🧮 algebra

1. **State the problem:** Solve the equation $-7 + 4m + 10 = 15 - 2m$ for $m$. 2. **Combine like terms on the left side:** $-7 + 10 = 3$, so the equation becomes $3 + 4m = 15 - 2m$

1. **State the problem:** Find a formula to quickly determine the exponent $n$ such that $2^n = x$ for a given number $x$. 2. **Use logarithms:** The key formula is based on logari

1. **State the problem:** Find an easy way to determine that $1024 = 2^{10}$ without memorizing it. 2. **Recall the concept of powers:** To find $2^{10}$, you multiply 2 by itself

1. **State the problem:** Find the values of the logarithms: a) $\log_2 1024$

1. **Problem Statement:** Complete the chart for each polynomial function by simplifying, finding the degree, and the leading coefficient.

1. **State the problem:** We need to evaluate $f(g(-3))$, which means first find $g(-3)$ and then substitute that result into $f(x)$. 2. **Analyze $g(x)$:** The graph of $g(x)$ is

1. The problem is to solve the expression $\frac{3}{8} \times \frac{2}{5}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b

1. **State the problem:** Calculate $\frac{3}{4} - \frac{1}{2}$ and simplify the answer if necessary. 2. **Formula and rules:** To subtract fractions, they must have a common denom

1. Masalah yang diberikan adalah menyederhanakan hasil operasi dari $\left(\sqrt{3} - 5\right) \left(5 + \sqrt{3}\right)$.\n\n2. Gunakan rumus perkalian dua binomial: $\left(a - b\

1. **Stating the problem:** Given $\log_3 5 = a$ and $\log_5 7 = b$, find the values of $\log_{15} 49$ and $\log_{49} \sqrt{15}$.\n\n2. **Recall the change of base formula:** For a

1. The problem asks to identify the inequality represented by the graph. 2. The graph shows a dashed line with a negative slope intersecting the y-axis near 3 and the x-axis near 3

1. Let's start by stating the problem: What are rational functions? 2. A rational function is a function that can be expressed as the ratio of two polynomials. In other words, it h

1. **State the problem:** We are given three parallel segments AD, BE, and CF with lengths expressed as algebraic expressions: $AD = 3x + 20$, $BE = 2x + 14$, and $CF = x + 25$. Si

1. Plantea el problema: Un fabricante vende tres modelos de coches A, B y C con precios 1.5, 2 y 3 millones respectivamente. 2. Define variables: Sea $x$, $y$, $z$ el número de coc

1. **State the problem:** Determine which systems of equations are equivalent to the system: $$\begin{cases} y = -5x - 8 \end{cases}$$

1. The problem states that a pie chart represents three uniform units: Scouts (Pengakap), Police Cadets (Kadet Polis), and KRS, with given numbers for Scouts (45) and KRS (115). We

1. The problem involves calculating the speed given the time and distance. 2. We know the formula for speed is $$\text{speed} = \frac{\text{distance}}{\text{time}}$$.

1. The problem gives a number sequence: $$150, m, 126, 114, 102, n$$ and asks to find the value of $$m - n$$. 2. To solve this, we first identify the pattern in the sequence. The s

1. Diberikan persamaan $3^n \times 3^2 = 27^{n+1}$. Kita diminta mencari nilai $n$. 2. Ingat bahwa $27$ dapat ditulis sebagai $3^3$, sehingga persamaan menjadi $3^n \times 3^2 = (3

1. The problem asks: What number is 65% of 840? 2. To find a percentage of a number, use the formula:

1. **State the problem:** We need to find the number for which 36 is 30% of it. 2. **Formula:** To find a number when a percentage of it is given, use the formula: