🧮 algebra

1. **State the problem:** We need to graph the inequality $$5x + 4y > -8$$ on the Cartesian plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, first express th

1. The problem asks to verify the correctness of the answers given for the polynomial function $h(x) = 2(x - 1)^3 (x + 4)^2$. 2. First, check the degree and leading coefficient.

1. **Problem:** Determine which ratios are correct based on the number of children riding bicycles and scooters at the park. 2. **Given:**

1. The problem asks to write equations for three lines given their descriptions and points. 2. For line l (red), it is a horizontal line crossing the y-axis at $y=3$. The equation

1. **Problem Statement:** We are given the equation for the total cost of notebooks and pencils: $$1.00 n + 0.25 p = 10.00$$

1. **Problem Statement:** Identify the slope and y-intercept of the line passing through points approximately $(-3,-2)$ and $(2,2)$. 2. **Formula for slope:** The slope $m$ of a li

1. **State the problem:** We have a system of equations with symbols representing unknown values: $$\text{pirate} + \text{pirate} + \text{squid} = 21$$

1. The problem asks to express 0.60 dollars as a fraction of a dollar. 2. Recall that 1 dollar equals 1 whole, so 0.60 dollars is 0.60 out of 1.

1. The problem asks to write $0.40 as a fraction of a dollar. 2. Recall that 1 dollar equals 1 whole, so $0.40 means 40 cents out of 100 cents.

1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = x^5 - 36x^3$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal to zero:**

1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = -2x^4 + 2x$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal to zero:**

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $-3 \leq x \leq 3$. 2. **Recall the formula:** The average rate of chang

1. **Problem statement:** A merchant marks up everything by 40%. Find the retail price of an item costing the merchant 15. 2. **Formula:** Retail price = Cost price + Markup

1. The problem is to factor the quadratic expression $x^2 - 7x - 78$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=-7$, and $c=-78$.

1. **State the problem:** We have a piecewise function defined as: $$

1. **State the problem:** We are given the system of equations: $$9x + y = 28$$

1. **State the problem:** Factor the expression $$5a^2 + 10ab - 3a - 6b$$. 2. **Identify the method:** We will use factoring by grouping, which involves grouping terms to find comm

1. **State the problem:** Factor the quadratic equation $$2x^2 = 3x + 35$$ into its factored form. 2. **Rewrite the equation:** Move all terms to one side to set the equation to ze

1. **State the problem:** We have two playlists: Han's playlist is described by the equation $$y = 4x + 20$$ where $x$ is the number of days and $y$ is the total number of songs.

1. **State the problem:** We need to find the Instantaneous Rate of Change (IROC) of the function $$y = 4\sqrt{100} - 2t$$ at $$t = 15$$ without using derivatives. 2. **Rewrite the

1. **State the problem:** Simplify the expression $$\frac{(2 a^3 b^2 c^{-2})^3}{16} a^{-4} b^5 c^{-6}$$. 2. **Apply the power to each factor inside the parentheses:**