🧮 algebra

1. The problem is to rearrange the equation $m = r + z$ to make $r$ the subject and then to make $z$ the subject. 2. To make $r$ the subject, subtract $z$ from both sides:

1. We start with the equation given: $$n = \frac{p - 2t}{15}$$ 2. Our goal is to make $p$ the subject, which means we want to express $p$ in terms of $n$ and $t$.

1. The problem describes a function machine that takes three inputs: $n$, $c$, and $a$. 2. Each input is transformed by the function machine into outputs: $8n$, $8c$, and $8a$ resp

1. Problem 11(a): Find an equation for the quadratic curve modeling the mouse hole entrance. - The entrance is symmetrical and 6 cm wide at the top, so the curve passes through poi

1. The problem gives input-output pairs: inputs 1, 2, 5, and A correspond to outputs 2, 4, 10, and 18 respectively. 2. We need to find the value of A such that the output is 18.

1. The problem states that a function machine takes an input $k$ and first adds 6, then subtracts 2, producing an output. 2. We start with the input: $k$.

1. The problem asks us to find the input value of a function machine that produces an output of 42 after passing through an intermediate value of -34. 2. We start by understanding

1. The problem states that an unknown input goes through two operations: division by 5, then subtraction by 1, resulting in an output of 3. 2. Let the unknown input be $x$.

1. The problem shows a function machine where the input is 6 and the operation is \( \times u \), meaning multiply by some unknown number \( u \). 2. To find the output, we multipl

1. **State the problem:** We have a function machine that takes an input number and applies three operations in sequence: add 3, multiply by 4, then subtract 3. We need to find the

1. The problem asks us to find the input value to a function machine that produces an output of 43 after an intermediate step of -22. 2. We interpret the function machine as having

1. Jelaskan kenapa kita tidak bisa memperoleh bilangan yang merupakan hasil dari bentuk ini: a. $\frac{0}{0}$ adalah bentuk tak tentu karena pembilang dan penyebut sama-sama nol. I

1. Use the discriminant to determine the number of solutions for each quadratic. The discriminant formula is $$\Delta = b^2 - 4ac$$ where the quadratic is $$ax^2 + bx + c = 0$$.

1. **State the problem:** We are given the nth term of a sequence as $T(n) = 3n + 35$. 2. **Given:** A term in the sequence has a value of 347. We need to find the position $n$ of

1. The problem states that the function machine takes an input $m$ and multiplies it by 43 to produce the output. 2. To find the output, we apply the function: $$\text{output} = m

1. The problem states that the $n^{th}$ term of the sequence is given by $$T(n) = 4n^2$$ and asks for the first three terms of the sequence. 2. To find the first term, substitute $

1. The problem shows a function machine where the input is 10, it is first multiplied by 6, then an unknown operation (represented by ?) is applied, and the output is 63. 2. We sta

1. The problem states that the nth term of the sequence is given by the formula $$T(n) = n^2 + 2$$. 2. We need to find the 5th term, which means substituting $n = 5$ into the formu

1. **State the problem:** Simplify and evaluate the expression $$\left[ \left( \frac{\sqrt{3}}{2} \right)^2 + 2 + 1 \right]^{2021}$$. 2. **Simplify inside the brackets:** Calculate

1. **State the problem:** We have two inputs, 4 and B, each multiplied by 2 to produce outputs A and 14 respectively. 2. **Write the equations:**

1. The problem asks to find the perimeter $P$ of a trapezoid in terms of $x$. 2. The trapezoid has four sides: the vertical side $3x$, the top side $2 + x$, the bottom side $2 + 5x