🧮 algebra

1. **State the problem:** Solve the quadratic equation $$c^2 = -3c + 54$$ for $c$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Evelyn bought $q$ meters of fabric. George bought 6 times as much fabric as Evelyn, so George initially has $6q$ meters. 2. **George returns 35 meters:**

1. **Stating the problem:** A man buys a certain number of shirts for 2000 FRW. Each shirt costs some price, and if the price per shirt was 200 FRW less, he could buy 5 more shirts

1. Solve the simultaneous linear equations with complex coefficients: Given:

1. المشكلة: حساب جذر العدد 5. 2. الصيغة المستخدمة: جذر العدد $a$ هو العدد $x$ الذي يحقق $x^2 = a$.

1. The problem is to graph the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general form of an exponential function is $y = a^x$, where $a$ is the base and $x$ is the ex

1. **Problem Statement:** Graph the piecewise functions given in exercises 23 to 26. 2. **Understanding Piecewise Functions:** A piecewise function is defined by different expressi

1. **Problem Statement:** Find the Least Common Multiple (L.C.M) and Greatest Common Factor (G.C.F) of 32 and 58. 2. **Definitions:**

1. **Stating the problem:** A man buys a certain number of shirts for 2000 FRW. Each shirt costs some price, and if the price per shirt were 200 FRW less, he could buy 5 more shirt

1. Let's clarify the problem: shading usually refers to highlighting the solution region of an inequality or system of inequalities on a graph. 2. To determine what to shade, ident

1. The problem is about understanding how to shade regions in graphs, especially for inequalities. 2. When you have an inequality like $y > 2x + 1$, you first graph the boundary li

1. **State the problem:** Evaluate the expression $$-2c^2 + (2c)^2$$ for $$c = 3$$. 2. **Write the expression:** $$-2c^2 + (2c)^2$$.

1. **State the problem:** Evaluate the expression $$(-5r)^2 + 11r$$ for $$r = -1$$. 2. **Recall the formula and rules:**

1. **State the problem:** Evaluate the expression $-2 - 7r$ for $r = -2$. 2. **Write the expression:**

1. The problem asks us to evaluate the expression $-5 + 2m$ for $m = -5$. 2. The expression is $-5 + 2m$.

1. The problem asks us to evaluate the expression $$-1 + 9g$$ for $$g = 0$$. 2. The expression is $$-1 + 9g$$.

1. **Problem Statement:** Determine the domain and range of the function $$y = -x + 4$$. 2. **Understanding the function:** This is a linear function with slope $$-1$$ and y-interc

1. **State the problem:** Solve the system of linear equations: $$12x + 15y = 33$$

1. The problem is to evaluate the expression $xe^{-2x^2}$ at $x=\frac{1}{2}$.\n\n2. The expression is $xe^{-2x^2}$. To evaluate it, substitute $x$ with $\frac{1}{2}$.\n\n3. Substit

1. The problem is to find the values of $x$ such that $f(x) = 0$. 2. This means we want to solve the equation $$f(x) = 0$$ for $x$.

1. The problem is to understand and analyze graphs of functions. 2. A graph of a function $y=f(x)$ shows the relationship between $x$ (input) and $y$ (output).