is given… | Substitute n with 1, 2, and 3 in the given formula \(30 - 2n\): |
| None | Simplify for all permissible values of the variab… | Rewrite the expression as: \(\frac{3x}{12} \times \frac{8x^2}{y} \times \frac{5x^2y^3}{9x^3y^2}\) |
| None | 8. Jeff travels $2 \mathrm{~h}$ by car and $3 \ma… | Let x be the average speed of the car in km/h, and the average speed of the bus is (x - 20) km/h. |
| None | This distance-time graph shows the journey a boat… | Let $d$ denote the number of miles in the distance from the port and let $r$ denote the fastest spe… |
| None | 1) Para ir do ponto $M$ ao ponto $S$, deve-se des… | \(\tan R = \frac{MS}{NP}\) |
| None | What is the value of $2(3)^{3}-(3)^{2} ?$ | Calculate the value of \((3)^{3}\): \(3^3 = 27\) |
| None | Use the given conditions to write an equation for… | Given the slope $m = -\frac{1}{3}$ and the point $(9, -4)$, we can use the point-slope form formula… |
| None | Use substitution to determine whether 2 is a zero… | Substitute x = 2 into the function \(f(x) = x^{4} - 2x^{3} + 2x^{2} - 7x - 6\): |
| None | It takes a bus 1 hour and 30 minutes to travel 36… | Convert the time taken to hours: 1 hour and 30 minutes = 1 + \(\frac{30}{60}\) = 1.5 hours |
| None | It takes an older pump twice as long to drain a c… | Let's denote the time it takes for the newer pump to drain the pool as x (in hours). Then, the olde… |
| None | (T/F) An $n \times n$ determinant is defined by d… | Calculate the determinant of a 3x3 matrix using the Laplace expansion: \(\det(A) = a_{11}C_{11} - a… |
| None | In an all boys school, the heights of the student… | Given a normal distribution with mean \(\mu = 70\) inches and standard deviation \(\sigma = 5\) inc… |
| None | The weight of oranges growing in an orchard is no… | \(95\%\) of the data lies within \(\pm 2\) standard deviations of the mean. |
| None | A cylinder has a base diameter of 10 inches and a… | \(r = \frac{D}{2} = \frac{10}{2} = 5\) |
| None | The angle of elevation to a nearby tree from a po… | \(\tan(74^{\circ}) = \frac{h}{54} \) |
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