🧮 algebra

1. **State the problem:** Jamal rides 6 miles downhill to the skate park and returns uphill on the same trail. His uphill speed is 1 mile per hour slower than his downhill speed. T

1. **State the problem:** Aaliyah runs and bikes for a total of 2 hours. She runs 4 miles and bikes 8 miles. Her bike speed is 4 mph faster than her running speed. We need to find

1. **State the problem:** We are given the quadratic function $$y = -x^2 - 6x - 3$$ and want to analyze its properties such as vertex, intercepts, and graph shape. 2. **Formula and

1. The problem is to "Show solution" which is ambiguous, so I will interpret it as solving a simple algebraic equation for demonstration. 2. Let's solve the equation $2x + 3 = 7$.

1. **State the problem:** Simplify the expression $$(4x+7)^2$$. 2. **Formula used:** The square of a binomial $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. **Énoncé du problème :** Montrer les propriétés de diagonalisation et valeurs propres pour des matrices données.

1. **State the problem:** Solve the equation $$\frac{5 - 3x}{2} = 12$$ for $x$. 2. **Formula and rules:** To solve for $x$, we first eliminate the denominator by multiplying both s

1. **State the problem:** Solve the equation $5 - \frac{3x}{2} = 12$ for $x$. 2. **Isolate the term with $x$:** Subtract 5 from both sides:

1. The problem is to draw a straight vertical line, which is a line at 90 degrees to the horizontal axis. 2. A vertical line has an equation of the form $x = a$, where $a$ is a con

1. The problem is to understand how to draw a straight vertical line on a graph. 2. A vertical line has the same $x$-coordinate for all points on the line.

1. The problem is to solve the equation $55x + 5 = 0$ for $x$ and then check the value when $x = 1$. 2. The equation is linear and can be solved using the formula for linear equati

1. **State the problem:** Solve the equation $-10x + 8y = 0$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation.

1. **State the problem:** Solve the equation $-10x + 8y = 0$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation.

1. **State the problem:** Find the least common multiple (LCM) of 8, 6, and 3. 2. **Formula and rules:** The LCM of numbers is the smallest number that is a multiple of all the giv

1. **State the problem:** Simplify the expression $$(x^{\frac{1}{2}})^7 \times \sqrt{x^9}$$. 2. **Recall the rules:**

1. **State the problem:** Find the least common multiple (LCM) of 8, 6, and 3. 2. **Formula and rules:** The LCM of numbers is the smallest number that is a multiple of all the giv

1. **State the problem:** We have a line L given by the equation $$4y + 12 = 16x$$ and a line R that is perpendicular to L and passes through the point $(-1, 5)$. We need to:

1. **State the problem:** Solve for $x$ in the equation $2(x-3)+3(x+1)=4(x-2)$. 2. **Write down the equation:**

1. The problem is to find the first four terms of the sequence defined by the formula $a_n = 61 - 6(n - 1)$ for $n = 1, 2, 3, \ldots$. 2. The formula for the $n$-th term of the seq

1. **State the problem:** Solve for $x$ in the equation $2(x-3)+3(x+1)=4(x-2)$.\n\n2. **Write down the equation:** $$2(x-3)+3(x+1)=4(x-2)$$\n\n3. **Distribute the constants:** Mult

1. **Solve the equation** $\frac{x - 6}{4x} = \frac{1}{2}$. 2. Multiply both sides by $4x$ to eliminate the denominator: