🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{5y^{12}}{10y^{5}}$$. 2. **Recall the rules:** When dividing terms with the same base, subtract the exponents: $$\frac{a^{m

1. **State the problem:** Simplify the expression $$\frac{x^{10}}{x^{3}}$$. 2. **Recall the exponent rule:** When dividing powers with the same base, subtract the exponents: $$\fra

1. **Problem 9:** A fruit seller buys lemons at P2 for a rupee and sells them at P5 for three rupees. Find his gain percent. 2. **Step 1:** Understand the cost price (CP) and selli

1. **State the problem:** The cost price (CP) of 20 articles equals the selling price (SP) of $x$ articles. The profit is 25%. We need to find $x$. 2. **Formula and rules:** Profit

1. **State the problem:** We need to solve the inequality $$4x + 5 > 3$$ to find out for which values of $x$ this is true. 2. **Subtract 5 from both sides:** To isolate the term wi

1. **State the problem:** We need to subtract $8.4\times 10^{9}$ and $5.2\times 10^{8}$ and write the answer in scientific notation. 2. **Recall the rule:** To subtract numbers in

1. **State the problem:** Add the numbers $7.9\times10^{4}$ and $2\times10^{5}$ and write the answer in scientific notation. 2. **Recall the rule:** To add numbers in scientific no

1. **State the problem:** Simplify the expression $$\sqrt{\sqrt[7]{m}}$$ by converting it to exponential form. 2. **Recall the rules:**

1. **State the problem:** Rewrite the expression $$\left(\frac{5x}{3yz}\right)^{-\frac{6}{5}}$$ using only positive rational exponents. 2. **Recall the rule:** A negative exponent

1. **State the problem:** Solve the system of linear equations: $$-3x + 4y - 2z = 19$$

1. **State the problem:** We are given the quadratic function $$y = x^2 + 2x - 3$$ and need to complete a table of values, plot the parabola, and identify key features.

1. **State the problem:** We are given the quadratic function $$y = x^2 - 1$$ and need to complete a table of values, plot the points, and identify key features of the parabola. 2.

1. **State the problem:** Solve the equation $$185x = 400$$ for $$x$$. 2. **Formula and rule:** To solve for $$x$$, divide both sides of the equation by the coefficient of $$x$$, w

1. **Stating the problem:** Solve the equation $\log 2 = \log x$ for $x$. 2. **Formula and rule:** If $\log a = \log b$, then $a = b$ because the logarithm function is one-to-one.

1. **State the problem:** We need to graph the linear equation $$9x + 6y = 12$$ using intercepts. 2. **Formula and rules:** To graph using intercepts, find where the line crosses t

1. Énonçons le problème : on cherche à simplifier l'expression $$r = 6x(-3) \times 6y \div 18x(-2y)(-4y)$$. 2. Rappelons les règles importantes :

1. **Stating the problem:** Simplify the expressions \(6x(-3) \times x\) and \(18x(-2)(-4)\).\n\n2. **Simplify the first expression:** \(6x(-3) \times x\) means multiply \(6x\) by

1. **Énoncé du problème :** Calculez la valeur de l'expression $$B = \frac{-2 \times 10}{5 \times (-4)}$$.

1. **State the problem:** We need to solve the system of linear equations: $$\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}$$

1. **State the problem:** We are given a function $f(x) = 2x + 3$ and asked to find the value of $f(4)$. 2. **Recall the formula:** The function $f(x)$ means for any input $x$, the

1. **State the problem:** We need to sketch the graph of the linear equation $$y = -2x - 2$$. 2. **Formula and rules:** This is a linear equation in slope-intercept form $$y = mx +