🧮 algebra

1. **State the problem:** John bought large and small bottles of drinks. Large bottles are sold 2 for 15, small bottles 3 for 10. He spent 100 more on large bottles than small bott

1. Planteamos el problema: Resolver la ecuación $$\frac{1 + 2x}{1 + 3x} - \frac{1 - 2x}{1 - 3x} = \frac{3x - 14}{1 - 9x^2}$$. 2. Observamos que el denominador del tercer término es

1. **Stating the problem:** Je hebt een harde schijf van 4 TB (terabytes) gekocht. Je hebt al 1400 GB aan bestanden erop gezet. Het advies is om 25% van het geheugen vrij te houden

1. **State the problem:** Factor the polynomial $$x^3 + 9x^2 + 14x - 24$$ completely given that $$x + 6$$ is a factor. 2. **Use synthetic division:** Since $$x + 6$$ is a factor, u

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 + 10x + 41$. 2. **Recall the quadratic form:** A quadratic expression is generally written as $ax^2 + bx

1. **State the problem:** We want to find the linear equation $y = mx + b$ that best fits the data points $(1,71), (2,91), (3,109), (4,125), (5,142), (6,157)$ using linear regressi

1. **State the problem:** Simplify the expression $$\frac{11}{2} \times \left( \frac{2}{5} + \frac{1}{2} - \frac{2}{3} \right) + \frac{3}{4} \div \frac{3}{5}.$$\n\n2. **Simplify in

1. **State the problem:** Calculate the sum of $\frac{1}{2} + \frac{1}{2}$.\n\n2. **Formula used:** When adding fractions with the same denominator, add the numerators and keep the

1. **State the problem:** Find the polynomial function with real coefficients that has zeros at $0$, $3$, and $3+i$. 2. **Recall the rule for complex roots:** If a polynomial has r

1. **State the problem:** Solve the quadratic equation $x^2 + 4x - 4 = 0$. 2. **Formula used:** The quadratic formula is given by

1. The problem is to calculate $2^{100}$. 2. The formula used is the exponentiation rule: $a^n$ means multiplying $a$ by itself $n$ times.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-6x - 2y - z = -17 \\ 5x + y - 6z = 19 \\ -4x - 6y - 6z = -20 \end{cases}$$

1. **State the problem:** Solve the system of equations using substitution: $$\begin{cases}-6x - 2y - z = -17 \\ 5x + y - 6z = 19 \\ -4x - 6y - 6z = -20 \end{cases}$$

1. **Problem a:** Find the missing value in the equation $a - 25 = 36$. 2. To solve for $a$, use the formula for solving linear equations: if $x - b = c$, then $x = c + b$.

1. **State the problem:** Rewrite the polynomial $12a^2b^4 - 36a^2b + 44abc$ as the product of a monomial and a polynomial. 2. **Identify the greatest common factor (GCF):**

1. **State the problem:** Multiply the expressions $$(7x^2 + a^2)(x^2 - 3a^2)$$. 2. **Recall the distributive property:** To multiply two binomials, multiply each term in the first

1. **State the problem:** We need to order the functions $f(x)$, $g(x)$, and $h(x)$ by their maximum values from smallest to largest. 2. **Find the maximum value of $f(x) = (6 - x)

1. **State the problem:** Identify the error in generating an expression equivalent to $$4 + 2x - \frac{1}{2} (10 - 4x)$$ and then correct the error. 2. **Original expression:** $$

1. **State the problem:** We are given that $a - b = b - c = 2$ and need to find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$

1. **Énoncé du problème :** Développer l'expression $4(x + 2)$ en utilisant la distributivité. 2. **Formule utilisée :** La distributivité s'exprime par $a(b + c) = ab + ac$.

1. The problem states that the zero of the linear function is the ordered pair $(2,0)$. This means the function crosses the x-axis at $x=2$. 2. A zero of a function is a point wher