🧮 algebra

1. **Problem Statement:** Factorise the expression $$9x^2 - 4$$. 2. **Formula and Rules:** This expression is a difference of squares, which follows the formula $$a^2 - b^2 = (a -

1. The problem is not specified clearly, so I will explain how to approach solving a general algebraic problem. 2. Typically, to solve an algebraic equation, you isolate the variab

1. **Solve the quadratic equation:** $12x^2 - 40 = 17x$ to 2 decimal places. Step 1: Rewrite the equation in standard form:

1. The quadratic function can have at most two x-intercepts. **True.** A quadratic function is a polynomial of degree 2, so it can have 0, 1, or 2 real x-intercepts.

1. The problem is to continue the expression or equation for the term involving $4d$. 2. Without additional context, we assume the task is to simplify or express terms involving $4

1. **Stating the problem:** We are given a proportional relationship between pens and copies: 3 pens = 5 copies. We want to find how many copies correspond to 9 pens. 2. **Formula

1. The problem asks which type of equation the quadratic formula can solve. The quadratic formula is used to solve quadratic equations of the form $$ax^2 + bx + c = 0$$.

1. **State the problem:** Factor the quadratic polynomial $$2x^2 + 11x + 15$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that

1. Problem 4a: Cost of 5 books and 10 copies are the same. Cost of 10 books and 20 copies is 3000. Find cost of 10 books. 2. Let cost of 1 book = $b$ and cost of 1 copy = $c$.

1. The problem asks which key properties of a parabola can be determined from the equation in factored form without graphing or solving. - Factored form is $y = a(x - r_1)(x - r_2)

1. **Problem statement:** We are given the expression $3x^2 - 4ax - 4a^2$ which is exactly divisible by $x + 2$. We need to find the value of $a$. 2. **Key concept:** If a polynomi

1. **State the problem:** Find the exact location of all relative and absolute extrema of the function $$f(x) = 3x^2 - 12x - 15$$ on the domain $$[0, 5]$$. 2. **Recall the formula

1. State the problems. Problem 1: Simplify the expression $\frac{3}{2z - \frac{3}{2}}$.

1. **State the problem:** We want to analyze and understand the function $$y = \frac{3}{2x - \frac{3}{2}}$$. 2. **Rewrite the denominator:** The denominator is $$2x - \frac{3}{2}$$

1. **State the problem:** We need to find the inverse function $f^{-1}(x)$ of a given function $f(x)$. 2. **Recall the definition:** The inverse function $f^{-1}(x)$ satisfies the

1. **State the problem:** We need to find a two-digit number divisible by 4, whose digits add up to 10, and when reversed, the new number is smaller than the original by 18. 2. **D

1. **State the problem:** Find the equation of the perpendicular bisector of the line segment AB where A = (1,7) and B = (5,15). 2. **Find the midpoint M of AB:** The midpoint form

1. **Problem statement:** Paul and Andrew tiled a hall of area 325 square feet. Paul worked first alone, then Andrew finished the job alone. The total time was 4.5 hours. We need t

1. **Problem statement:** (a) Find the coordinates where the graph of $y = 5x - 3$ crosses the y-axis.

1. Problem statement: Solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. Formula used: The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$,

1. Masalah: Menentukan sistem pertidaksamaan yang membatasi daerah yang diarsir pada grafik dengan titik-titik sudut (0,4), (3,6), dan (7,0). 2. Langkah pertama adalah menentukan p