🧮 algebra

1. Stating the problem: Solve the equation $x + \frac{5}{4} = -\frac{1}{2}$ for $x$. 2. To isolate $x$, subtract $\frac{5}{4}$ from both sides:

1. **State the problem:** Calculate $-\frac{8}{15} + 0.6$. 2. **Convert 0.6 to a fraction:**

1. Stating the problem: Simplify the expression $$\frac{-8}{15} + 0$$. 2. Since adding zero to any number does not change its value, the expression remains $$\frac{-8}{15}$$.

1. Stating the problem: Solve the equation $x - \frac{3}{4} = \frac{2}{7}$ for $x$. 2. To isolate $x$, add $\frac{3}{4}$ to both sides of the equation:

1. Stating the problem: Calculate the product of $2.8$ and $-\frac{20}{7}$. 2. Express the multiplication explicitly:

1. The problem involves a function machine where the input is first transformed by multiplication by 5, then the output of this step is processed further. 2. Input to function mach

1. **Express the following in factors:** (i) Simplify $\frac{(n+2)!}{(n+2)!} = 1$ because any nonzero number divided by itself equals 1.

1. The problem asks to solve two subproblems: 1a and 1b. 2. Since the specific problems 1a and 1b are not visible from the provided Google Drive link, I cannot directly access them

1. **State the problem:** Solve the equation $8f=96$ for $f$. 2. **Isolate $f$:** To solve for $f$, divide both sides of the equation by 8.

1. The problem gives the equation $17_r = 5$ and asks to find $r$. 2. The notation $17_r$ means the number 17 in base $r$.

1. The problem states that 3 times a number $f$ equals 15, or mathematically, $3f=15$. 2. To find the value of $f$, divide both sides of the equation by 3 to isolate $f$:

Problem: You want formulas and methods to change the subject of a formula, that is, to make a chosen variable the subject of an equation. 1. Linear equations.

1. On considère $f(x) = \frac{x^{2} - 4x + 6}{x^{2} - 4x + 8}$. a. Le domaine de définition $D_f$ correspond aux $x$ tels que le dénominateur soit non nul :

1. **Problem 1(a)(i): Find the value of $x$ in the matrix equation** Given matrix:

1. We are asked to solve the equation $$3 \sin(2x) + 5x - 4 = 0$$ for $x$. 2. This is a transcendental equation because it contains both the sine function and a linear term in $x$,

1. **State the problem:** Complete the missing values in the ratio table: | Left | Right |

1. Identify the problem: We need to complete the ratio table by finding the missing values in the right column, given the left column values and existing right column values. 2. An

1. **State the problem:** We are given a ratio table with paired values where the ratios are consistent. The table is:

1. We are given a ratio table with two columns where the left column values correspond to the right column values. 2. The table provided is:

1. Stating the problem: We need to complete the missing values in the ratio table where each pair forms equivalent ratios. 2. First, identify ratio pairs given:

1. The problem states that a polynomial $p$ is graphed with zeros at approximately $x = -3.5$, $x = -1$, and $x = 1$. 2. We note that the zero at $x = -3.5$ corresponds to the fact