🧮 algebra

1. **State the problem:** We are given two inequalities: $$y \leq \frac{7}{4}x + 3$$

1. Plantegem el problema: Resolem l'equació $$x(3x-1) + 2x(x+1) = 9 - 3(2-x)$$ per trobar els valors de $x_1$ i $x_2$. 2. Desenvolupem i simplifiquem cada costat de l'equació:

1. **State the problem:** Solve the quadratic equation $$6x - x(x - 13) = 18$$ for $x$. 2. **Rewrite the equation:** Expand the term $x(x - 13)$:

1. **Statement of the problem:** Solve the quadratic equation $$x^2 + 8x = 0$$. 2. **Rewrite the equation:** The equation can be factored by taking $$x$$ common:

1. **Problem 11:** What percent of this circle is shaded? Since the problem does not provide a specific fraction or angle of the shaded part, we cannot calculate the exact percenta

1. **State the problem:** Find the slope of the line passing through the points $(-2, 5)$ and $(4, -1)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. The problem asks to identify which scenario represents a proportional relationship. 2. A proportional relationship means the ratio between two quantities is constant and the gra

1. **State the problem:** Find the discriminant of the quadratic equation and determine how many real solutions it has. The equation is given as:

1. **State the problem:** Find the discriminant of the quadratic equation and determine how many real solutions it has. 2. **Rewrite the equation:** Given $7 = -9x^2$, rewrite it i

1. **State the problem:** Solve the system of equations for $y$ in terms of $x$: $$0 = -2y + 10 - 6x$$

1. **State the problem:** Solve the system of equations: $$4x + 2y = 10$$

1. **State the problem:** Simplify the expression $\frac{2x^2 - 8}{4x}$. 2. **Write the formula and rules:** To simplify a rational expression, factor numerator and denominator and

1. **Stating the problem:** We have a 4x4 grid with shapes in each cell and totals for each row and column. We need to find the missing column total marked with a question mark. 2.

1. **State the problem:** Factor the quadratic expression $x^2 + 14x + 45$. 2. **Recall the factoring formula:** For a quadratic expression $ax^2 + bx + c$, we look for two numbers

1. **State the problem:** Factor the quadratic expression $x^2 + 11x + 24$. 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 $-15 = 5 - 8 - 4h$ for $h$. 2. **Simplify the right side:**

1. **State the problem:** Simplify the expression $$\left(\frac{x^2-4x-5}{x^2-3x-10}\right)\left(\frac{9x+3x^2}{x^2-9}\right)$$ and state the restrictions on $x$. 2. **Factor all p

1. **Problem 4:** Simplify \( \frac{2w^{-3}p}{4w^{3}p^{-2}} \) to an equivalent expression with exponents and fewest factors. 2. Use the quotient rule for exponents: \( \frac{a^{m}

1. The problem is to factor the expression $81x^{12} - 1$. 2. Recognize this as a difference of squares: $a^2 - b^2 = (a - b)(a + b)$.

1. Problem: Multiply and write each product in scientific notation. (a) Multiply \((4 \times 10^{-5})(2.1 \times 10^{-7})\).

1. **Problem:** Factor the expression $ (a + b)x^2 + 8x(a + b) + 15(a + b) $. 2. **Step 1: Factor out the greatest common factor (GCF).**