🧮 algebra

1. **State the problem:** We need to evaluate three fractions: $$\frac{18^3}{0.395}, \quad \frac{0.28 \times 37.4}{77.8}, \quad \frac{63.7 \times \sqrt{3.93}}{0.425}$$

1. The problem asks to identify the graph representing the inequality $x \leq 1$. 2. The inequality $x \leq 1$ means all values of $x$ that are less than or equal to 1.

1. The problem involves understanding and comparing the inequalities: $x < 80$, $x \geq 80$, and $x > 80$. 2. Inequalities describe ranges of values for $x$:

1. **Stating the problem:** Solve the equation $$s = \frac{s(z-1)}{\frac{1}{3}(z+1)}$$ for $s$ or simplify it. 2. **Rewrite the denominator:** The denominator is $$\frac{1}{3}(z+1)

1. The problem asks to write the linear equation $y + 1 = -3(x - 1)$ in slope-intercept form and simplify. 2. The slope-intercept form of a linear equation is given by:

1. **State the problem:** Evaluate the expression $(-10) \div (-2)^2 + 5^3$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication/Division (lef

1. **State the problem:** Solve for $p$ in the equation $$-9(2p + 1) = -15p$$. 2. **Distribute the $-9$ on the left side:**

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 $x^2 - y^2 = (x - y)(x + y)$.