🧮 algebra

1. **State the problem:** Sarah is 5 years older than her brother, and the sum of their ages is 35 years. 2. **Define variables:** Let $x$ represent the brother's age.

1. The problem asks: How much money does he have left if he bought 5 cards? 2. To solve this, we need to know the initial amount of money he had and the cost of each card.

1. **State the problem:** We want to find the equation that represents the amount of money $y$ he has left after some transactions involving $x$. 2. **Analyze the options:** The op

1. **State the problem:** Kiko saved 120 and buys gift cards costing 10 each. We want to find the unknown value represented by a variable.

1. **State the problem:** We need to find the value of the expression $5b + c^3$ when $b=7$ and $c=4$. 2. **Write the expression:** The expression is $5b + c^3$.

1. **State the problem:** Find the x-intercepts of the function and solve the equation $3x^2 - 72 = 0$ using the square root property. 2. **Identify x-intercepts:** Given points $(

1. **Problem statement:** Prove that for all natural numbers $a$ and $b$, the equation $$(a^2 + b^2)^2 - (a^2 - b^2)^2 = (2ab)^2$$ holds true. 2. **Formula and rules:** This proble

1. **State the problem:** Simplify the expression $$\frac{2y - 8}{y^2 - 3y - 4} + \frac{3}{y + 1}$$. 2. **Factor the denominators and numerator where possible:**

1. The problem asks for the coefficient of the variable in the expression $5z + \left(9 \div 3\right)$. 2. The expression consists of two parts: a variable term $5z$ and a constant

1. **State the problem:** Solve the equation $$\sqrt{x} - 1 = x - 3$$ and determine which statements about the solutions are true. 2. **Isolate the square root:** Add 1 to both sid

1. **State the problem:** Simplify the expression $$\left(\sqrt[8]{16x^{12}}\right)^6$$. 2. **Recall the rules:** The eighth root can be written as a fractional exponent: $$\sqrt[8

1. **State the problem:** Simplify the expression $$\left(\sqrt[8]{16x^{12}}\right)^6$$. 2. **Recall the rule for radicals and exponents:**

1. **State the problem:** We need to find the equation of the trend line passing through the two yellow points on the scatter plot, which are approximately at coordinates $(1,1)$ a

1. **State the problem:** Solve the equation $x + x - 4 - 1 + x + x - 4 = 95$ for $x$. 2. **Combine like terms:** Group all $x$ terms and constants separately.

1. The problem asks for the equation of the vertical asymptote of the given graph. 2. A vertical asymptote occurs where the function approaches infinity or negative infinity as $x$

1. **State the problem:** Solve for $x$ in the equation $x = x$. 2. **Analyze the equation:** The equation $x = x$ is an identity, meaning it is true for all values of $x$.

1. **State the problem:** Solve the equation $h(b+11) = (b+11) + 14$ for $h(b+11)$. 2. **Understand the equation:** The equation states that the function $h$ evaluated at $b+11$ eq

1. **Problem:** Determine if the conjecture "All perfect squares are divisible by 2" is true or false. 2. **Explanation:** A perfect square is a number that can be expressed as $n^

1. The problem is to express the functions and their compositions in Maple syntax. 2. Maple uses := for function definitions and standard mathematical notation.

1. **Problem:** Determine if the conjecture "All perfect squares are divisible by 2" is true or false. 2. **Explanation:** A perfect square is a number that can be expressed as $n^

1. **State the problem:** We need to find the slope of the line on the graph that shows the cost of transporting sugar versus the weight of sugar in tons. 2. **Recall the formula f