🧮 algebra

1. **State the problem:** Factorize the expression $$x^2 + 5x + 6x^2 + 5x + 6$$. 2. **Combine like terms:** Group the terms with the same powers of $x$.

1. **Problem 11:** Solve $$1 = \frac{v + 2}{v - 4} + \frac{7v - 42}{v - 4}$$ Since denominators are the same, combine numerators:

1. Solve the equation $$\frac{1}{v} + \frac{3v + 12}{v^2 - 5v} = \frac{7v - 56}{v^2 - 5v}$$ - First, factor the denominators: $$v^2 - 5v = v(v - 5)$$.

1. **Problem Statement:** Factorize the expression $$m^2 - 6m - 18mk + 108k$$. 2. **Identify the terms:** The expression has four terms: $$m^2$$, $$-6m$$, $$-18mk$$, and $$108k$$.

1. **Problem Statement:** Determine the range of the function given the points at $x=1$ with $y$-values 2, 3, 4, and 5. 2. **Understanding the Range:** The range of a function is t

1. **Stating the problem:** Factorize the expression $$5a^6 b^2 - 15a^3 b^5 + 35a^4 b^4$$. 2. **Identify the greatest common factor (GCF):**

1. The problem asks us to determine the range of the function given the points on its graph. 2. The range of a function is the set of all possible output values (y-values).

1. **State the problem:** We want to find the number of cookies $x$ Nancy must sell to maximize her monthly profit given by the function $$P(x) = 50\sqrt{x} - 0.5x - 75.$$\n\n2. **

1. **State the problem:** We need to find the selling price of a single book so that the publisher earns a 22% profit, given that 1,250 copies are published and shipping costs R52,

1. **State the problem:** Factorize the expression $$x^2 + 5x + 6x^2 + 5x + 6$$. 2. **Combine like terms:** Group the terms with the same powers of $x$.

1. **State the problem:** Solve the inequality $$-1 \leq 1 - \frac{4t}{5}$$ for $t$. 2. **Write down the inequality:** $$-1 \leq 1 - \frac{4t}{5}$$

1. **State the problem:** Solve the inequality $$-1 \leq 1 - \frac{4t}{5}$$. 2. **Isolate the variable term:** Subtract 1 from both sides:

1. The problem asks to find the antilogarithm of 2.5620. 2. The antilogarithm (or inverse logarithm) of a number $x$ is given by $10^x$ when the logarithm base is 10.

1. The problem asks to express the number 0.0062143 in standard form. 2. Standard form (also called scientific notation) expresses numbers as $a \times 10^n$ where $1 \leq |a| < 10

1. **State the problem:** Solve the equation $$\frac{5x + 1}{2} - \frac{x - 2}{6} = \frac{2x + 4}{3}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fract

1. The problem asks which graph represents the relation $y = -x$. 2. The equation $y = -x$ is a linear function where the slope is $-1$ and the y-intercept is $0$.

1. **Problem:** Solve the equation $$x^4 - 6x^2 + 8 = 0$$. 2. **Formula and approach:** This is a quartic equation but can be treated as a quadratic in terms of $y = x^2$.

1. **State the problem:** We are given the equation $$5x + 12 - x - 26 = 2x + 43$$ and need to find which of the given options is equivalent to this equation. 2. **Simplify the ori

1. The problem asks which graph represents a given relation. However, the relation itself is not specified in the question. 2. To determine which graph represents a relation, we ne

1. **State the problem:** We have two parking plans, A and B, each with a fixed monthly fee plus a cost per day parked. We want to find the system of equations representing the tot

1. **State the problem:** We are given the function $$g(a) = \frac{5a + 3}{2a}$$ and need to find the expression for $$g(a) - g(2a)$$. 2. **Write the expressions:**