🧮 algebra

1. **State the problem:** Subtract the fractions $\frac{9}{8} - \frac{3}{4}$. Make sure the answer is fully reduced. 2. **Formula and rules:** To subtract fractions, find a common

1. **State the problem:** We need to determine whether $\frac{4}{5}$ is less than, greater than, or equal to $\frac{8}{11}$. 2. **Recall the rule for comparing fractions:** To comp

1. **State the problem:** Simplify the expression $$(63x^2 + 9x) - (5x + 40)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the

1. **State the problem:** Solve the quadratic equation $x^2 - x - 2 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **Problem (b):** Calculate the time taken for a flight from Dublin to New York that covers 5112 km at an average speed of 818 km/h. 2. **Formula:** Time = Distance \div Speed

1. **State the problem:** Simplify the expression $ (9x)(7x+1) $. 2. **Use the distributive property:** Multiply each term inside the parentheses by $9x$. The distributive property

1. Stating the problem: Solve the inequality $$\frac{x^2 - 4}{x^{-x} - 2} > 0$$. 2. Analyze the numerator and denominator separately.

1. **Problem Statement:** (a) Find the height of a cuboid suitcase with length 40 cm, width 24 cm, and maximum volume 52800 cm³.

1. The problem asks to solve "inequality one" and "inequality two" but no specific inequalities were provided. 2. To solve an inequality, we typically isolate the variable on one s

1. **Problem statement:** Expand and simplify each expression. 2. **Part a:**

1. **State the problem:** Pedro can make a total of 140 tacos or burritos combined, and he must sell at least 600 worth of tacos and burritos daily.

1. **State the problem:** Use Newton's method to estimate the real root of the equation $$7x^3 + x - 5 = 0$$ accurate to five decimal places. 2. **Recall Newton's method formula:**

1. **State the problem:** Simplify the complex fraction $$\frac{3 - 3i}{-i}$$ and write the answer in the form $a + bi$. 2. **Recall the formula and rules:** To divide complex numb

1. **State the problem:** Simplify the expression $$-(3 - 7i) - (-10 - 9i)$$ and write the answer in the form $$a + bi$$. 2. **Recall the rules:**

1. The problem is to solve the equation where the expression equals $-4$. 2. To solve for the variable, we first write down the equation explicitly.

1. **State the problem:** We are given the system of equations: $$x - 2y = 4$$

1. **State the problem:** Simplify the expression $$3q + 10 + \frac{5}{3q^5 r^5}$$ and express it as a single fraction in simplest form. 2. **Rewrite the expression:** To combine a

1. **State the problem:** Simplify the expression $$9w + 9 + \frac{5}{w^2x}$$ and express it as a single fraction in simplest form. 2. **Rewrite the expression:** The first two ter

1. **Problem:** Graph and identify the pieces of the function $$f(x) = \frac{x^2 + 2x - 8}{x + 1}$$ 2. **Find x-intercepts:** Set numerator equal to zero:

1. Il problema chiede di calcolare l'espressione numero 267, ma nel testo fornito l'ultimo esercizio è il 222. 2. Poiché il problema 267 non è presente, non posso risolverlo.

1. **Stating the problem:** Simplify the expression $$25.23: 1(2+3.2): 5+123.3.5+(3.22)_{(2.3.5)}:6:3-122:3:4$$. 2. **Clarify notation and operations:** Here, ":" denotes division,