🧮 algebra

1. **Stating the problem:** Calculate the total salary if the base salary is 334 and there is an additional 13 for every item sold beyond 100.

1. The problem asks to write a function for the graph related to $f(x) = 5^x$ where the graph is vertically shifted upwards by a constant $k$. 2. The general form for vertical shif

1. **State the problem:** Write the quadratic function in vertex form $f(x) = a(x-p)^2 + q$ for each graph.

1. **Problem Statement:** We have three graphs of the form $f(x) = ax^2$ labeled $r$, $s$, and $t$. We need to identify which graphs correspond to $a > 0$ and which correspond to $

1. **State the problem:** We need to find the length of a rectangular tank given its volume, width, and height. 2. **Formula:** The volume $V$ of a rectangular prism is given by

1. **Problem statement:** Find the domain and range of the function $$y = (x + 1)(x - 3)$$. 2. **Recall the domain and range definitions:**

1. **State the problem:** A hiker starts a 150-mile hike and walks 11 miles each day. We want to find how many miles remain after $x$ days. 2. **Formula:** The miles remaining afte

1. **State the problem:** We want to divide the polynomial $$y = 2x^6 - 10x^5 - 5x^2 + 26x - 5$$ by the factor $$x - 5$$ using polynomial long division. 2. **Recall the formula and

1. The problem asks for an example of an ordered pair in each quadrant and on each axis of the Cartesian coordinate plane. 2. Recall the coordinate plane is divided into four quadr

1. **Problem Statement:** Determine if the graph of the line passing through points $(-10, 10)$ and $(10, -10)$ defines a function, and find its domain and range. 2. **Check if the

1. **State the problem:** A zookeeper wants to fence a rectangular habitat for goats. The length $x$ should be at least 80 feet, and the perimeter should be no more than 300 feet.

1. **State the problem:** We need to find the vertex, axis of symmetry, and y-intercept of a parabola. 2. **Given information:** The vertex is at $(2, -1)$.

1. **State the problem:** Simplify the expression $9a + a + b + 2b + 4a$ and verify if it equals $14a + 3b$. 2. **Combine like terms:** Group the terms with $a$ and the terms with

1. **State the problem:** Simplify the expression $4 + 7h + h + 11 + 4j + 4h$. 2. **Combine like terms:** Group the constants and the terms with $h$ and $j$ separately.

1. **State the problem:** Factor the quadratic expression $16b^2 - 40b + 25$. 2. **Recall the formula:** A quadratic trinomial $ax^2 + bx + c$ can be factored as $(mx + n)^2$ if it

1. **State the problem:** Simplify or analyze the quadratic expression $4x^2 + 4x + 1$. 2. **Recognize the form:** This is a quadratic trinomial of the form $ax^2 + bx + c$ where $

1. **Zadání problému:** Máme zakázku, kterou vyrábí automaty pracující společně stejným tempem. 2. **Dáno:**

1. **State the problem:** Find the equation of the line passing through points $(-7,6)$ and $(6,-7)$ in slope-intercept form $y=mx+b$. 2. **Find the slope $m$:** Use the formula $$

1. **State the problem:** Factor the trinomial $23x + 21x^2 - 20$ completely. 2. **Rewrite the polynomial in standard form:**

1. **State the problem:** Simplify the expression $$(a + 8)(a^2 - 8a + 64)$$. 2. **Recall the formula:** This expression resembles the product of a binomial and a trinomial that ca

1. **State the problem:** Divide the complex numbers $(-2 + i)$ by $(1 + 3i)$. 2. **Formula and rule:** To divide complex numbers, multiply numerator and denominator by the conjuga