🧮 algebra

1. The problem asks to find the geometric means of the sequence: 0.5, ____, ____, ____, 2048. 2. The geometric means are the terms between the first and last term in a geometric se

1. The problem asks to find the sixth term of the expansion of $ (c + d)^{10} $. 2. The general term in the binomial expansion of $ (a + b)^n $ is given by:

1. Problem statement: Diana wants to buy three equally priced pants for a total of 84 euros. She has 140 euros in cash. 2. Find the price of one pant by dividing the total cost by

1. **Problem statement:** Helmut earns 25 euros for 2.5 hours of work. We want to find out how much he earns after 12 hours. 2. **Formula and rule:** Since the pay is proportional

1. **State the problem:** Simplify the fraction $\frac{2444}{27}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common divis

1. **State the problem:** Solve the linear equation $5x - 10 = 2x + 20$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of th

1. **State the problem:** Simplify the expression $$(2x^2 - 2x - 12)(3x^2 - 10x + 3).$$ 2. **Factor each polynomial:**

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 2x - 12}{3x^2 - 10x + 3}$$ and determine which of the given options matches the simplified form. 2. **Factor numera

1. **State the problem:** Calculate the sum and difference of the fractions $\frac{14}{27} + \frac{5}{27} - \frac{16}{27}$ and simplify the result. 2. **Formula and rules:** When a

1. **Stel het probleem vast:** We hebben punten $A(k,1)$ en $B(-1,2)$ en een rechte $r: 2x - 3y - 2 = 0$.

1. **State the problem:** We have three equations involving three items: red apple (A), banana bunch (B), and coconut half (C). The equations are: $$A + B + B = 18$$

1. **State the problem:** Find the distance between points $M(5, -6)$ and $N(-3, -10)$ rounded to the nearest tenth. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)

1. **Probleemstelling:** We onderzoeken de bevolkingsgroei tussen 1500 en 1000, berekenen de gemiddelde bevolkingstoename per jaar tussen 400 v.Chr. en 1500 n.Chr., bepalen in welk

1. Masalah: Perkalian aljabar koefisien dengan variabel. 2. Rumus dasar perkalian aljabar adalah mengalikan koefisien dan variabel secara terpisah:

1. **State the problem:** We need to find the equation of a straight line that is parallel to line AB and passes through point P. 2. **Formula and rules:**

1. **State the problem:** Solve the equation $$4^x - 3(2^x) = -2$$ for $x$. 2. **Rewrite the equation using properties of exponents:** Note that $$4^x = (2^2)^x = 2^{2x} = (2^x)^2$

1. **Stating the problem:** Given the straight line AB with equation $y = 2x + 6$, find the equation of a straight line parallel to AB that passes through point $P(6,4)$.

1. **State the problem:** Solve the system of linear equations: $$7x + 3y = 3$$

1. **Problem Statement:** Find which of the given numbers lies between $\frac{3}{4}$ and $\frac{7}{8}$.\n\n2. **Step 1: Convert fractions to decimals for easier comparison.**\n$\fr

1. **State the problem:** Jenn earns 150 per hour and tutored for 3 hours on Monday, 2 hours on Wednesday, and 4 hours on Saturday. We need to find how much she earned for the whol

1. Diberikan persamaan kuadrat $$x^2 - 7x + 5 = 0$$. Tentukan nilai dari: (1) $$x_1^2 + x_2^2$$