🧮 algebra

1. **State the problem:** Solve the inequality $-7k - 5(7 + 7k) < 133$. 2. **Apply the distributive property:** Multiply $-5$ by each term inside the parentheses:

1. **State the problem:** Solve the inequality $-7k - 5(7 + 7k) < 133$. 2. **Apply the distributive property:**

1. **Problem Statement:** We need to write an equation for a rational function graphed with vertical asymptotes at $x = -1$ and $x = 2$, and the function approaches zero as $x \to

1. **Problem Statement:** We need to find a rational function $y = \frac{N(x)}{D(x)}$ with vertical asymptotes at $x=2$ and $x=4$, x-intercepts at $x=3$ and $x=6$, and a horizontal

1. **Problem Statement:** We need to find a rational function $y = \frac{P(x)}{Q(x)}$ with vertical asymptotes at $x = -4$ and $x = 1$, $x$-intercepts at $x = -6$ and $x = -3$, and

1. **Problem Statement:** Find the y-intercept, x-intercepts, vertical asymptotes, and horizontal asymptote of the function

1. **State the problem:** Factorise the expression $3x + 12$. 2. **Recall the factoring rule:** To factorise an expression, find the greatest common factor (GCF) of all terms and f

1. **State the problem:** We need to find a simplified expression for the shaded area of a large rectangle with a smaller rectangle cut out from it. 2. **Identify the dimensions:**

1. **State the problem:** Simplify the expression $$\frac{4}{5}x + 5y - \frac{1}{3}x$$. 2. **Identify like terms:** The terms $$\frac{4}{5}x$$ and $$-\frac{1}{3}x$$ are like terms

1. **State the problem:** We need to find the value of $C$ given the formula $C = 5a + 4d$ when $a = -3$ and $d = 6$. 2. **Formula used:** The formula is $C = 5a + 4d$.

1. The problem is to simplify the expression $n + b$. 2. This is a simple algebraic expression involving the addition of two variables, $n$ and $b$.

1. **State the problem:** We need to find the equation of a cubic polynomial given its graph. 2. **Identify the roots:** The graph crosses the x-axis at $x = -2$, $x = 1$, and $x =

1. **State the problem:** We need to find a linear model for the altitude $A$ (in feet) of a jet $t$ minutes after takeoff, given it passed 12,000 feet at 8 minutes and climbs at 1

1. **Problem statement:** We need to write a linear function for the distance $d$ (in miles) the plane is from its destination $t$ hours after reaching cruising altitude, given the

1. **State the problem:** We need to find a linear model for the total monthly salary $T$ of a sales executive who earns a base salary plus a commission based on sales $s$. 2. **Id

1. **State the problem:** We have two points representing the number of drills sold and their prices: $(3000, 70)$ and $(4000, 60)$. We want to find the slope of the line between t

1. **State the problem:** We are given two points on a line representing temperature $T$ in an oven at times $t$ minutes: $(4, 390)$ and $(16, 210)$. We need to find the slope of t

1. **State the problem:** Solve the inequality $$2x^2 + 18x \geq -8x - 72$$. 2. **Rewrite the inequality:** Move all terms to one side to set the inequality to zero:

1. **State the problem:** We are given two points on a line representing the value of a building over time: $(0, 60000)$ and $(30, 0)$. We need to find the slope of the line betwee

1. **State the problem:** We are given two points on a line representing the distance traveled by a motorist over time: (3, 120) and (6, 240). We need to find the slope of the line

1. **State the problem:** We are given three points $(1,4)$, $(2,7)$, and $(4,13)$ representing gallons $g$ of water at time $t$ minutes. We need to determine if these points lie o