🧮 algebra

1. **State the problem:** Josie scored 1276 points in Round 1 and 1234 points in Round 2. We need to find the percentage decrease in her score. 2. **Formula for percentage decrease

1. **State the problem:** We have the numbers 45, 46, 41, h, 41, 41, 43, 43, 46 and the mean of these numbers is 43. We need to find which value of $h$ (either 41 or 59) satisfies

1. **State the problem:** We have a data set with numbers 7, 7, 4, 4, 6, 7, and an unknown number $k$. We know the mean of these numbers is 6. We need to find the value of $k$. 2.

1. **State the problem:** We need to find the ratio of glass to plastic in a recycling bin where there are 4 kg of glass and 500 g of plastic. 2. **Convert units to be consistent:*

1. **State the problem:** We have three number cards with values $8$, $2$, and a missing number $x$. The median of these three numbers is $8$, and the range is $7$. 2. **Recall def

1. The problem states that the weight $y$ of a goldfish is modeled by the linear equation $$y = 10x - 2000$$ where $x$ is the length in millimeters. 2. We are asked to find the wei

1. The problem is to find the percentage value, which you mentioned as 19.71%. Let's clarify what this percentage represents and how to calculate it if needed. 2. The general formu

1. **Problem statement:** A gardener has 18 metres of timber fencing to enclose a rectangular vegetable patch using a straight stone wall as one side. The width is $x$ metres. We n

1. **State the problem:** Solve the quadratic equation $$-2x^2 + 18x - 30 = 0$$. 2. **Write down the formula:** The quadratic formula to solve $$ax^2 + bx + c = 0$$ is $$x = \frac{

1. Let's clarify the step where division was performed. 2. When dividing an expression, the sign of the first number can be negative; division rules apply as usual.

1. **State the problem:** Solve the equation $$30 = 18x - 2x^2$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to factorize the expression given by the equation $$0 = 09 - 8t \times xe$$. 2. First, simplify the constant term: $$09 = 9$$, so the equation becomes $$0 = 9 - 8

1. **State the problem:** A gardener has 18 metres of timber fencing to enclose a rectangular vegetable patch using a stone wall as one side. The width of the patch is $x$ metres.

1. **State the problem:** Simplify the expression $$3 + \frac{(9 - 1)}{4}$$ using the order of operations (PEMDAS). 2. **Recall the order of operations:** Parentheses first, then E

1. **State the problem:** Simplify the expression $2 + (6 \div 6) \times 8$ using the order of operations (PEMDAS). 2. **Recall the order of operations:** Parentheses, Exponents, M

1. The problem asks to create a table for the reflection about the origin of the function $f(x) = (x + 2)^2 + 1$. 2. The reflection about the origin of a function $f(x)$ is given b

1. **State the problem:** We want to simplify the expression $e^{\ln a^x}$. 2. **Recall the properties of logarithms and exponentials:** The natural logarithm $\ln$ and the exponen

1. **State the problem:** Add the fractions $\frac{1}{2}$ and $\frac{4}{5}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wh

1. The problem is to multiply the numbers $2$, $-\frac{2}{3}$, and $\frac{3}{4}$.\n\n2. The multiplication rule for fractions and integers is to multiply the numerators together an

1. **Problem Statement:** We want to find pairs of numbers from the set $\{1, 2, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9\}$ that can produce the numbers in the set $\{

1. The problem is to understand how to factor algebraic expressions. 2. Factoring means rewriting an expression as a product of simpler expressions.