🧮 algebra

1. The problem asks which number pattern can be described by an exponential equation. 2. An exponential function has the form $$y = a \cdot b^x$$ where $a$ is a constant, $b$ is th

1. **State the problem:** We are given the function $f(x) = 35 \cdot 2^x$ and asked to describe its behavior as $x$ increases. 2. **Recall the formula and properties:** The functio

1. El problema es encontrar la ecuación de la recta que pasa por dos puntos dados. 2. La fórmula para la pendiente $m$ de la recta que pasa por dos puntos $P_1(x_1,y_1)$ y $P_2(x_2

1. **State the problem:** Solve the linear equation $3x - 4y = 18$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by m

1. Staðfesta verkefnið: Reikna út tjáninguna $$\sqrt{75} + 2 \cdot \sqrt{30} \div \sqrt{15} + 2 \cdot \sqrt{6}$$. 2. Nota reglu um að deila rótum: $$\frac{\sqrt{a}}{\sqrt{b}} = \sq

1. **State the problem:** Find the coordinates of the point where Line A and Line B intersect. 2. **Understanding intersection:** The intersection point of two lines is where their

1. **Stel het probleem vast:** We willen de waarden van $p$ vinden waarvoor de vectoren $\overrightarrow{A}$ en $\overrightarrow{B}$ loodrecht op elkaar staan. 2. **Belangrijke reg

1. **State the problem:** Expand the logarithm $\log_v u^5 w$ as a sum or difference of logarithms with base $v$. 2. **Recall the logarithm properties:**

1. The problem is to simplify the fraction $\frac{70}{50}$. 2. The formula for simplifying a fraction is to divide both numerator and denominator by their greatest common divisor (

1. **State the problem:** Simplify the expression $\frac{150}{25}$. 2. **Recall the division rule:** Dividing two numbers means finding how many times the denominator fits into the

1. **State the problem:** Solve the inequality $x + 3 < -7$. 2. **Isolate the variable:** To solve for $x$, subtract 3 from both sides of the inequality.

1. **State the problem:** We are given two expressions, $9k + 7$ and $2k^2 + 3$, which represent consecutive integers. We know $9k + 7$ is the smaller integer. 2. **Write the relat

1. **State the problem:** Find the degree and leading coefficient of the polynomial $$-9v^4 - 4v - 8 + v^5$$. 2. **Rewrite the polynomial in standard form:** Arrange terms in desce

1. **State the problem:** Solve for $v$ in the equation $$(v^2 - 3v - 4)(4v - 4) = 0.$$\n\n2. **Use the zero product property:** If a product of two factors equals zero, then at le

1. The problem asks to draw the line given by the equation $$2x - y - 1 = 0$$ on a coordinate grid with a specific scale. 2. First, rewrite the equation in slope-intercept form to

1. The problem asks to convert 163% to a decimal. 2. Recall that percent means per hundred, so 163% means 163 per 100.

1. **State the problem:** Solve the equation $x - (5x + 3) - 3 = -(-x + 2)$ for $x$. 2. **Apply the distributive property and remove parentheses:**

1. **State the problem:** Solve the linear equation $6x + 8 = 2x - 28$ for $x$. 2. **Write down the equation:**

1. Problemet är att bestämma en tredjegradsfunktion som skär x-axeln i punkterna $x=-2$, $x=1$ och $x=5$, och som går genom punkten $(-1,3)$. Vi ska skriva funktionen i utvecklad f

1. **State the problem:** Solve for $ab$ given the equations: $$(a - 6)(a + 6) = 49$$

1. The problem asks to identify which inequality matches a graph with a line of slope $-\frac{3}{4}$ and y-intercept 3, where the line is solid and the shaded area is above the lin