🧮 algebra

1. **Problem:** Find $x$ such that $$(-5)^{x+1} \times (-5)^5 = (-5)^7.$$ 2. **Formula and rules:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n

1. **State the problem:** Karl's truck starts with 400 liters of fuel and consumes 0.8 liters per kilometer driven. We want to find the relationship between the fuel remaining and

1. **State the problem:** We have a parabola defined by the equation $y = mx^2$ and two points on the curve: $(4, A)$ and $(8, B)$. The derivative is given by $\frac{dy}{dx} = 2mx$

1. The problem asks to express the transformed variables $X$ and $Y$ in terms of the original variables $x$ and $y$ from the given function $$y = \frac{2x}{x^3 - 8}.$$\n\n2. To lin

1. Let's start by stating the problem: What is a monic quadratic trinomial? 2. A quadratic trinomial is a polynomial of degree 2 with three terms, generally written as $$ax^2 + bx

1. **Problem Statement:** Fit a second degree polynomial of the form $$y = a + bx + cx^2$$ to the given data points: $$\begin{array}{c|ccccccc} X & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ y &

1. **State the problem:** We have a line $l$ with equation $2y = x$ and a curve $C$ with equation $y = 2x - \frac{1}{8}x^3$. The region $R$ is bounded by $l$, $C$, and a vertical l

1. **State the problem:** Calculate $$\frac{2.5 \times 10^{8} \times 8.3 \times 10^{9}}{5.6 \times 10^{-3} - 9.7 \times 10^{-4}}$$ and express the answer in standard form to 2 sign

1. المشكلة: لدينا دالة ك (س) = أ . (س) ونريد فهم العلاقة بين المتغيرات وكيفية حساب القيم المعطاة. 2. القاعدة الأساسية: الدالة ك (س) = أ . (س) تعني أن ك تعتمد على س بطريقة خطية بمعا

1. Resolver la ecuación lineal $4x + 4 = 10x + 9$. - Restamos $4x$ y $9$ de ambos lados para agrupar términos semejantes:

1. **State the problem:** Mahesh's age 16 years from now will be 3 times his present age. We need to find Mahesh's present age. 2. **Define variables:** Let Mahesh's present age be

1. **Problem Statement:** A bank manager spends fractions of his salary on various expenses and saves 3250. We need to find fractions spent on food and education, travelling, other

1. **Problem:** Find the value of $x$ in the equation $$9x + \frac{7}{8} = \frac{1}{8}$$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by moving constants to the other s

1. The problem involves evaluating the truth of statements about sets, numbers, algebraic expressions, and solving linear equations. 2. For the true/false section:

1. **Problem statement:** A bank manager spends fractions of his salary on various expenses and saves 3250. We need to find fractions spent on food and education, travelling, other

1. **State the problem:** Find the equation of the line perpendicular to the given line $3x + 5y = -9$ that passes through the point $(3, 0)$. 2. **Rewrite the given line in slope-

1. The problem states: 64 is 4 times the difference between Sarah's age $a$ and 44, and Sarah is older than 44. 2. We translate this into an equation: 64 equals 4 times $(a - 44)$

1. The problem is to calculate the values of $x$ and $y$. 2. Since no equations or additional information are provided, we cannot determine specific values for $x$ and $y$.

1. Diberikan soal: Hitung nilai dari $3^4 \cdot 3^6 \cdot 3^{-2}$. 2. Gunakan aturan pangkat untuk perkalian dengan basis yang sama: $$a^m \cdot a^n = a^{m+n}$$

1. **State the problem:** We need to find the prime factorization of 208 in the form $2^a \times b$, where $a$ and $b$ are integers and $b$ is not divisible by 2. 2. **Recall the p

1. **State the problem:** Harley needs twice as many biscuits as raspberries. Raspberries come in boxes of 12, biscuits in packets of 9.