🧮 algebra

1. **State the problem:** Solve the equation $\frac{K+k}{k} = 6$ for $K$. 2. **Understand the formula:** The equation is a fraction where the numerator is $K+k$ and the denominator

1. **State the problem:** Noah's pay $p$ is directly proportional to the hours $h$ he works. Given $p=192$ when $h=8$, find $h$ when $p=336$. 2. **Write the formula for direct prop

1. **State the problem:** Factor the quadratic expression $$g^2 + 12g - 13$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two num

1. **State the problem:** Simplify the expression $$(3x^2 + 2x - 7) - (x^2 - x + 6)$$. 2. **Apply the subtraction:** Distribute the minus sign to each term inside the second parent

1. **State the problem:** Factor the quadratic expression $m^2 + 18m + 17$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. **State the problem:** Solve the equation $$\frac{x}{7} = 14$$ for $x$. 2. **Formula and rule:** To solve for $x$ when it is divided by a number, multiply both sides of the equa

1. **State the problem:** Factor the quadratic expression $f^2 + 5f + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. The problem asks whether the solution to a system of equations is any ordered pair that makes both equations true. 2. A system of equations consists of two or more equations wit

1. **State the problem:** Simplify the expression $$[(-7 + \frac{12}{5}) \cdot \left(-\frac{15}{4}\right) \cdot \left(-\frac{5}{2}\right)] : \left(\frac{5}{4}\right)$$ 2. **Rewrite

1. **State the problem:** We are given a recurrence relation with initial terms: $$a_1 = -4, \quad a_2 = 5$$

1. **State the problem:** We are given a sequence defined by the recurrence relation: $$a_1 = 0, \quad a_2 = 1, \quad a_n = a_{n-1} + a_{n-2} \text{ for } n \geq 3$$

1. **State the problem:** We are given the cubic function $$y = x^3 - 3x^2 + 5x - 3$$ and we want to analyze it. 2. **Recall the function:** $$y = x^3 - 3x^2 + 5x - 3$$ is a cubic

1. **State the problem:** Factor the quadratic expression $$p^2 + 12p + 20$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two num

1. **State the problem:** Factor the quadratic expression $n^2 + 6n + 8$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** We are given a function $y=5^x$ with domain $x \geq 0$ and points $(1,4)$ and $(2,16)$ that the graph passes through. 2. **Check if the points lie on the

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{18}{128}}$$. 2. **Recall the cube root property:** The cube root of a fraction is the fraction of the cube roots,

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{18}{125}}$$. 2. **Recall the cube root property:** The cube root of a fraction is the fraction of the cube roots,

1. **State the problem:** Simplify the expression $$\sqrt{2} \cdot \frac{\sqrt{2}}{3} + \sqrt{3} \cdot \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3}$$. 2. **Reca

1. The problem is to understand the steps from the left term to the right term. 2. Since the user did not provide explicit expressions, I cannot show exact algebraic steps.

1. The problem is to understand how to transform the term on the left side of an equation or expression into the term on the right side. 2. Generally, this involves applying algebr

1. **State the problem:** Expand the expression $ab^3 c^4$ using multiplication. 2. **Recall the rules:** When variables are multiplied, write them together with multiplication sym