🧮 algebra

1. **State the problem:** We need to find the value of the composite function $f(g(-2))$. 2. **Understand the functions:** From the description, $g$ is a wavy curve oscillating bet

1. **State the problem:** We need to determine if the point $(6,-4)$ lies on the line given by the equation $y = -3x + 14$. 2. **Recall the formula:** A point $(x,y)$ lies on the l

1. **State the problem:** James sells pencils for 2 each and stickers for 0.5 each. He wants to make at least 10 dollars daily. 2. **Define variables:** Let $p$ be the number of pe

1. **State the problem:** We are given the function $$f(x) = -0.3 (x - 2)^2 + 4$$ which models height in feet as a function of distance in feet. We know the point $(0, 2.8)$ lies o

1. **State the problem:** Simplify the expression $\frac{8a^2}{6a^4}$. 2. **Formula and rules:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} =

1. The problem is to simplify the expression $5(2 + w) + 6w$ step-by-step and identify the reason for each step. 2. Start with the given expression:

1. Problem statement: The expression to simplify is $5(2 + w) + 6w$. 2. Formula used: Distributive property $a(b + c) = ab + ac$.

1. The problem is to simplify the expression: $$250 \left( 1 + 0.12 \times \frac{292}{365} \right)$$

1. **State the problem:** Simplify the expression $$(3 \times 5 - 3)^2 + (3 - 3 \times 6^2)$$. 2. **Recall order of operations:** Perform multiplication and exponents before additi

1. **State the problem:** Solve the inequality $$-45 \leq m + 27 - 9m \leq -29$$. 2. **Simplify the inequality:** Combine like terms inside the inequality.

1. **Stating the problem:** We are given a parabola that opens downwards with x-intercepts near $-6$ and $6$, and a vertex near $(0,7)$. We want to find the equation of this parabo

1. **State the problem:** We are given the linear function $g(x) = -x - 4$ and need to find the value of $g(-2)$. 2. **Formula used:** To evaluate a function at a given input, subs

1. **State the problem:** We are given points on a graph: $(-3,9)$, $(-2,5)$, $(-1,3)$, and $(0,2)$, and we need to find the equation of the curve that fits these points. 2. **Anal

1. **State the problem:** Solve the equation $a^2 - 49 = 0$ by factoring. 2. **Recall the formula:** This is a difference of squares, which factors as $x^2 - y^2 = (x - y)(x + y)$.

1. **State the problem:** Solve for $v$ in the equation $\frac{v}{9} = \frac{8}{12}$.\n\n2. **Use the cross-multiplication method:** For equations of the form $\frac{a}{b} = \frac{

1. **State the problem:** Emma wants to find the number of hours $h$ for which the total cost of hiring the local photographer equals the total cost of hiring the out-of-town stude

1. **State the problem:** Shelley starts jogging from the trailhead at 5 miles per hour, while Naomi is already 1.3 miles ahead, walking at 2.4 miles per hour. We need to find how

1. **State the problem:** Simplify the expression $$-12x^2 - 6x^2$$. 2. **Recall the rule:** When combining like terms, add or subtract the coefficients of terms with the same vari

1. **State the problem:** Jackson has quarters (q) and dimes (d). The total value is 12.65 dollars. The number of quarters is seven less than twice the number of dimes. 2. **Define

1. **State the problem:** Express the expression $$\frac{2^n \times 4^{n-1}}{8^{n-2}}$$ as a power with a single base. 2. **Recall the bases and their relationships:**

1. **Problem:** Simplify the expression $$\left(\frac{12x^3 y^2}{9xy}\right) \left(\frac{18x^5 y^3}{4x^2 y^2}\right)$$. 2. **Formula and rules:**