🧮 algebra

1. **State the problem:** Find the slope of the line passing through the points $(-4, 0)$ and $(4, -2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. **State the problem:** Solve the equation $$3 \cdot 4^x + 6 \cdot 2^x = 24$$ for $x$. 2. **Recall the formula and rules:** Note that $4^x = (2^2)^x = 2^{2x}$. This allows us to

1. **State the problem:** Find the slope of the line passing through the points (0, 4), (1, 2), and (-1, 6). 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$

1. **State the problem:** We need to determine which pizza is the better buy by comparing the unit price per square inch for each pizza. 2. **Formula for area of a circle:**

1. **State the problem:** Solve the equation $$4 \log(x) = 2 \log(x) + \log(4) + 2$$ for $x$. 2. **Recall logarithm properties:**

1. **State the problem:** Solve the equation $$\log_3(x + 2) + \log_3(x - 1) = 2$$ for $x$. 2. **Recall the logarithm property:** The sum of logarithms with the same base can be co

1. **State the problem:** Solve the equation $5x - 3 = 2s + 6$ for $x$ in terms of $s$. 2. **Formula and rules:** To isolate $x$, we need to get all terms involving $x$ on one side

1. **State the problem:** Solve the equation $5a - 1 = 14$ for $a$. 2. **Formula and rules:** To solve for $a$, isolate the variable by performing inverse operations. Addition/subt

1. El problema consiste en simplificar la expresión algebraica dada: $$\frac{27x^3 - 8}{x^2 - 16} \div \frac{3x^3 - 5x^2 - 12x + 20}{x^2 - 4} - \frac{x - 2}{x + 4}$$

1. **State the problem:** Solve the inequality $$6(1 + 5x) \geq 246$$ given the condition $$x < -1$$. 2. **Write the formula and rules:** To solve inequalities, we first expand and

1. **State the problem:** Solve the inequality $$24 < 8x - 3 + x$$. 2. **Combine like terms:** On the right side, combine $$8x$$ and $$x$$ to get $$9x$$.

1. **State the problem:** Find the equation of the line passing through the point $P(-1, 2)$ with slope $m = -\frac{5}{1} = -5$. 2. **Formula used:** The point-slope form of a line

1. **Stating the problem:** We have a car's value depreciating over 5 years, with given values for each year. We want to understand the pattern and complete the table. 2. **Formula

1. **State the problem:** We are given data showing the number of bacteria at different times and need to find an equation that models this data. 2. **Identify the pattern:** The b

1. **Problem:** Simplify the expression $-\frac{9}{5} \cdot \frac{8}{15}$. 2. **Formula:** To multiply fractions, multiply the numerators and multiply the denominators:

1. The problem is to find the equation of the line that fits the given table of values for $x$ and $y$: $$\begin{array}{c|c} x & y \\ \hline -1 & 11 \\ 0 & 8 \\ 1 & 5 \\ 2 & 2 \end

1. **State the problem:** Given the table of values for $X$ and $Y$, find the equation of the line that fits these points. 2. **Formula used:** The points suggest a linear relation

1. The problem asks to write a quadratic function in vertex form $f(x) = a(x - h)^2 + k$ for a parabola with vertex at $(4, 2)$ and opening downward. 2. The vertex form of a quadra

1. **State the problem:** Solve the equation $$(e^x - 2)(e^x - 3) = 0$$ for $x$. 2. **Formula and rule:** For a product of two factors to be zero, at least one of the factors must

1. **State the problem:** We are given the quadratic function $$y = -(x + 5)^2 + 4$$ and need to identify its maximum or minimum value, determine whether it is a maximum or minimum

1. The problem is to solve the expression \(( )( ) 2 30\).\n2. It appears the expression is incomplete or unclear. Assuming you want to multiply two numbers and then multiply by 2