🧮 algebra

1. **State the problem:** We want to find which expression reflects the graph of $f$ across the y-axis. 2. **Recall the rule for reflection across the y-axis:** Reflecting a functi

1. **State the problem:** We need to find the slope and y-intercept of the line given by the equation $$y = \frac{3}{4} - \frac{5}{4}x$$ and also find the slope of the line passing

1. **State the problem:** We need to find the sum $h(x)$ of two functions $f(x)$ and $g(x)$ where: $$f(x) = 4x^2 - 2x + 6$$

1. **State the problem:** We need to find how many milligrams of Medication A should be mixed when Medication B is 8 milligrams, given the original proportion of 60 mg Medication A

1. **State the problem:** We know the tax on a property assessed at $960,000$ is $15,360$. We want to find the tax $x$ on a property assessed at $820,000$ using proportions. 2. **F

1. **State the problem:** You need $1 \frac{1}{4}$ cups of sugar to make 20 cookies. How many cups of sugar are needed to make 14 cookies?

1. **State the problem:** We need to find the unknown number $n$ in the proportion $$\frac{7}{n} = \frac{4}{\frac{9}{4}}$$ and reduce the answer to lowest terms. 2. **Understand th

1. **State the problem:** We need to find the unknown number $x$ in the proportion $$\frac{13}{14} = \frac{x}{111}$$. 2. **Formula used:** In a proportion $$\frac{a}{b} = \frac{c}{

1. **State the problem:** We need to find the values of $a$, $b$, and $c$ in the quadratic equation $$3x^2 - 8x + 15 = 0$$. 2. **Recall the standard form:** A quadratic equation is

1. **State the problem:** We need to sort the given expressions into three groups: those equivalent to $2\sqrt{5}$, those equivalent to $5$, and those that are neither. 2. **Recall

1. **State the problem:** Factor the polynomial $$2x^4 - 10x^2 + 8$$ completely. 2. **Identify the structure:** Notice that the polynomial is a quadratic in terms of $x^2$. Let $y

1. **State the problem:** Simplify the expression $$\frac{(3x^{-2}y^{3})^{2}}{12x^{4}y^{-1}}$$. 2. **Apply the power to each factor inside the parentheses:**

1. **Problem Statement:** We want to understand what a quadratic equation is and how to solve one visually. 2. **What is $x^2$?**

1. **State the problem:** We are given two points $A(2, -3)$ and $B(7, k)$, and the gradient of the line passing through them is $\frac{3}{2}$. We need to find $k$ and then show th

1. **State the problem:** We want to find the percentage increase in the hippopotamus's mass from birth to two months old. 2. **Formula for percentage increase:**

1. **State the problem:** We need to factor the quadratic expression $$x^2 - 9x + 18$$.

1. **State the problem:** Factorise the quadratic expression $$x^2 + 5x + 6$$. 2. **Recall the formula:** To factorise a quadratic of the form $$x^2 + bx + c$$, find two numbers th

1. The problem is to find the value of $M$. 2. To find $M$, we need an equation or context relating $M$ to other known values.

1. **State the problem:** We need to find two equations of lines passing through the point $(4, -2)$: one parallel and one perpendicular to the line $4x + 7y = 9$.

1. **State the problem:** We need to find two lines passing through the point $(5, -3)$: one parallel and one perpendicular to the line $5x + 7y = 9$. 2. **Find the slope of the gi

1. **State the problem:** We need to find the slope of the line passing through the points $(-3, 0)$ and $(1, -3)$ and represent the "rise" and "run" visually. 2. **Formula for slo