🧮 algebra

1. **State the problem:** Factor the quadratic expression $2x^2 - 3x - 20$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. **Problem Statement:** We are given the amount of medication in the body over time $t$ hours during a 6-hour period, with the amount $a$ in mg. The data is:

1. **Problem Statement:** Given the quadratic function in vertex form $f(x) = 3(x - 4)^2 + 2$, find the vertex, determine if it has a maximum or minimum value, find the axis of sym

1. **State the problem:** Simplify the expression $$\frac{30x^{-8}y^{9}z^{7}}{6y^{-4}z^{-2}}$$ and write the answer using only positive exponents. 2. **Recall the rules:**

1. **Problem:** Find the sale price of shorts originally priced at 35 with a 20% discount. 2. **Formula:** Sale Price = Original Price - (Discount Rate \times Original Price)

1. **State the problem:** We want to complete the equation $$-2(z + 3) - z = \square - 4(z + 2)$$

1. **State the problem:** We are given points on a graph that show the relationship between Height and Width, described by the equation $$\text{Height} = \text{Constant} \times \te

1. The problem asks to find the constant in the equation $$\text{Height} = \text{Constant} \times \text{Width}$$ given points on the graph: (0.5, 1), (2, 4), (3, 6), and (5, 10). 2

1. Algebraic Fraction (Addition and Subtraction): - Problem: Simplify $\frac{a}{b} + \frac{c}{d}$ or $\frac{a}{b} - \frac{c}{d}$.

1. Let's start with algebraic fraction addition and subtraction. The key formula is to find a common denominator: $$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$$. Always mul

1. Problem 2.98: Klient banku spłacił pożyczkę w wysokości 13923 w czterech ratach, z których każda następna była o 10% większa od poprzedniej. Oblicz kwotę pierwszej i czwartej ra

1. **State the problem:** We are given a graph of a linear function passing through points near $(-10,10)$ and $(10,-10)$, and we need to find which equations have the same slope a

1. The problem is to solve the quadratic equation $$7x^2 + 2x + 8 = 0$$ using the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to find the coordinate of the point that divides the segment between points A and B in the ratio 3:2. 2. **Identify given points:** Point A is at

1. **State the problem:** Divide the polynomial $x^3 + x^2 - x + 2$ by $x + 4$ using long division. 2. **Recall the long division formula:** When dividing $P(x)$ by $D(x)$, we find

1. **Problem statement:** We are given the equation of a stone archway as $$10x^2 + 9y - 90 = 0$$ and need to write an inequality representing the region below the archway. 2. **Re

1. **State the problem:** Simplify the sum of the two polynomials: $$(2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6)$$

1. **State the problem:** Graph the quadratic inequalities: a) $y > -x^2 - 3x - 4$

1. The problem is to find the square root of 100000. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Fully factorise the expression $$36c^2 - d^2$$. 2. **Recognize the formula:** This is a difference of squares, which follows the rule $$a^2 - b^2 = (a - b

1. We are asked to solve the quadratic equation $m^2 = 4(2m + 5)$. 2. First, expand the right side: