🧮 algebra

1. **State the problem:** We need to graph the function $f(x) = x^2 - 2x + 7$ and plot its vertex and another point on the parabola. 2. **Formula and rules:** The function is a qua

1. **State the problem:** We have a product with a current selling price of 325.

1. **State the problem:** Solve the equation $$8r^6 + 21sr^3 - 27 = 0$$ for $r$. 2. **Rewrite the equation:** Notice that $r^6 = (r^3)^2$. Let $x = r^3$. Then the equation becomes:

1. **State the problem:** Aaron purchased a shirt that originally costs 165 but received a 10% discount. We need to find out how much he actually paid. 2. **Formula for discount pr

1. **State the problem:** Aaron purchased a shirt that originally costs 1.65 but received a 10% discount. We need to find out how much he actually paid. 2. **Formula for discount p

1. **State the problem:** We have the linear equation $$C = 140S + 2500$$ which represents the total cost $$C$$ as a function of the amount of sugar transported $$S$$. 2. **Underst

1. **State the problem:** We are given a relation $H$ represented by four points: $(-3,3)$, $(4,4)$, $(4,0)$, and $(0,-3)$. We need to find the domain and range of $H$ using set no

1. **State the problem:** Find the equation of the line passing through the points $(-3,7)$ and $(0,0)$ in slope-intercept form $y=mx+b$. 2. **Recall the formula:** The slope $m$ o

1. **Stating the problem:** We are given the function $$F(x,y) = (n + 2) 5^{x^{10 - n}} y^{m + 2} - x^n y^8 + m x^3 y^{m - 5}$$ and asked to find the "position" of this function, w

1. **State the problem:** Solve the equation $ (x+2)^2 = 64 $. 2. **Recall the formula:** The equation is a quadratic in the form $ (a)^2 = b $, which implies $ a = \pm \sqrt{b} $.

1. The problem gives two functions: $$p_N(x) = -x + 13.2$$ and $$K(x) = 0.1x^3 - 0.9x^2 + 3x + 16$$. 2. We want to understand or analyze these functions. Let's start by stating wha

1. **Stating the problem:** We are given two inequalities:

1. **State the problem:** Solve the system of inequalities: $$y \leq 2x + 3$$

1. **Problem statement:** We have two equations from the costs of sodas and burgers:

1. **State the problem:** Sam covers 9 meters when he walks 12 paces. We need to find how far he travels when he walks 16 paces. 2. **Formula and explanation:** The distance covere

1. **State the problem:** We need to find how much space should be allowed for 48 seedlings if 64 seedlings require 24 cm\textsuperscript{2} of space. 2. **Identify the relationshi

1. **State the problem:** Calculate $\frac{5}{7} - \frac{1}{4}$.\n\n2. **Formula and rules:** To subtract fractions, find a common denominator, then subtract the numerators.\n\n3.

1. **Problem:** Calculate $\frac{5}{7} - \frac{1}{4}$. 2. **Formula:** To subtract fractions, find a common denominator and subtract the numerators.

1. **State the problem:** Simplify the expression $$(3^7)^3$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents:

1. The problem is to find $\frac{1}{4}$ of 240. 2. The formula to find a fraction of a number is:

1. **State the problem:** Ann and Bob share 240 in the ratio 3:5. Ann gives half of her share to Colin, and Bob gives a tenth of his share to Colin. We need to find the fraction of