🧮 algebra

1. **State the problem:** Calculate the value of the expression $\frac{1}{3} \times 3.14 \times 4^2 \times 6$. 2. **Recall the order of operations:** We first evaluate exponents, t

1. **State the problem:** Given the function $P(x) = x(x - 3)(x + 2)$, find the y-intercept, the x-intercepts, and the end behavior as $x \to \infty$ and $x \to -\infty$. 2. **Find

1. **State the problem:** Flaumback drives to a job interview in 1.5 hours at 60 km/h. We want to find how many minutes longer the drive takes if he drives at 50 km/h instead. 2. *

1. **State the problem:** Calculate the value of the expression $\frac{1}{3} \times 3.14 \times 3^2 \times 7$. 2. **Recall the order of operations:** Multiply and exponentiate from

1. **State the problem:** Determine the end behavior of the polynomial function graphed. 2. **Recall end behavior rules:** For a polynomial function $f(x)$, the end behavior depend

1. **State the problem:** Solve the system of equations by graphing: $$y = -x^2 + 4x + 2$$

1. **State the problem:** Solve the quadratic equation $2x^2 - 2x = 112$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Evaluate the expression $2+5(8-5)$.\n\n2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication, then addition.\n\n3.

1. **State the problem:** Simplify the equation $$-

1. The problem asks us to solve the equation using the Zero-Product Property: $$(3x - 7)(2x + 1) = 0$$ 2. The Zero-Product Property states that if the product of two factors is zer

1. **State the problem:** Solve the equation $ (x + 7)(4x - 5) = 0 $ using the Zero-Product Property. 2. **Recall the Zero-Product Property:** If the product of two factors is zero

1. **State the problem:** Solve the inequality $3 + y > 9$. 2. **Isolate the variable:** To solve for $y$, subtract 3 from both sides:

1. **Problem:** Determine if 64 is both a power of 2 and a power of 4. 2. **Recall:** A number $a$ is a power of $b$ if $a = b^n$ for some integer $n$.

1. **Problem statement:** Given the polynomial $x^2 + 4x + 2a$, its zeroes are $a$ and $\frac{2}{a}$. We need to find the value of $a$. 2. **Formula used:** For a quadratic polynom

1. **State the problem:** A gas barbecue has a series of discounts: $420 less, 33.3\%, 20\%, and 5\%$ off the original price. Then, it is marked up by 60\% of the regular selling p

1. **State the problem:** Solve the system by substitution: $$y = 7x - 22$$

1. **Stating the problem:** Solve question 2 related to sales, cost, markup, markdown, or profit/loss calculations involving percentages. 2. **Identify the problem:** Since the use

1. **State the problem:** Solve the inequality $$-5 < 1 + \frac{3}{2}(-4x + 6)$$ for $x$. 2. **Recall the distributive property:** Multiply $\frac{3}{2}$ by each term inside the pa

1. **State the problem:** Solve the quadratic equation $$3x^2 + 3x - 6 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b

1. **Problem statement:** Given functions $f(x) = 3x + 5$ and $g(x) = x^2 - 2$, perform the following operations: a) $f(x) + g(x)$

1. **State the problem:** Solve the inequality $$-4 + 4(4r - 8) \leq 10r - 9 - 6$$ for $r$ and write the answer in simplest form. 2. **Apply the distributive property:** Multiply 4