🧮 algebra

1. The problem is to solve for $y$ in the equation: $$20.48 = 8y$$

1. **State the problem:** Solve for $4x$ given the equation $2x + 15 = 7(4x - 9)$. 2. **Write the equation:**

1. The problem asks for the x-intercept of the line given by the equation $$4x - 5y = 2$$ in the xy-plane. The x-intercept is the point where the graph crosses the x-axis, so the y

1. **State the problem:** We need to find an equation that represents the relationship between $x$ and $y$ given the table: $$\begin{array}{c|cccc}

1. The problem is to find the factors of 12. 2. Factors of a number are integers that divide the number exactly without leaving a remainder.

1. The problem asks for the range of a parabola that opens upwards with vertex at approximately $(2,1)$. 2. The vertex form of a parabola is given by $$y = a(x-h)^2 + k$$ where $(h

1. **Problem (ক):** Given $a^x = b$, $b^y = c$, and $c^z = a$, show that $xyz = 1$. 2. **Step 1:** Express $b$ and $c$ in terms of $a$:

1. The problem is to understand why the answer $r = 1.05$ makes sense in the equation $350r = 367.50$. 2. Recall that $r$ represents a multiplier applied to 350 to get 367.50.

1. **Problem statement:** Given the exponential expressions \(P = a^x\), \(Q = a^y\), and \(R = a^z\), prove the following: (ক) If \(a^x = b\), \(b^y = c\), and \(c^z = a\), then s

1. The problem is to find the value of $r$ in the equation $350r = 367.50$. 2. We start with the equation:

1. **Problema:** Resolver la ecuación $2 \log x - 3 + \log \left(\frac{x}{10}\right) = 0$. 2. **Fórmulas y reglas importantes:**

1. **State the problem:** Simplify the expression $4(x-3)-3(x-5)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. The problem states that $f$ is a one-to-one function with $f(-5) = -11$ and $f(2) = -12$. 2. Recall the definition of an inverse function: if $f(a) = b$, then $f^{-1}(b) = a$.

1. **Problem:** Describe the regions that represent $a^2 - b^2$ in a large square of area $a^2$ containing a smaller square of area $b^2$. Show how to rearrange these regions to il

1. **State the problem:** We are given the function $f(x) = 14 - x^2$ and asked to find its inverse $f^{-1}(x)$, which can be written in two parts. 2. **Find the inverse function:*

1. The problem asks to find the point where the graphs of $y=f(x)$ and $y=f(4x)$ intersect. 2. The intersection means the $x$-values satisfy $f(x) = f(4x)$.

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{49}{27}} \cdot j^{\frac{1}{3}}$$ where $j$ is a variable. 2. **Recall the cube root and exponent rules:**

1. The problem is to find the cube root of 64, written as $\sqrt[3]{64}$. 2. The cube root of a number $x$ is a value $a$ such that $a^3 = x$.

1. **State the problem:** Find the domain, vertical asymptote, and end behavior of the function $$h(x) = -\log(3x - 4) + 7$$. 2. **Domain:** The logarithm is defined only when its

1. **State the problem:** Two angles are supplementary, meaning their measures add up to 180 degrees. One angle is twelve degrees more than twice the other angle. 2. **Define varia

1. **Problem Statement:** We have a bacteria population starting at 500 and doubling every 3 hours. We want to write an exponential function to model the population after $t$ hours