🧮 algebra

1. Find 4% of 5600. Step: $4\% = \frac{4}{100} = 0.04$,

1. Stating the problem: We need to verify if $$((x+y)(z^2+w^2))^2 = (x+y)^2 + 2(x+y)(z^2+w^2) + (z^2+w^2)^2$$ is true. 2. Expanding the left side: $$((x+y)(z^2+w^2))^2 = ((x+y)(z^2

1. The problem is to calculate $\frac{12}{5} \times 1.5$. 2. First, rewrite $1.5$ as a fraction: $1.5 = \frac{3}{2}$.

1. We are asked to compute the expression $-\frac{4}{3} : \frac{13}{9}$. This means we need to divide $-\frac{4}{3}$ by $\frac{13}{9}$. 2. Recall that dividing by a fraction is the

1. The problem is to solve the equation for $x$: $$\frac{x}{\frac{5}{7}} = -\frac{21}{20}.$$\n\n2. Rewrite the equation to isolate $x$: $$x \times \frac{7}{5} = -\frac{21}{20}.$$\n

1. Let's state the problem: Verify the given algebraic identity: $$((sx+y)(z^2+w^2))^2 = (s+y)^2 + 2(s+y)(z^2+w^2) + (z^2+w^2)^2$$

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 $x$,