🧮 algebra

1. **Stating the problem:** Make the letter $r$ the subject of the formula $c = 2\pi r$.

1. **State the problem:** We want to find the best fit line for the data points (50, 64.7), (60, 51.3), (70, 40.5), (90, 25.9), (100, 7.5) using the least squares method for the mo

1. **State the problem:** We want to find the best fit line for the data points (50, 64.7), (60, 51.3), (70, 40.5), (90, 25.9), (100, 7.5) using the least squares method for the mo

1. **Problem Statement:** Perform the indicated operations and write answers in standard form for the following expressions: (a) $(-5x^2 - x + 4) + (-3x^2 - 5x + 2)$

1. **Stating the problem:** Solve the equation $x + a = b$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract $a$ from both sides of the equation. This uses the subtractio

1. **State the problem:** We are given data points $(50,64.7)$, $(60,51.3)$, $(70,40.5)$, $(90,25.9)$, and $(100,7.5)$ and a model $XY^A = B$. We want to find the best linear fit u

1. **State the problem:** Find the value of $$\left( \frac{5}{12} - \frac{7}{9} \cdot 0.25 \right)^{-1} \cdot 1 \frac{2}{9}$$. 2. **Rewrite the mixed number:** Convert $$1 \frac{2}

1. The problem is to find the best fit line for a set of data points using the Least Squares Method. 2. The formula for the best fit line is $y = mx + b$, where $m$ is the slope an

1. **Problem statement:** Given a parabola $y=ax^2+bx+c$ with $a\neq0$ that intersects the x-axis at points $A(-1,0)$ and $B(4,0)$, vertex $D(0,4)$ on the y-axis, and intersects th

1. **State the problem:** We need to find the expression for $h(x+1)$ given the function $h(x) = 3x^4 + x^3 - 4x^2 + x - 2$. 2. **Formula and approach:** To find $h(x+1)$, substitu

1. **State the problem:** We are given the polynomial expression $$12t^5 - 20t^4 + 8t^2 - 16$$ and want to analyze its structure, possibly factor it, and understand its behavior.

1. **State the problem:** We have an arithmetic sequence with the first three terms: $8p$, $7p - 3$, and $4p + 2$. The sum of the first $n$ terms is $-1914$. We need to find the va

1. **State the problem:** Solve the exponential equation $$\left(\frac{1}{9}\right)^{3x+5} = \left(\frac{1}{243}\right)^{x-6}$$ for $x$. 2. **Rewrite bases as powers of a common ba

1. **State the problem:** Calculate the value of $$\left(\frac{1}{3} + \frac{1}{2}\right) \cdot 0.06 + \frac{1}{25} \div 1 \frac{1}{5}$$. 2. **Rewrite mixed numbers and decimals:**

1. The problem asks us to calculate the value of the function $f(x)$ at $x = -\frac{1}{4}$. 2. To solve this, we need the explicit formula for $f(x)$, which is not provided in the

1. **Problem statement:** Evaluate each expression and give the final answers as exact simplified fractions. 2. **Recall important rules:**

1. The problem is to find the equation of the line passing through the points $A(2,3)$ and $B(4,7)$. 2. The formula for the slope $m$ of a line through two points $(x_1,y_1)$ and $

1. The problem involves finding the missing values (either a circle or a square) in rectangles where the product of the top and bottom numbers equals the number inside the rectangl

1. **Problem Statement:** Ronda plays a game guessing an integer between 0 and 100. Her score after one guess $x$ is given by the function $$f(x) = -|x - 57| + 300$$ where 57 is th

1. Planteamos el problema: Resolver un sistema de ecuaciones lineales usando el método de Gauss-Jordan. 2. El método de Gauss-Jordan consiste en transformar la matriz aumentada del

1. **State the problem:** Solve the system of linear equations: $$3n - 4n + 2o = 5$$