🧮 algebra

1. **Problem statement:** Alex threads white and black beads alternately onto a string. Two groups of 5 beads each are hidden (covered). We need to find how many white beads are hi

1. **State the problem:** Jessica is building a model skyscraper with each floor 4 inches tall and an 8-inch spire on top. The total height must be at least 50 inches. We need to f

1. The problem is to analyze the linear equation $y = 2x - 1.5$ and understand its properties. 2. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and

1. The problem asks which table shows a proportional relationship between weight and price. 2. A proportional relationship means the ratio between weight and price is constant.

1. **State the problem:** We are given the polynomial function $P(x) = x^2 + x + 2$ and asked to find the value of $P(0)$. 2. **Recall the formula:** To find $P(0)$, substitute $x

1. The problem states that $(f \circ g)(0) = 2$, which means $f(g(0)) = 2$. 2. From the graph, observe the function $g(x)$, which is a downward-opening parabola intersecting the y-

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}7x + 2y = 24 \\ 8x + 2y = 30\end{cases}$$

1. **State the problem:** A photograph scale shows that every $1 \frac{1}{4}$ inches represents 100 yards in real life. The mountain height in the photo is 8 inches. Find the actua

1. Énonçons le problème : Résoudre l'équation $$x + 1 + \sqrt{x} - 1 = 0$$. 2. Simplifions l'équation en combinant les termes constants : $$x + \sqrt{x} + (1 - 1) = 0 \Rightarrow x

1. **State the problem:** Solve the equation $\sqrt{6x+7} = 2$ for $x$. 2. **Recall the formula and rules:** To solve an equation involving a square root, we isolate the square roo

1. **State the problem:** Simplify the expression $\left(\frac{5}{x}\right)^6 \left(\frac{1}{x}\right)^3$ using properties of exponents and write it in radical form. 2. **Recall th

1. The problem is to rewrite the expression $$\sqrt[3]{x^7}$$ using rational exponents. 2. Recall the rule for radicals and exponents: $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$ where $n$

1. **State the problem:** Solve the quadratic equation $4x^2 + 4x - 5 = 0$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, th

1. **State the problem:** Solve the inequality $$|5 - 7x| + |2x + 3| \geq 10x + 1$$. 2. **Identify critical points:** The expressions inside the absolute values change sign at poin

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the denominator to e

1. **State the problem:** We have the infinite series $$\sum_{n=1}^\infty 2 \left(-\frac{1}{2}\right)^{n-1}$$ and we want to find the first term $a_1$, the common ratio $r$, and th

1. **State the problem:** Calculate the value of the expression $4(2.5 - 17)$.\n\n2. **Apply the order of operations:** First, solve the expression inside the parentheses.\n\n3. Ca

1. **State the problem:** Simplify and evaluate the expression $$4(x - 1) + 8x^2$$ when $$x = 2.5$$. 2. **Write the expression:** $$4(x - 1) + 8x^2$$.

1. **State the problem:** Simplify the expression $$\frac{y^2 - 2ps + 2s}{2y - 4p + 4}$$. 2. **Identify the numerator and denominator:**

1. The problem is to find the 7th row of Pascal's triangle. 2. Pascal's triangle rows are numbered starting from 0, where the 0th row is [1]. The nth row contains the binomial coef

1. **State the problem:** Complete the table illustrating the distributive property by expanding and simplifying the given expressions. 2. **Recall the distributive property formul