🧮 algebra

1. **State the problem:** Kirby can complete the job in $5$ hours, and Traci can complete the same job in $11$ hours. We want to find how long it takes for both working together to

1. **State the problem:** We need to divide the polynomial $$3x^2 - 28x$$ by the binomial $$3x - 1$$ and then check the result. 2. **Recall the formula:** Polynomial long division

1. **State the problem:** Divide the polynomial $$20w^2 + 20w + 28w^3 + 31$$ by the binomial $$4w + 4$$ and express the result as quotient plus remainder over divisor. 2. **Rewrite

1. **State the problem:** We need to identify the graph of the quadratic function $$f(x) = 3x^2 + 18x + 25$$. 2. **Formula and rules:** The graph of a quadratic function $$f(x) = a

1. **State the problem:** Find the vertex and axis of symmetry of the quadratic function $$f(x) = 3(x + 5)^2 + 1$$. 2. **Recall the vertex form of a quadratic function:** $$f(x) =

1. **Understand the Problem** We need to find two consecutive positive integers whose product is 240.

1. **Understand the Problem** We need to find two consecutive positive integers, say $n$ and $n+1$, such that their product is 240.

1. **State the problem:** Solve the equation $$ (v-2)^3 + 64 = 0 $$ for real $v$. 2. **Rewrite the equation:** Recognize that $$64 = 4^3$$, so the equation becomes $$ (v-2)^3 + 4^3

1. **State the problem:** Solve the equation $$1 = x - \frac{20}{x}$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by $x$ to eliminate the fraction:

1. The problem asks where the point with coordinates $x = -1$ and $y = -8$ is located on a graph. 2. In a Cartesian coordinate system, a point is represented as $(x, y)$ where $x$

1. **Problem:** Solve the quadratic equation $x^2 - 4 = 0$ (pure quadratic). 2. **Formula and rules:** A pure quadratic equation has the form $ax^2 + c = 0$. To solve, isolate $x^2

1. **State the problem:** Simplify the expression $$\frac{2}{5} - \frac{3x}{1 - \frac{4}{5}}$$. 2. **Simplify the denominator:** Calculate $$1 - \frac{4}{5}$$.

1. **State the problem:** Simplify the expression $$-3x(1-\frac{4}{3})$$. 2. **Recall the distributive property:** When you have a number multiplied by a difference inside parenthe

1. **State the problem:** We need to divide the square root of a cylinder by 70 percent of $2.87$. 2. **Clarify the terms:** The "square root of a cylinder" is ambiguous in math te

1. **State the problem:**\nWe have two numbers $c$ and $d$ rounded to 1 decimal place: $c = 47.3$ and $d = 4.6$. We want to find the lower and upper bounds of the difference $c - d

1. **State the problem:** Add the two fractions $$\frac{7}{b+3} + \frac{4}{b+3}$$.

1. **State the problem:** We need to find the coefficients $a$, $b$, $c$, and $d$ of the cubic polynomial $$y = ax^3 + bx^2 + cx + d$$ given that the curve crosses the x-axis at $x

1. **State the problem:** We need to find the coefficients $a$, $b$, $c$, and $d$ of the cubic polynomial $$y = ax^3 + bx^2 + cx + d$$ given the roots and a point on the graph. 2.

1. **State the problem:** Find the quadratic equation $y = ax^2 + bx + c$ passing through points $(-2,43)$, $(1,10)$, and $(5,22)$. 2. **Use the general quadratic form:** $y = ax^2

1. **State the problem:** Find the equation of the line passing through the points $(-2,43)$, $(1,10)$, and $(5,22)$. 2. **Check if points are collinear:** A single line can only p

1. **State the problem:** A group of 10 people planned to pay equally for a pizza. One person left, so 9 people paid instead, each paying 60 cents more. We need to find the total b