🧮 algebra

1. **State the problem:** Calculate $4.8 \times 10^6 + 3.7 \times 10^7$ and express the answer in standard form. 2. **Recall the standard form:** A number in standard form is writt

1. Il problema chiede di creare esercizi simili all'esercizio 6, quindi iniziamo definendo un esercizio tipo. 2. Supponiamo che l'esercizio 6 fosse risolvere un'equazione di primo

1. Problema este să calculăm cubul sumei $1 - 64t^{15}$. 2. Formula pentru cubul sumei a două expresii $a$ și $b$ este $$ (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 $$

1. The problem involves simplifying and factoring cubic expressions such as $100e^3 + 400 \, 40e + 16$, $125 + 216b^3$, and $429a^3 - 27b^3$. 2. Recall the sum and difference of cu

1. **Factorize completely:** (a)(i) Factorize $2r^2 - 8r$.

1. **State the problem:** Solve the equation $8p - p + 2 = 0$ for $p$. 2. **Combine like terms:** The terms with $p$ are $8p$ and $-p$. Combine them:

1. **Problem Statement:** (a) Factorize completely:

1. **Problem statement:** Given that $(x-1)$ and $(x+3)$ are factors of the cubic polynomial $$x^3 + ax^2 + bx + 12,$$ find the values of $a$ and $b$, the remaining factor, and the

1. **State the problem:** Solve the equation $8p_p + 2 = 0$ for $p$. 2. **Interpret the notation:** The expression $8p_p$ is ambiguous. Assuming it means $8p \cdot p$ (i.e., $8p^2$

1. Problema: Calcolare il valore delle espressioni date. 2. Formula e regole importanti:

1. **State the problem:** Simplify the expression $\frac{1}{2} \left( \frac{3}{2}x + \frac{1}{5} \right)$.\n\n2. **Recall the distributive property:** For any numbers $a$, $b$, and

1. **State the problem:** We need to find the equation of the trend line passing through the two yellow points on the scatter plot, which are approximately at $(5,1)$ and $(6,9)$.

1. **State the problem:** Simplify the expression $\frac{1}{2} \left( \frac{3}{2}x + \frac{1}{5} \right)$.\n\n2. **Recall the distributive property:** $a(b + c) = ab + ac$. We will

1. The problem is to understand what a logarithm is and how to work with it. 2. A logarithm answers the question: to what power must we raise a base number to get another number? T

1. **State the problem:** Express \(5 - 2\sqrt{10} \div 3\sqrt{5} + \sqrt{2}\) in the form \(m\sqrt{2} + n\sqrt{5}\) where \(m\) and \(n\) are rational numbers. 2. **Rewrite the ex

1. Énonçons le problème : Étudier le signe du polynôme $P(x) = -3x - 15$. 2. Rappel : Pour étudier le signe d'un polynôme du premier degré $ax + b$, on cherche les valeurs de $x$ p

1. **State the problem:** Express $8 - 3\sqrt{6}$ in the form $m\sqrt{3} + n\sqrt{2}$ where $m$ and $n$ are rational numbers. 2. **Recall the form:** We want to find rational numbe

1. (a) (i) Calculate the exact value of \( \frac{1 \frac{4}{5} - \frac{1}{3}}{2 \frac{2}{5}} \). Step 1: Convert mixed numbers to improper fractions.

1. The problem is to solve the quadratic equation using the method shown in the photo, which is likely the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to find the equation of an exponential function of the form $$y = a(2)^x + d$$ given that the graph is a vertical reflection and shift of $$y = 2^

1. (a) (i) Calculate the exact value of $1 \frac{4}{5} - 1 \frac{3}{2} \frac{2}{5}$. Step 1: Convert mixed numbers to improper fractions.