🧮 algebra

1. We need to simplify each algebraic expression by combining like terms. 2. Calculate each:

1. Stated problem: Given the equation $y(x-1)=z$, solve for $x$. 2. Start by isolating $x$ on one side. Divide both sides of the equation by $y$, assuming $y \neq 0$:

1. The problem is to calculate $\frac{1}{2} \times 6 \times 11$. 2. First, multiply $6$ and $11$: $$6 \times 11 = 66$$.

1. The problem is to convert a temperature from Fahrenheit to Celsius. Given the temperature $100.7^\circ F$, we want to find the equivalent in Celsius $^\circ C$. 2. Recall the fo

1. Stating the problem: We want to describe the sequence 144, 72, 36, 18, 9 in mathematical terms. 2. Observe the pattern in the sequence: Each term seems to be divided by 2 to get

1. Start by stating the problem: Simplify and expand the expression $$-2x^2 + 9x - 4 - (-2 - x)(3x - 12)$$. 2. Expand the product $$(-2 - x)(3x - 12)$$ using the distributive prope

1. El problema plantea cambiar la letra \(t\) por otra letra en una expresión matemática o variable. 2. Generalmente, en matemáticas o programación, cualquier letra o símbolo usado

1. The problem is to find the absolute value of $-9$. 2. The absolute value of a number is its distance from zero on the number line, regardless of direction.

1. Problem: Analyze voting data for homework-free day, calculate circle dimensions from circumference, find HCF using prime factorization, and solve wage and profit questions for a

1. We are given that the sales price of the car is 12,590 after a 20% discount. 2. Let the original price be $p$.

1. State the problem: An employee wants to buy a dishwasher originally priced at 450 during a 15% off sale and receives an additional 20% off the lowest price. We need to find the

1. **State the problem:** Sally can paint a house in 4 hours, John can paint the same house in 6 hours. We want to find how long they take together to paint one house. 2. **Find in

1. (a) Problem: A box contains 80 plant seeds. Ben takes $\frac{1}{8}$, Clara takes $\frac{1}{4}$. Find: (i) fraction taken, (ii) number left. Step 1: Calculate fraction taken: $\f

1. **State the problem:** Lynn can type a whole page in $p$ minutes. We want to find out what fraction of the page she can type in 5 minutes. 2. **Understand the rate:** Her typing

1. Bonjour! Comme tu es en 4ème et que tu n'as pas encore vu les vecteurs, on va commencer par des notions simples en algebra. 2. Par exemple, résolvons une équation du premier deg

1. **Problem statement:** We consider the function $f(x) = 2x\ln x - 1$ defined on $(0, +\infty)$. We need to analyze limits, derivatives, solve equations involving $f$, and study

1. The problem is to understand why, in certain exercises, the last part is compared to 1. 2. Often in math, comparing a quantity to 1 helps determine if it is greater than, equal

1. State the problem: Solve the system of equations $$\begin{cases} x+y+z=6 \\ 2x-y+2z=14 \\ x+4y-z=2 \end{cases}$$

1. We need to determine whether the function $f(x) = \sin^9 x \cos^5 x$ is even, odd, or neither. 2. Recall the definitions:

1. **Statement of the problem:** Calculate various results for the given sets of numbers and expressions.

1. **State the problem:** Find the number of positive integers less than or equal to 10030 that are not divisible by 3, 4, 7, or 11. 2. **Use the principle of inclusion-exclusion:*