🧮 algebra

1. Problem: Given $x - 5 = -8$, evaluate $(x^2 - 5)(x^{-3} - x)$. 2. First, solve for $x$:

1. The problem asks if the relationship between $x$ and $y$ in the table is proportional and to find the constant of proportionality if it exists. 2. A proportional relationship me

1. **State the problem:** Simplify the expression $24y^2 + 16y$ by factoring. 2. **Recall the factoring formula:** To factor an expression, find the greatest common factor (GCF) of

1. **State the problem:** Expand and fully simplify the expression $$(2x - 1)(x - 5)(x + 6)$$. 2. **Use the distributive property (FOIL for binomials) step-by-step:** First, multip

1. **Stating the problem:** We want to find a formula for the number of matches $T_n$ used to make $n$ hexagons joined side-by-side, where each additional hexagon shares one match

1. **State the problem:** Solve the inequality $$\frac{3}{x-4} \leq \frac{2}{x-3}$$ for $x$. 2. **Rewrite the inequality:** Bring all terms to one side:

1. **Problem a:** Prove by mathematical induction that $$2 + 7 + 12 + \cdots + (5n - 3) = \frac{n}{2}(5n - 1)$$ for all positive integers $n$. 2. **Base case:** For $n=1$, the left

1. **State the problem:** Solve the equation $$\frac{7}{3x + 1} = \frac{2}{x + 2}$$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products

1. The problem is to solve the equation of everything, which is not a specific mathematical equation. 2. To solve an equation, we need a clear expression or formula.

1. **Identify the domain and range of** $y=\sqrt{x-2}+5$. 2. **Domain**: The expression inside the square root must be non-negative.

1. **State the problem:** We are given the function $f(t) = 243 \left(\frac{3}{5}\right)^t$ which models the number of stray cats $t$ years after an animal control program started.

1. **State the problem:** We need to find the percentage increase in the price of a sofa that was originally 540 and increased by 135. 2. **Formula for percentage increase:**

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{