🧮 algebra

1. Plantegem el problema: Tenim dues funcions $f(x)=x^2 - ax - 4$ i $g(x)=\frac{x^2}{2} + b$. Volem trobar els valors de $a$ i $b$ perquè les gràfiques de $f$ i $g$ siguin tangents

1. **State the problem:** Simplify the expression $$\frac{x^6 y^4 z^{-3}}{x^{-2} y^7 z^{-6}}$$ so that all exponents are positive. 2. **Recall the rule for dividing powers with the

1. **State the problem:** Solve the equation $ (x - 2)(x - 1) = 6 $ for $x$. 2. **Use the distributive property (FOIL) to expand the left side:**

1. **State the problem:** Simplify the expression $$\left(\frac{3pq^6}{p^4q}\right)^{-2}$$ and express the answer with positive exponents. 2. **Rewrite the expression inside the pa

1. **State the problem:** Solve the equation $$2y(y + 6) = 14$$ and find the solution set. 2. **Expand the left side:** Use the distributive property:

1. **State the problem:** We have a small box of cereal with mass $k$ grams. 2. The jumbo box is five times as heavy as the small box.

1. **State the problem:** Solve the equation $$4b^2 = 7b$$ for $b$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the quadratic equation $$x^2 + 19x = 0$$. 2. **Formula and rules:** To solve quadratic equations set equal to zero, factor the expression and use th

1. **State the problem:** Solve the equation $$2x(3x + 17) = 12$$ and check the solutions. 2. **Expand the left side:** Use the distributive property $$a(b+c) = ab + ac$$.

1. **State the problem:** Jane rents a bike for 2 hours. We want to find how much cheaper the bike with training wheels is compared to the bike without training wheels.

1. **State the problem:** We need to find the total price of a large jade plant after a 5% discount and then add 7.5% sales tax. 2. **Identify the original price:** The original pr

1. **State the problem:** Solve the quadratic equation $$x^2 + 19x = 0$$ by factoring. 2. **Write the equation:** $$x^2 + 19x = 0$$

1. **Stating the problem:** Part A: Find the selling price of a small jade plant given the markup and the final selling price.

1. **State the problem:** Solve the quadratic equation $$3v^2 + 17v + 24 = 0$$ for $v$. 2. **Formula used:** The quadratic formula for solving $ax^2 + bx + c = 0$ is

1. **State the problem:** Rita has $b. Sharon has 11.50 less than Rita. If Sharon has $h, express $h$ in terms of $b$. 2. **Write the relationship:** Since Sharon has 11.50 less th

1. **State the problem:** We have a function $$f(x) = \frac{2x + 1}{g(x)}$$ where $$g(x) = \frac{1}{3}x - 1$$. We want to find the value of $$k$$ such that the range of $$f$$ is $$

1. **State the problem:** Simplify the expression $$3 + \frac{x^2}{-2x+8}$$. 2. **Identify the formula and rules:** We need to simplify the fraction by factoring and reducing if po

1. **State the problem:** We are given a trapezoid with two parallel sides and need to find the value of $x$ given the lengths of the sides: left vertical side $10x - 2$, right ver

1. **Problem 1: Solve the inequality** $3 + y > 9$ 2. **Step 1: Isolate $y$ by subtracting 3 from both sides:**

1. Let's start by stating the problem: solving a series means finding the sum of its terms, either finite or infinite. 2. The general formula depends on the type of series. For exa

1. **State the problem:** Solve the inequality $-26 + 4y > 2$ for $y$. 2. **Add 26 to both sides:**