🧮 algebra

1. **State the problem:** Simplify and solve the expression involving products and powers of binomials and polynomials given as: $$\left(\frac{(a+2)(a+1)}{(a+2)(a-1)}\right)^3 = \f

1. **Problem 4:** Determine the equation in vertex form for the parabola given the vertex and a point. 2. The vertex form of a parabola is given by:

1. **State the problem:** Write the quadratic equation $y = -x^2 - 4x + 5$ in vertex form, identify the axis of symmetry, extrema, and zeros. 2. **Recall vertex form:** The vertex

1. **State the problem:** Solve for $x$ in the equation $y = f(x)$ where $f(x) = -5x + 1$.

1. **State the problem:** Solve the equation $$x |x - 8| = 24x + 4$$ for $x$ and identify which solutions are roots or extraneous. 2. **Understand the absolute value:** The express

1. The question asks whether the mathematical constant $e$ should be written with a positive exponent. 2. The constant $e$ is approximately equal to 2.71828 and is the base of natu

1. **State the problem:** Sarah’s Pet Store has at most 16 cats and dogs combined, and at most 9 cats. 2. **Define variables:** Let $x$ be the number of cats and $y$ be the number

1. **State the problem:** We have a model rocket launched from a deck, and its height $A$ in meters after $t$ seconds is given by the quadratic function $$A = -5t^2 + 100t + 15.$$

1. **State the problem:** We want to find the year when women made up 30% of the labor force using the function $$f(x) = \frac{68.35}{1 + 0.036e^{-0.117x}}$$

1. **State the problem:** We have the function $$f(x) = \frac{68.35}{1 + 0.036e^{-0.117x}}$$ modeling the percent of women in the labor force, where $x$ is years since 1950. 2. **P

1. **Stating the problem:** We have a sequence of figures numbered 1, 2, 3 with respective numbers of squares 5, 12, and 21. 2. **Drawing figures 1 and 3:**

1. Stating the problem: Solve the equation $$7 + x = \frac{5x}{3} - 3$$. 2. Write down the equation clearly:

1. **State the problem:** From the set \(\left\{\frac{22}{7}, 3.14, \pi\right\}\), write down an irrational number. 2. **Recall definitions:**

1. The question asks: What property is shown? 2. To answer this, we need to identify the context or example where a property is demonstrated.

1. **State the problem:** Find the slope of the line shown in the graph using the rise over run method. 2. **Recall the formula for slope:**

1. Stating the problem: Solve for $x$ in the equation $$\frac{6}{11} - \left(\frac{8}{5} + \frac{9}{11} - 2\right) \div \left[\frac{7}{30} - \left(\frac{2}{15} + \frac{7}{5} - \fra

1. **State the problem:** Solve the expression $$\left(\frac{3}{2} - \frac{23}{42} + \frac{8}{21}\right) = \left(\frac{17}{6} - \frac{29}{15}\right) \cdot \left(\frac{5}{2} - \frac

1. **Stating the problem:** We have a group of 150 referees choosing different sports. The pie chart sectors are given as follows: - Volleyball: 22% of the group

1. Planteamos el sistema de ecuaciones dado: $$\begin{cases} 2x + y - z = 6 \\ x - y + 2z = -1 \\ -x + 3y = 1 \end{cases}$$

1. **Problem 5a:** Given the function $y = x \cdot \left(x - \frac{3}{4}\right)$, find the zeros, vertex, stretch factor, general form, and y-intercept. 2. **Formula and rules:**

1. The problem is to find the number that must be added to a given number to get 14000. 2. Let the number you have be $x$ and the number to add be $y$.