🧮 algebra

1. **State the problem:** We are asked to estimate two expressions by rounding each number to 1 significant figure and then computing the results. ---

1. **State the problem**: Given the polynomial $$f(x) = x^4 - 2x^3 + 48x^2 + 4x - 100$$ and one zero $$1 - 7i$$, find all zeros of $$f(x)$$ in exact form. 2. **Recall complex conju

1. Let's state the problem: Evaluate the expression $7 - 8(2) * -3 + 13$. 2. According to the order of operations (PEMDAS/BODMAS), we first calculate the multiplication inside the

1. **State the problem:** We are given a pair of simultaneous equations represented by two graphs: a green line and a purple downward-facing parabola. We want to find their solutio

1. **Problem statement**: We have multiple exercises involving functions and their combinations. ### Exercise 1.14

1. **State the problem:** Jim sold 10 tickets. Singh sold three times Jim's number plus 4 more tickets. Each ticket costs 5. We are to find the total money received by both boys. 2

1. The problem states: given any two consecutive even numbers, find the common multiples of the sum of their squares. 2. Let the first even number be $2n$ where $n$ is an integer.

1. **Problem Statement:** Prove that the difference between the squares of any two consecutive integers is equal to the sum of these integers. Then, find two consecutive integers w

1. Let's start by stating the problem: simplify the equation provided. Since the equation was not explicitly given, please provide the exact equation you'd like to simplify. 2. If

1. The problem is to solve the equation $$3(y=2)*x-1/y-2=3(y=2)*2/3$$ for $x$ and $y$. 2. First, clarify the expression. Assuming "3(y=2)" means substituting $y=2$ into the equatio

1. **Énoncé du problème :** Nous devons expliquer la multiplication et la simplification du numérateur et du dénominateur de l'expression donnée : $$\frac{\left(2x + 4\right)^{\fra

1. The problem is to find the least common multiple (LCM) or \textit{ppcm} of 174 and 406.\n2. Start by finding the prime factorizations of 174 and 406.\n3. Prime factorization of

1. لنحسب **القاسم المشترك الأكبر (pgcd)** للعددين 406 و174.\n 2. نستخدم خوارزمية إقليدس:

1. The problem is to solve the linear equation $3x + 4x - 34 = 0$ for $x$. 2. Combine like terms on the left side: $3x + 4x = 7x$, so the equation becomes $7x - 34 = 0$.

1. **Problem:** A water balloon is catapulted from a building with height function $$h(t) = -5t^2 + 30t + 10$$. We want to determine:

1. **State the problem:** We need to simplify the expression $$\frac{(2n + 3)^2 - (2n + 1)^2}{6n + 6}$$ for all positive values of $n$, and find $a$ and $b$ such that the simplifie

1. The problem asks to evaluate the expression $6 \times 0$. 2. According to the multiplication property of zero, any number multiplied by zero equals zero.

1. **Solve the system by Gauss-Jordan elimination:** Given system:

1. **Stating the problem:** We need to determine which expressions are even for all integer values of $n$. An expression is even if it is divisible by 2 for every integer $n$. 2. *

1. The problem gives the expression involving variables $a$ and $b$ with multiple terms and then a graph description. 2. First, simplify the algebraic expressions step-by-step:

1. **State the problem:** We want to understand the expressions: