🧮 algebra

1. The problem involves understanding the relationship between budget increase percentages and average team performance scores relative to targets. 2. Given the performance target

1. **State the problem:** Solve the equation $$\frac{2x - 2}{7} = -6$$. 2. **Formula and rules:** To solve for $x$, first eliminate the denominator by multiplying both sides by 7.

1. **State the problem:** Solve the quadratic equation $$x^2 - 6x = -9$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Factorise fully the expression $6 + 36x$. 2. **Identify common factors:** Look for the greatest common factor (GCF) of the terms $6$ and $36x$.

1. **State the problem:** Solve the quadratic equation $$3x^2 + 5x - 2 = 0$$ to find the roots (values of $x$). 2. **Formula used:** For a quadratic equation $$ax^2 + bx + c = 0$$,

1. Uzdevums: Atrast pareizo kāpinātāju $x$ vienādojumam $$2^x = 8$$. 2. Izmantojam kāpināšanas likumu: ja $a^x = a^y$, tad $x = y$, ja $a > 0$ un $a \neq 1$.

1. **Problem:** Find the domain and range of the rational function $g(x) = \frac{2}{x - 5}$. 2. **Domain:** The domain is all real numbers except where the denominator is zero.

1. The problem is to verify if $$\left( \frac{4}{5} \right)^2 = \frac{25}{16}$$ is true. 2. The formula for squaring a fraction is $$\left( \frac{a}{b} \right)^2 = \frac{a^2}{b^2}$

1. **Problem:** Find the domain and range of the rational function $$f(x) = \frac{x+3}{x-4}$$. 2. **Domain:** The domain of a rational function is all real numbers except where the

1. **State the problem:** Solve the equation $$2x^4 - 3x^2 + 1 = 0$$ for $x$. 2. **Identify the type of equation:** This is a quartic equation but can be treated as a quadratic in

1. **Problem:** Determine if the statement "The solution set for $x^2 = 81$ is \{9\}" is true or false. 2. **Formula and rules:** To solve $x^2 = 81$, we use the property that if $

1. **State the problem:** Simplify the expression $$\frac{3x + 6}{8} \div \frac{5x + 10}{6}$$. 2. **Recall the rule for dividing fractions:** Dividing by a fraction is the same as

1. **Problem statement:** Transform the conic given in polar coordinates $$r = \frac{4}{4 - 2 \cos \theta}$$ into rectangular coordinates and show it reduces to the ellipse equatio

1. **State the problem:** Solve the quadratic equation $$x^2 - 25 = 0$$. 2. **Formula and rules:** This is a difference of squares equation, which can be factored using the identit

1. **State the problem:** Simplify the expression $ (3054 - 741) \times 12 + 36 $.\n\n2. **Apply the order of operations:** First, perform the subtraction inside the parentheses.\n

1. **State the problem:** Simplify the expression $\frac{8520}{5} - 524 + 21$. 2. **Apply division first:** Calculate $\frac{8520}{5}$.

1. The problem is to simplify the expression \(\sqrt{x}6\). 2. The expression \(\sqrt{x}6\) can be interpreted as \(6\sqrt{x}\) since multiplication is commutative.

1. The problem is to solve the equation $$2x^2 - 4x - 6 = 0$$ for $x$. 2. We use the quadratic formula to solve equations of the form $$ax^2 + bx + c = 0$$, which is:

1. The problem is to solve the equation $$2x^2 - 4x - 6 = 0$$ for $x$. 2. We use the quadratic formula to solve equations of the form $$ax^2 + bx + c = 0$$, which is:

1. The problem is to solve the equation $$2x^2 - 4x - 6 = 0$$ for $x$. 2. We use the quadratic formula to solve equations of the form $$ax^2 + bx + c = 0$$, which is:

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then