🧮 algebra

1. **State the problem:** We have the temperature model $$T = -5t + 200$$ where $T$ is temperature in °F and $t$ is time in minutes. 2. **Identify intercepts:**

1. **State the problem:** Simplify the fractions $\frac{108}{16}$, $\frac{25}{100}$, and $\frac{81}{3}$. 2. **Recall the formula:** To simplify a fraction $\frac{a}{b}$, divide num

1. **State the problem:** Solve the equation $$2^{2x+2} - 3 \times 2^x - 10 = 0.$$ 2. **Rewrite the equation using properties of exponents:** Recall that $$2^{2x+2} = 2^{2x} \times

1. **State the problem:** We want to express $155$ as the sum of a power of $2$ and a cube number. 2. **Recall definitions:**

1. **State the problem:** We need to express the number $56$ as a product of its prime factors. 2. **Recall the prime factorization method:** Prime factorization means breaking dow

1. **State the problem:** Find the foci of the hyperbola given by the equation $$\frac{x^2}{52} - \frac{y^2}{20} = 1$$. 2. **Identify the form and parameters:** This is a horizonta

1. **State the problem:** Find the foci of the hyperbola given by $$\frac{y^2}{45} - \frac{x^2}{5} = 1$$. 2. **Identify the form:** This is a vertical hyperbola centered at the ori

1. **State the problem:** We need to find the maximum number of sea lions that can live in a cuboid pool with dimensions $4$ m, $13$ m, and $6$ m, given that each sea lion requires

1. **State the problem:** We need to graph the piecewise function:

1. **State the problem:** We are given the function $$b(x) = -0.003(x - 13.56)(x + 2.1)$$ which models the height of a pumpkin thrown by a bear robot as a function of horizontal di

1. **State the problem:** We are given three equivalent forms of a quadratic function: - Vertex form: $$y = -0.2(x - 2.47)^2 + 3.042$$

1. Solve $|8 + p| = 2p - 3$. - The absolute value equation $|A| = B$ implies $B \geq 0$ and $A = B$ or $A = -B$.

1. **State the problem:** Find the equation of the line passing through the points $(-2, 1)$ and $(-1, -8)$ in point-slope form. 2. **Recall the formula:** The point-slope form of

1. **State the problem:** Find the equation of the line passing through points $(3, -8)$ and $(7, -10)$ in point-slope form. 2. **Formula:** The point-slope form of a line is given

1. **State the problem:** Find the equation of the line passing through the points $(5, 10)$ and $(4, 2)$ in point-slope form. 2. **Recall the formula for point-slope form:**

1. **State the problem:** Find the equation of the line passing through the points $(8, 3)$ and $(1, 6)$ in point-slope form. 2. **Recall the point-slope form formula:**

1. **State the problem:** Find the equation of the line passing through the points $(9, 3)$ and $(1, 1)$ in point-slope form. 2. **Recall the formula:** The point-slope form of a l

1. **State the problem:** We need to graph the function $$y = \log_2(x - 1) - 2$$ including its vertical asymptote and curve. 2. **Identify the vertical asymptote:** The logarithmi

1. **State the problem:** Solve the equation $2x + 2y = 32$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: subtraction and di

1. **State the problem:** We need to solve the system of equations using substitution: $$y = 3x + 5$$

1. **State the problem:** Determine the symmetry of the graph of the equation $$y = x^2 + 6$$ without graphing. 2. **Recall symmetry rules:**