🧮 algebra

1. **State the problem:** Make $x$ the subject of the formula given by $$6y = x^2$$. 2. **Recall the formula and rules:** The equation relates $x^2$ to $6y$. To isolate $x$, we nee

1. The problem states that the marking scheme assigns the value of $c$ as 10. 2. This means $c = 10$ is given directly by the marking scheme.

1. **State the problem:** We are given a function $f(x) = 2x + 5$ and an expression involving $f(x)$: $$f(x)f(x) - ff(x) = ax^2 + bx + c.$$ We need to find the values of $a$, $b$,

1. **State the problem:** We have an L-shaped polygon made of two rectangles with side lengths involving $x$. The area is given as 10 m², and the equation for $x$ is $$3x^2 + 2x -

1. **State the problem:** Make $x$ the subject of the formula given by $$2y(6x + 1) = 5z$$. 2. **Expand the left side:** Use the distributive property to expand:

1. **State the problem:** We need to make $x$ the subject of the formula given by $$y = 1 - 9x$$. 2. **Write down the formula:** $$y = 1 - 9x$$.

1. **State the problem:** Solve the equation $|x-2|=9$ for $x$. 2. **Recall the definition of absolute value:** For any real number $a$, $|a|=b$ means $a=b$ or $a=-b$ where $b\geq0

1. **State the problem:** Three times a number decreased by 5 equals 16. 2. **Translate the problem into an equation:** Let the number be $x$. Then, three times the number is $3x$.

1. Problemet handlar om att Jonathan Sexton har 3/4 liter vatten och ger bort 1/3 av detta till en lagkamrat. 2. Vi ska räkna ut hur mycket vatten han ger bort: $$\frac{1}{3} \time

1. Problemet är att hitta lutningen på den linjära funktionen given av ekvationen $$2y - 8x + 4 = 0$$. 2. För att hitta lutningen på en linjär funktion i formen $$Ax + By + C = 0$$

1. We are asked to simplify or evaluate the expression $$125 + 80a^2$$. 2. This expression consists of two terms: a constant term 125 and a term with a variable $$80a^2$$.

1. **State the problem:** Solve the equation $3(x + 5) + 2(2x + 3) = 0$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor out

1. The problem asks to match each algebraic expression with its corresponding graph. 2. The algebraic expressions given are:

1. **State the problem:** We need to find the value of the expression $4p - 3m$ when $p = 5$ and $m = 2$. 2. **Write the expression:** The expression given is:

1. **Problem statement:** We have three lines r, s, and t with given points P and Q. We need to find the slope $m$, y-intercept $b$, and coordinates of points P and Q for each line

1. **Problem statement:** Calculate the slope (malda) of the lines p and q given their points. 2. **Formula for slope:** The slope $m$ of a line passing through points $(x_1,y_1)$

1. **Stating the problem:** Calculate the following polynomial operations given:

1. The problem asks for the function $g(x)$ which is the reflection of $f(x) = 6 \left(\frac{1}{3}\right)^x$ across the y-axis. 2. Reflection across the y-axis means replacing $x$

1. The problem asks how the functions $f(x) = 0.7 \times 6^x$ and $g(x) = 0.7 \times 6^{-x}$ are related. 2. Recall that reflecting a function $f(x)$ over the y-axis means replacin

1. Problem: Simplify $(-2x - x) \cdot (-2)$. Formula: Use distributive property $a(b+c) = ab + ac$.

1. **State the problem:** We have three functions: $$f(x) = - \frac{6}{11} \left(\frac{11}{2}\right)^x, \quad g(x) = \frac{6}{11} \left(\frac{11}{2}\right)^{-x}, \quad h(x) = - \fr