🧮 algebra

1. **State the problem:** Solve the system of linear equations for $i$ and $g$ given: $$\begin{cases} 5i + 2g = 5020 \\ 3i + 8g = 7840 \end{cases}$$

1. **State the problem:** Simplify the expression $\frac{3}{4} - \frac{1}{3}$. 2. **Formula and rules:** To subtract fractions, they must have a common denominator. Find the least

1. **State the problem:** Evaluate the expression $8 \div 2(2 + 2)$. 2. **Simplify inside the parentheses:** Calculate $2 + 2$.

1. **Stating the problem:** We want to simplify the expression $$\sqrt{x^{\frac{2}{3}}}$$. 2. **Recall the property of radicals and exponents:** The square root of a number is the

1. Problem: Interpret the function $c(x) = 0.19x + 38$ for $x=1500$ kilowatt-hours. 2. Formula: $c(x) = 0.19x + 38$ where $x$ is kilowatt-hours and $c(x)$ is total cost.

1. **State the problem:** Rewrite $\left(\sqrt{17}\right)^{34}$ in exponential form. 2. **Recall the rule:** The square root of a number can be written as an exponent of $\frac{1}{

1. **State the problem:** We are given the amount of mold on a fruit at different times and need to find the initial amount of mold (at time 0 seconds). 2. **Identify the pattern:*

1. Énoncé du problème : Factoriser le polynôme $x^3 + 5x^2 + 3x - 9$ en utilisant la méthode de Horner. 2. Rappel de la méthode de Horner : Cette méthode permet de diviser un polyn

1. **State the problem:** Solve the quadratic equation $$x^2 + 27x - 10 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions

1. The problem is to write an equation for a graph that resembles a square root function shifted slightly. 2. The general form of a square root function is $$f(x) = a\sqrt{x - h} +

1. **State the problem:** Simplify the expression $\frac{3}{4} - \frac{1}{3}$.\n\n2. **Formula and rules:** To subtract fractions, they must have a common denominator. Find the lea

1. The problem is to write an equation for a graph that starts near the point $(5,0)$ on the x-axis and curves upward to the right. 2. This shape suggests a function that is define

1. **State the problem:** We want to find the fraction that you multiply the first number 68 by to get the second number 26. 2. **Write the equation:**

1. **State the problem:** Simplify the expression $$(3x^2 + 3x - 3) - (6x^2 - 4x - 2)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus si

1. The problem is to simplify the expression $$-\frac{5}{3} \times \left(\frac{1}{2}\right)$$. 2. The formula for multiplying fractions is $$\frac{a}{b} \times \frac{c}{d} = \frac{

1. **State the problem:** We have a quadratic function $y = x^2 + bx + c$ with points $P(-3, -9)$ and $Q(2, -4)$ on the curve. We need to find $b$ and $c$, the y-intercept, and the

1. **State the problem:** We need to find the perimeter of an L-shaped polygon with given side lengths: top horizontal $4x - 6$, left vertical $x + 13$, bottom horizontal $2x + 1$,

1. **Stating the problem:** We want to understand the graph of a quadratic function of the form $$y = x^2 + bx + c$$ where $$b$$ and $$c$$ are integers (elements of $$\mathbb{Z}$$)

1. **State the problem:** Find the real solution(s) of the equation $$8x^3 = 64$$. 2. **Write the formula and rules:** To solve for $x$, we want to isolate $x$ by dividing both sid

1. Problemet er å bruke den andre kvadratsetningen til å regne ut kvadrattallet 292. 2. Den andre kvadratsetningen sier at $ (a-b)^2 = a^2 - 2ab + b^2 $.

1. **State the problem:** Solve the inequality $$3x - (-5) \leq -7$$. 2. **Rewrite the inequality:** Subtracting a negative is the same as adding, so rewrite as $$3x + 5 \leq -7$$.