🧮 algebra

**Part I — Identifying Key Features of Polynomial Functions** 1. Given each polynomial function, find its factored form, leading coefficient, degree, and end behavior.

1. **State the problem:** We are given a piecewise function:

1. The problem is to add the two fractions $\frac{25}{4}$ and $\frac{9}{4}$ and express the result as a mixed number. 2. Since the denominators are the same, we can add the numerat

**Problem 1:** 12% of 72 is what number? 1. This is a percentage problem where the percentage is 12%, the base is 72, and we need to find the rate (the part).

1. Stating the problem: Factor and simplify the cubic polynomial $$4x^3 + 16x^2 + 12x$$. 2. First, look for the greatest common factor (GCF) among all the terms.

1. Stating the problem: Convert the decimal number 9.519 into a simplified mixed fraction. 2. Separate the integer and decimal parts:

1. Énoncé du problème : On considère la fonction $f(x) = \frac{a x + 2}{2 x + 1}$ avec $a \in \mathbb{R}$. Il faut étudier la position relative des courbes $(C)$ et $(D)$, démontre

1. The problem is to express the decimal 0.285 as a fraction and potentially as a mixed number. 2. First, write 0.285 as a fraction with denominator 1000 because it has three decim

1. The problem states a percentage completion of 31% towards a goal of 40 units. 2. To find out how many units correspond to 31%, calculate $\frac{31}{100} \times 40$.

1. The problem asks us to analyze and find key features of two polynomial functions given by: A. $y = x^3 + 2x^2 - 16x - 32$

1. The problem involves understanding and expressing the value 5.605 in various number formats. 2. The first rectangle labeled "Number" shows a simple value represented by one vert

1. The problem is to understand and express the operation $M^N$ where $M$ and $N$ typically denote numbers or variables, and the caret symbol $^$ indicates exponentiation. 2. Expon

1. Stating problem 19: Price of chicken is 3 times price of bread. Total spent on 1 bread + 1 chicken = RM5 - RM1 = RM4. 2. Let price of bread = $x$. Then price of chicken = $3x$.

1. Given functions and operations: \( f(x) = \sqrt{x} + 5, \quad g(x) = \frac{x - 10}{3}, \quad h(x) = (x + 2)^2 \)

1. The problem states that Hadi's car uses 50 liters of petrol for 510 km. 2. Calculate the petrol consumption per kilometer:

1. **State the problem:** Solve the inequality $p - 1 + 7 \ge 5 - 1$.\n\n2. **Simplify both sides:** On the left side, combine $-1$ and $7$:\n$$p - 1 + 7 = p + 6.$$\nOn the right s

1. Stating the problem: Solve the inequality $X + 5 - 5 \geq 9 - 5$. 2. Simplify both sides: On the left side, $5 - 5 = 0$, so the inequality becomes $X \geq 9 - 5$.

1. **State the problem:** Solve the inequality $-\frac{z}{2} + 4 \geq 2$ for $z$. 2. **Isolate the variable term:** Subtract 4 from both sides to get

1. Problem 1: The function is defined by $q(p)=\frac{1}{1-p}$, where $p\neq 1$. 1.i. Why is 1 excluded from the domain?

1. **State the problem:** Simplify expressions containing mixed numbers by converting to improper fractions, then perform addition, subtraction, multiplication, or division, and si

1. The problem states the equation of a circle: $$(x + 3)^2 + (y + 5)^2 = 25$$ 2. This is a circle in standard form with center at $$(-3, -5)$$ and radius $$r = \sqrt{25} = 5$$.