🧮 algebra

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

1. **State the problem:** A baker made 3 kinds of bagels: plain, cheese, and sesame seed. Three-eighths of the bagels were plain, one-fifth were cheese, and the rest were sesame se

1. The problem is to divide the fraction $\frac{-2}{9}$ by $-4$. 2. Recall the division of fractions rule: dividing by a number is the same as multiplying by its reciprocal.

1. **State the problem:** Simplify the expression $$(-2 x^2) (x^2)^3 + (2 x^2)^4 - (-2 x)^3 (+ 3 x^2) + (5 x)^2 (-x)^3$$. 2. **Recall exponent rules:**

1. **State the problem:** Multiply the fractions $\frac{8}{9} \times \frac{5}{12} \times \frac{18}{35}$.\n\n2. **Formula and rules:** To multiply fractions, multiply the numerators

1. **State the problem:** Chris bought candy dispensers for 16 and paid 1.20 in sales tax. We need to find the sales tax rate. 2. **Formula:** Sales tax rate is calculated by \( \t

1. **State the problem:** Find 8.5% of 48. 2. **Formula:** To find a percentage of a number, use the formula: