| Topic | Problem | Solution |
|---|---|---|
| None | Solve the following graphically \[ \begin{array}{… | Rewrite the first equation in terms of y: \(y = \frac{3x}{2} + 3\) |
| None | b) the sum of the first 6 terms of the following … | This 6-term geometric series has first term $a_0 = 7$ and ratio $2$, so it has value |
| None | A ball is dropped from a platform $20 \mathrm{~m}… | Let's find the total distance traveled by the ball after the 16th bounce and when it stops. We know… |
| None | An electronics store receives a shipment of 19 gr… | Translate the problem into English: An electronics store receives a shipment of 19 graphing calcula… |
| None | $2+2$ | Calculate the sum of 2 and 2: \(2 + 2\) |
| None | $\sqrt[5]{\frac{128 x^{7} y^{15}}{x y^{7}}}$ | Simplify the expression inside the fifth root: \(\frac{128x^{7}y^{15}}{xy^{7}} = 128x^{6}y^{8}\) |
| None | Katya has 24 empty oil containers that can each h… | Let the number of containers be \(n = 24\) and the capacity of each container be \(c = 14.9\) litre… |
| None | d) A $15 \mathrm{~m}$ pole is leaning against a w… | We have a right triangle with the pole as the hypotenuse, the distance from the wall as one leg, an… |
| None | $2+2=$ | Calculate the sum of 2 and 2: \(2+2\) |
| None | $\int \frac{5 x^{4}+7 x^{2}+x+2}{x\left(x^{2}+1\r… | \(\int \frac{5 x^{4}+7 x^{2}+x+2}{x\left(x^{2}+1\right)^{2}} d x = \int \frac{A}{x} + \frac{Bx + C}… |
| None | $\int \frac{10}{(x-1)\left(x^{2}+9\right)} d x$ | Rewrite the given function using partial fraction decomposition: $$\frac{10}{(x-1)(x^2+9)} = \frac{… |
| None | A rectangular carpet is $4 \mathrm{~m}$ long and … | Given a rectangular carpet with length \(4 \mathrm{~m}\) and width \(6 \mathrm{~m}\), and a scale o… |
| None | Solve the system by the elimination/addition meth… | \(\begin{array}{l} 3x+2y=10 \\ -4x-3y=-13 \end{array}\) |
| None | $\begin{array}{l}\frac{1}{2} x-\frac{2}{3} y=6 \\… | \(\frac{1}{2}x - \frac{2}{3}y = 6\) and \(\frac{1}{4}x + \frac{1}{3}y = -1\) |
| None | Fill in the gap to factorise this expression. \[ … | Divide both terms on the left side of the equation by 3: \(\frac{3x}{3} = x\) and \(\frac{3}{3} = 1… |
| None | Find the exact value of $\cos \frac{5 \pi}{6}$. | Find the reference angle for \(\frac{5 \pi}{6}\) by subtracting \(\frac{\pi}{2}\) from \(\frac{5 \p… |
| None | L 6.1.3 Quiz: Two-Variable Data and Scatterplots … | Understand the concept of correlation coefficient and negative linear relationship. |
| None | Ex. 13 Determine the number of ways in which the … | First, count the occurrences of each letter in the word ANDTHEREAFTER: \(A: 2, N: 1, D: 1, T: 2, H:… |
| None | An iterative formula is shown below. \[ x_{n+1}=\… | Given the iterative formula: \(x_{n+1} = \sqrt{8x_n - 5}\) and \(x_1 = 3\) |
| None | Use the diagram to work out the solution to these… | Since both equations are already in the form of y, we can set them equal to each other: \(-2x + 7 =… |
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