🧮 algebra

1. The problem is to understand the graph of the function $$g(x) = (0.5)^{x + 3} - 4$$. 2. This is an exponential decay function because the base $$0.5$$ is between 0 and 1.

1. **State the problem:** Multiply the mixed numbers $1 \frac{2}{3}$ and $1 \frac{1}{6}$ and express the answer as a mixed number in simplest form. 2. **Convert mixed numbers to im

1. **State the problem:** Solve the equation $$4^x - 13 \times 2^x + 40 = 0$$. 2. **Rewrite the equation using powers of 2:** Note that $$4^x = (2^2)^x = 2^{2x} = (2^x)^2$$.

1. El problema consiste en encontrar la ecuación general de una recta a partir de su forma punto-pendiente o cualquier otra forma. 2. La ecuación general de la recta se expresa com

1. El problema es encontrar la ecuación en forma general de una recta. 2. La forma general de la ecuación de una recta es $$Ax + By + C = 0$$ donde $A$, $B$ y $C$ son constantes re

1. **State the problem:** We need to make $x$ the subject of the formula given by $$2y^2 = \frac{5(x - 3)^5}{3y}.$$ 2. **Write down the formula and explain:** The goal is to isolat

1. **State the problem:** Calculate the value of $193^2 - 7^2$. 2. **Use the difference of squares formula:**

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: