🧮 algebra

1. **State the problem:** We have three mothers with different incomes and a rebate system for before and after school care costing $10,000 per year. We want to find who has the le

1. **State the problem:** A container with 240 litres of soft drinks is shared among four teams. The first team takes $\frac{1}{3}$ of the total. The second team takes $\frac{1}{2}

1. Solve $4x^2 - 16x = 0$ by factoring: $$4x(x - 4) = 0$$

1. The problem presents several equations involving variables with deltas (\(\Delta t\), \(\Delta x\), etc.) and algebraic expressions. We will analyze and simplify each equation w

1. The problem presents a system of equations with variables $e_0$, $e_2$, $n_a$, $a_2$, $P_2$, $hf$, $x$, $T$, and constants. 2. Let's rewrite the equations clearly:

1. Problem: Find the x-coordinate of the line with slope $-2$ passing through $(3,7)$ when $y=17$. Step 1: Use point-slope form: $y - y_1 = m(x - x_1)$.

1. The problem is to analyze the function $y=3x^4-\cos x$. 2. This function combines a polynomial term $3x^4$ and a trigonometric term $-\cos x$.

1. **State the problems:** We have two problems:

1. Problem: Determine which functions are inverses of $y=\cos x$ on the interval $[0; \pi]$. - The inverse function of $\cos x$ on $[0; \pi]$ is $y=\arccos x$.

1. **State the problem:** Simplify the expression $$\frac{3}{5}x + 3 - \frac{1}{5}x - 2$$ by grouping like terms. 2. **Rewrite the expression:** Group the terms to see like terms c

1. **State the problem:** Simplify the expression $$\frac{3}{5}x + 3 - \frac{1}{5}x - 2$$. 2. **Group like terms:** Combine the terms with $x$ and the constant terms separately.

1. State the problem: Understand transformations of functions including translations, reflections, stretches, and compressions. 2. Example question 1: Given the function $f(x) = x^

1. Stating the problem: Simplify the expression $$m=\frac{-3}{\frac{12+(-2)}{-3.5}}+13$$. 2. Simplify inside the parentheses: $$12+(-2)=10$$.

1. Mari kita periksa setiap pernyataan satu per satu untuk menentukan apakah faktorisasi yang diberikan benar. 2. Pernyataan I: $16x^2 - 9 = (4x + 3)(4x - 3)$

1. **Stating the problem:** We have multiple questions:

1. Let's state the problem: We need to factorize the denominator of question 14. 2. Since the exact expression is not provided, let's consider a common example denominator such as

1. Let's clarify what it means to round exact roots. Exact roots are the precise solutions to an equation, often expressed in radical form or as fractions. 2. When rounding, we app

1. **State the problem:** We are given two numbers in scientific notation: Earth is about $4.5$ billion years old and primate fossils date back about $45$ million years.

1. **State the problem:** We need to solve the quadratic equation $$x^2 - 3x + 1 = 0$$ and find its exact roots and approximate roots rounded to 2 decimal places. 2. **Use the quad

1. The problem is to express the equation $x^2 - 3s + 1 = 0$ in a clear form. 2. Notice that the equation involves two variables, $x$ and $s$, but it is quadratic only in $x$.

1. **State the problem:** Solve the equation $5 \times (x - 24) = 125 + 24$ for $x$. 2. **Simplify the right side:** Calculate $125 + 24$.