🧮 algebra

1. Calculate $-30 + 6 \cdot (-2)^3$.\nFirst, evaluate the exponent: $(-2)^3 = -8$.\nThen multiply: $6 \cdot (-8) = -48$.\nAdd: $-30 + (-48) = -78$.\n 2. Compute $(9-3)^2 - 10 \div

1. The problem states that 12 sheets weigh 40g. 2. We need to find how many sheets weigh 1g.

1. The problem appears to involve calculating percentages and amounts related to a value of 700 with a rate of 24%, over a period or quantity of 12 (months, years, etc.) or price o

1. **State the problem:** We are given the implicit equation $$xy^3 - 4x^2 = 10y^2$$ and want to analyze its components. 2. **Rewrite the equation:** The equation relates $x$ and $

1. **State the problem:** Solve the equation $|x - 3| + 1 = 4$ for $x$. 2. **Isolate the absolute value:** Subtract 1 from both sides:

1. The problem gives the sequence: 50, 53, 58, 65 and asks for the seventh term. 2. First, find the pattern. Calculate the differences between consecutive terms:

1. What is an equivalent fraction? Explain with an example. 2. Simplify the fraction $\frac{8}{12}$ to its equivalent fraction in lowest terms.

1. The problem provides the function $p(t) = 600(1.025)^t$. 2. This is an exponential growth function where $600$ is the initial amount and $1.025$ is the growth factor.

1. **Énoncé du problème :** Comparer les nombres donnés et simplifier les expressions. 2. **Calcul de z :**

1. We are given the system of inequalities: $$3(2x-5) > 4x+7$$

1. The problem is to simplify the expression \sqrt{x}16 + 9. 2. First, note that \sqrt{x} is the square root of $x$ and 16 is a constant. The expression can be written as $16\sqrt{

1. The problem is to understand and explain how to format a mathematical expression correctly. 2. Formatting expressions in math usually involves writing them clearly using mathema

1. The problem is to simplify or analyze a quadratic expression. 2. A quadratic expression generally has the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq

1. **State the problem:** Simplify the expression $$\frac{2 \times 12 \times (C + y)}{2} \div (1 \times 24 \times 5)$$. 2. **Simplify numerator:** In the numerator, $$2 \times 12 \

1. **Problem Statement:** (a) Raj travels 15 km at a speed of $x$ km/h. Find the time taken by Raj in minutes.

1. Stating the problem: Simplify the fraction $$\frac{8 \times 12 \times (-7)}{4 \times 12 \times 5}$$

1. The problem presents the function $$t = \frac{3 w^3 + a}{w^3 - 2}$$ and provides a curve passing through points $(-2,8)$ and $(2,-2)$ on the coordinate plane. 2. We will use the

1. Stating the problem: Simplify or analyze the quadratic expression $2x^2 + 9x - 5$. 2. Identify the coefficients: The quadratic is in standard form $ax^2 + bx + c$ with $a=2$, $b

1. We are asked to factorise the expression $64x^2y^2 - 36y^2z^2$ fully. 2. First, identify the common factor in both terms. Both terms contain $y^2$, so factor it out:

1. **State the problem:** We need to factorize the quadratic expression $x^2 - 2x - 35$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=

1. **State the problem:** Simplify the expression $ (3-4x)^2 $. 2. **Apply the square of a binomial formula:** Recall that $(a-b)^2 = a^2 - 2ab + b^2$.