🧮 algebra

1. **Problem Statement:** Alex needs to rent a minivan for a week. Two companies offer different pricing schemes: - Easyvans charges a flat fee of 230 plus 0.10 per kilometer.

1. **State the problem:** Simplify and analyze the function $$r(z) = z^{-8} - z^{\frac{1}{2}}$$. 2. **Recall the rules:**

1. **State the problem:** Factor the trinomial $$h^2 + 3h - 40$$ into the form $$(h + a)(h - b)$$ where $a$ and $b$ are numbers to be found. 2. **Recall the factoring rule:** For a

1. **Problem:** Multiply the rational expressions \(\frac{2a^2 b}{b^2 c} \times \frac{b}{a}\). 2. **Formula and rules:** When multiplying rational expressions, multiply numerators

1. The problem describes a parabola with points labeled a, b, and c, where c is the vertex, b is on the same y-coordinate as the dock but on the opposite side of the parabola, and

1. **State the problem:** Simplify the expression $$(2x^2 - 2x + 5)(x + 4)$$ and write it in the form $$ax^3 + bx^2 + cx + d$$. 2. **Use the distributive property (FOIL for polynom

1. **Problem statement:** Linda is water-skiing and the boat follows a parabolic path with vertex at the origin $(0,0)$. The dock is at $(30,30)$ and the boat starts at $(-30,60)$.

1. **State the problem:** Solve the inequality $5 - x \leq 3$ and express the solution in interval notation. 2. **Write the inequality:**

1. **State the problem:** Simplify the expression $$\frac{y^2 + y - 56}{y^2 + 3y - 40}$$. 2. **Factor numerator and denominator:**

1. **Simplify the monomial: -7a + 43a** Step 1: State the problem.

1. Simplify the monomial: $-7a + 43a$ 2. First, state the problem: Combine like terms $-7a$ and $43a$.

1. **State the problem:** You and 3 friends (4 people total) went to lunch. The original bill was 82. You have a 20% off coupon. 2. **Calculate the discounted price:**

1. **State the problem:** The Sweater Shack offers a 20% discount on sweaters. The regular price is 15. We need to find the discount amount and the sale price. 2. **Formula for dis

1. **State the problem:** We need to find how many representatives from California are in the U.S. House of Representatives, given that there are 435 representatives total and 12.2

1. **State the problem:** A video game originally costs 32. There is a 20% discount on the game. We need to find the discount amount. 2. **Formula:** The discount amount is calcula

1. **Problem:** Simplify the expression $ (x^{-4})^2 $. 2. **Formula:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \times n} $$

1. The problem asks us to compare the slopes of two functions, Function A and Function B, based on given points and a graph description. 2. The slope formula for a line passing thr

1. **State the problem:** We need to determine the unit price for each option and explain why the given unit prices $2.42, $2.33,$ and $2.58$ correspond to the quantities and total

1. **State the problem:** We need to evaluate the function $f(x) = 5x^2 + 4x$ at $x = a$ and simplify the expression. 2. **Write the function with the given input:** Substitute $x$

1. The problem asks to evaluate the function $g(x) = \sqrt{x} + 2$ for the expression $g(x+h)$ and simplify the answer. 2. The function $g(x)$ is defined as $g(x) = \sqrt{x} + 2$.

1. **Problem statement:** We have two affine functions $h(x) = -\frac{5}{2}x + 6$ and $g(x)$ passing through points $B(6,0)$ and $C(0,3)$. Points $A(\frac{3}{2},0)$ and $D(0,6)$ ar