🧮 algebra

1. **State the problem:** Evaluate the expression $$9.1 + (-3 \frac{4}{5})$$. 2. **Convert the mixed number to an improper fraction:**

1. The problem is to graph the set of values $x$ such that $-1 < x \leq 3$ on a number line. 2. This set describes all numbers greater than $-1$ but less than or equal to $3$.

1. **State the problem:** Diego walks between 9 and 12 miles per week and works out at the gym between 4.5 and 6 hours per week. We need to write a system of inequalities to repres

1. **State the problem:** Find the common difference in the arithmetic sequences (A) 5, 9, 13 and (B) -3, -1, 1. 2. **Formula:** The common difference $d$ in an arithmetic sequence

1. **State the problem:** Solve the system of inequalities:

1. The problem is to find the common difference in an arithmetic progression (A.P.). 2. An arithmetic progression is a sequence of numbers where the difference between consecutive

1. **State the problem:** Find the product of the binomials $(x+3)(x+4)$ and verify the sum $x^2 + 3x$. 2. **Formula used:** The product of two binomials $(a+b)(c+d)$ is given by t

1. **State the problem:** We need to find the length of a rectangle given its area and width. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. The problem asks to express the area of rectangles formed by tiles as a product of length and as a sum of parts. 2. For part (a), the rectangle has dimensions $(x + 3)$ and $(x^

1. The problem states: A rectangle has an area of 3 square feet and a width of $\frac{1}{2}$ foot. We need to find the length of the rectangle. 2. The formula for the area of a rec

1. Énonçons le problème : Résoudre les équations \( \frac{4x+2}{2x-1} = 0 \) et \( \frac{4}{x-1} - \frac{2}{3-2x} = 0 \). 2. Pour la première équation, une fraction est nulle si et

1. The problem is about drawing graphs of functions, typically in coordinate planes. 2. To draw a function, you need to understand its formula and key features like intercepts, ext

1. The problem is about drawing graphs of functions, typically in coordinate planes. 2. To draw a function graph, you need to understand the function's formula and key features lik

1. **State the problem:** Factor the expression $x^2$. 2. **Recall the factoring rules:**

1. **Problem:** For each pair of functions, identify one characteristic they share and one characteristic that distinguishes them. 2. **Pair a) $f(x) = \frac{1}{x}$ and $g(x) = x$*

1. **State the problem:** Find the 8th term of the arithmetic progression (A.P.) with the first three terms given as $-3, -1, 1$. 2. **Identify the formula:** The $n$th term of an

1. **State the problem:** Find an open interval about $c=4$ such that for all $x$ in this interval, the inequality $|f(x) - L| < \varepsilon$ holds, where $f(x) = x + 1$, $L = 5$,

1. **State the problem:** Calculate the value of $-2 \frac{7}{10} \div \frac{12}{7}$. 2. **Convert mixed number to improper fraction:** $-2 \frac{7}{10} = -\left(2 + \frac{7}{10}\r

1. **State the problem:** Find the slope of the line passing through the points $(-3, -1)$ and $(2, 2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. Let's start by understanding the general form of a sinusoidal function: $$y = a \sin(bx + c) + d$$ or $$y = a \cos(bx + c) + d$$. 2. In this formula, the amplitude is the absolu

1. **State the problem:** We need to divide the mixed number three and one-half by the mixed number four and two-thirds. 2. **Convert mixed numbers to improper fractions:**