| Topic | Problem | Solution |
|---|---|---|
| None | \( 3 t^{2}-24 t+36=36 \) | \( 3t^{2} - 24t + 36 - 36 = 0 \) |
| None | $\frac{b}{6}+1=4.5$ | Subtract 1 from both sides: \(\frac{b}{6} = 3.5\) |
| None | 7. If the area of a square is $50 \mathrm{~cm}^{2… | Find the side length by taking the square root of the area: \(side = \sqrt{50} \approx 7.07 \mathrm… |
| None | $\frac{1}{2} \times\left(-\frac{2}{3}+5\right)$ | Calculate the value inside the parentheses: \(-\frac{2}{3} + 5\) |
| None | (3) \( 2 x+15=43-5 x \) (4) \( 3+4 x=9 x+13 \) | \( 2x+15=43-5x \) → \( 7x = 28 \) → \( x = 4 \) |
| None | $\frac{1}{2} \times\left(-\frac{2}{3}+\frac{5}{1}… | First, we need to calculate the sum inside the parentheses: $-\frac{2}{3}+\frac{5}{1}$.\\ |
| None | Find the polynomial function \( f \) with real co… | \(f(x)=a(x+1)(x-2)(x^2+2)\) |
| None | If the cost function for a commodity is \[ C(x)=\… | Differentiate the cost function: \( MC(x) = \frac{dC}{dx} = \frac{1}{30} x^{2} + 4x + 2\) |
| None | Meal tickets at the circus cost $\$ 4.00$ for chi… | Let x be the number of adult meal tickets and y be the number of child meal tickets. We have the fo… |
| None | $y$ is directly proportional to $x^{2}$. Given th… | Given that $y$ is directly proportional to $x^{2}$, we can write the equation as $y=kx^{2}$, where … |
| None | Definition po pelle vecteur normal à une droite t… | \( \vec{n} \cdot \vec{d} = 3(-2) + (-2)(3) = 0 \) |
| None | \( \sqrt{9-12 x}=9 \) | \( (\sqrt{9-12 x})^2 = (9)^2 \) |
| None | Find the distance between the points \( (7,1) \) … | \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) |
| None | Pythagorean theorem: word problems U5U An envelop… | \( a^2 + b^2 = c^2 \) |
| None | A plane flies 405 miles with the wind and 315 mil… | Let x be the speed of the plane in still air. Then, the speed with the wind is \(x + 20\) and again… |
| None | $2 \times \frac{2}{9}$ | Given the expression: \(2 \times \frac{2}{9}\) |
| None | Julie is building a skateboarding ramp by proppin… | Form a right triangle with height 57 cm, base 76 cm, and the wood piece as hypotenuse. |
| None | You are asked to design the manipulator arm for a… | Step 1: Calculate normal stress: \(\sigma = \cfrac{P_{max}}{A} \), where \(P_{max} = 640 \mathrm{Lb… |
| None | (1) \( 5 x+6=2 x+15 \) 3 (2) \( 7 x-4=20+3 x \) (… | ['\\( 5x-2x=15-6 \\)', '\\( 3x=9 \\)', '\\( x=3 \\)'] |
| None | 4) How tall is the palm tree? Mariachi must know … | Let the height of the palm tree be denoted as \(h\). |
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