🧮 algebra

1. The problem asks to express 400% as a fraction and as a decimal. 2. Recall that percent means "per hundred," so 400% means 400 per 100.

1. **State the problem:** Solve for $k$ in the equation $$\frac{K+k}{k} = 6.$$ 2. **Rewrite the equation:** Multiply both sides by $k$ to eliminate the denominator:

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

1. The problem asks to write 342% as a fraction and as a decimal. 2. Recall that percent means "per hundred," so 342% means 342 per 100.

1. The problem asks to classify each of the five expressions as functions or not functions. 2. Recall that a function assigns exactly one output for each input.

1. **State the problem:** Darius fills 18 gallons of gas for 45.60. We want to find the cost for Ben to fill 21 gallons. 2. **Formula:** Cost is proportional to gallons. Use unit r

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