🧮 algebra

1. The problem is to analyze the function $$g(x) = |x| + |\sin(4\pi)|.$$\n\n2. First, recall that the absolute value function $|x|$ returns the non-negative value of $x$.\n\n3. Nex

1. **State the problem:** Solve the linear equation $5 - 2y = 7$ for $y$. 2. **Use the formula and rules:** To solve for $y$, isolate $y$ on one side by performing inverse operatio

1. **Problem statement:** Find the graph of the function $$g(x) = |x| + \frac{1}{\sin(4\pi)}$$.

1. **State the problem:** We are given the height of a rocket as a function of time: $$h = -2(t+1)(t-9)$$ and need to answer several questions about the rocket's height and timing.

1. **State the problem:** Solve the equation $$-6 = \frac{p}{4} - 6$$ for $p$. 2. **Add 6 to both sides** to isolate the term with $p$:

1. **State the problem:** You sold 300 shirts at 20 each. For every 1 increase in price, sales drop by 5 shirts. Find the number of shirts to sell to maximize revenue and the maxim

1. **Énoncé du problème** : Trouver le point d'intersection entre les fonctions $y_1 = 4\sqrt{x}$ et $y_2 = 2x + 2$, puis déterminer les bornes d'intégration entre ces courbes et l

1. The problem is to identify the vertical asymptote (VA) and the possible presence of a horizontal or oblique (slant) asymptote (CA) for a function with denominator $x+1$. 2. A ve

1. **State the problem:** We need to find the equation of a rational function with a point of discontinuity (hole) at $(-3,-5)$, a $y$-intercept at $(0,4)$, and an $x$-intercept at

1. **State the problem:** We need to sketch the graph of the piecewise function:

1. **State the problem:** We are given the inverse function $f^{-1}(x)$ as a set of points: $\{(1, -10), (-5, -8), (10, -7), (0, -6), (6, 0)\}$. We want to understand the domain an

1. **State the problem:** Solve the system of equations: $$5y = 2x - 6$$

1. The problem asks how to solve part B, but since the original question is not provided, I will explain a general approach to solving algebraic problems labeled as B. 2. Typically

1. **State the problem:** Solve the system of equations using substitution: $$3y = -4x - 1$$

1. **State the problem:** Find the gradient of the line passing through points (0, 7) and (4, 0). 2. **Formula:** The gradient (slope) $m$ of a line through points $(x_1, y_1)$ and

1. Stating the problem: Simplify the expression $$\frac{8mn}{3} \div \frac{4mn^2}{5}$$ and choose the correct option. 2. Recall the rule for division of fractions: $$\frac{a}{b} \d

1. **State the problem:** We need to find the difference in lengths between two beams, one of length $\sqrt{72}$ meters and the other $\sqrt{18}$ meters. 2. **Recall the formula:**

1. **State the problem:** We need to find the total number of school items being shipped if each box contains $2xy + 3y^2$ items and there are $4x$ boxes. 2. **Write the expression

1. **State the problem:** Simplify the expression $$-4(9x + 2) + 6(7 - 8x)$$ and find which multiple choice answer matches. 2. **Use the distributive property:** Multiply each term

1. The problem states that the temperature at 1 a.m. was $3 \frac{1}{2}$ degrees Fahrenheit, which is $3.5$ degrees. 2. The temperature changes by $-1 \frac{1}{2}$ degrees per hour

1. **State the problem:** Simplify the expression $$\left[(c^2 d)^4 \times (c^3 d^5)^2\right]^3 \div (c^4 d^7)^5$$. 2. **Recall exponent rules:**