🧮 algebra

1. **State the problem:** We need to find which linear inequality corresponds to the graphed solution set. 2. **Analyze the graph:** The graph shows a dashed increasing line passin

1. Il problema chiede di risolvere la disequazione $\log_3 x^2 - \log_3 x < 3$. 2. Usiamo la proprietà dei logaritmi: $\log_a b - \log_a c = \log_a \frac{b}{c}$.

1. **State the problem:** Solve the system of equations: $$-x_2 - x_3 - 4 = 0$$

1. Problema 282: Calcola il sesto termine dello sviluppo di $\left(a^2 + b\right)^8$.\n\n2. Formula: Il termine generale dello sviluppo binomiale è $$T_{k+1} = \binom{n}{k} A^{n-k}

1. The problem is to understand what the absolute value means. 2. The absolute value of a number is its distance from zero on the number line, regardless of direction.

1. **State the problem:** Simplify the expression $$\left(\frac{1}{x-1} + \frac{3}{1-x^2}\right) : \left(1 - \frac{1}{x-1} + \frac{2}{x+2}\right) \cdot \frac{x^2 + 3x + 6}{x^3}.$$\

1. **State the problem:** Officer Brimberry wrote 8 tickets last week and 3 tickets this week. We need to find the percent decrease in the number of tickets. 2. **Formula for perce

1. **Stating the problem:** Choose the best term from the box (percent, proportion, rate, ratio) to fill in the blanks for questions 1 to 4. 2. **Step 1:** Understand the definitio

1. The problem asks: How many gallons of oil are in the gun when it is full? 2. The equation given is $$y = -\frac{1}{32}x + 6$$ where $y$ is the gallons of oil remaining and $x$ i

1. **Problem statement:** Find the percent of each number given. 2. **Formula:** To find $p\%$ of a number $N$, use the formula:

1. **State the problem:** Elijah bought a chest of drawers originally priced at $50.40 with a 40% discount and then a 6.25% sales tax is applied. We need to find the total cost aft

1. **State the problem:** Marco's dinner cost 100. We need to find the total cost including a 6% sales tax and a 15% tip on the original 100. 2. **Formula for sales tax and tip:**

1. **State the problem:** Find the system of linear equations for two lines intersecting at the point $(-2, -1)$. 2. **Identify points and slopes:**

1. **State the problem:** Find the equations of two parallel lines given points on each line. 2. **Formula and rules:** The equation of a line in slope-intercept form is $$y = mx +

1. Problemet: Vi har funktionen $f(x) = 3x^2 + 4x$ och en tangentlinje vid punkten där $x=2$. Tangentens ekvation är $y = kx - 12$. Vi ska bestämma lutningen $k$. 2. Formeln för lu

1. **State the problem:** Solve the system of equations: $$0 = 2x_2 - 2x_1 - 4$$

1. **State the problem:** Last year, there were $z$ zebra mussels in a river section. This year, there are $z^3$ zebra mussels, and this year the number is 729. Find $z$. 2. **Writ

1. **State the problem:** Solve the rational equation $$\frac{1}{5 - x^4} + \frac{1}{x^4 - 3} = 2$$. 2. **Rewrite the equation:** Notice that the denominators are $$5 - x^4$$ and $

1. **State the problem:** Simplify the expression $$\frac{x^4 - 9x^2}{x^2 - 1 + 5}$$. 2. **Rewrite the denominator:** Combine like terms in the denominator:

1. **State the problem:** Determine the domain on which the function represented by a downward-opening parabola with vertex at approximately $(-1,7)$ is increasing. 2. **Recall the

1. **State the problem:** We need to determine the domain on which the given quadratic function is decreasing. 2. **Identify the function type:** The graph is a downward-opening pa