🧮 algebra

1. The problem asks to find the mean height of two black bars and adjust a light bar to that mean height. 2. The mean (average) of two numbers $a$ and $b$ is given by the formula:

1. The problem states: "The sum of the opposite of a number $x$ and six is less than or equal to five."\n\n2. Let's translate the words into a mathematical inequality. "Opposite of

1. The problem asks to determine whether given values are solutions to an equation, but the equation and values are missing from the question. 2. To check if a value is a solution

1. We are asked to evaluate the expression $4^3 - 7(8 + 2) \div 5$. 2. Recall the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Add

1. The problem involves using the Remainder and Factor Theorems to analyze the polynomial $P(x)$ given by values at certain points. 2. The Factor Theorem states that if $(x - a)$ i

1. **State the problem:** Find the slope of the line given by the equation $$-5x - 3y = 14$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y =

1. **State the problem:** We need to find the expected adult weight of Britney's golden retriever puppy. 2. **Given information:** The expected adult weight is given by the formula

1. **State the problem:** Simplify the expression $$\frac{18 \cdot 7a^5 b^6 c}{14a^5 b^9}$$. 2. **Write the expression clearly:**

1. The problem states that the price $P$ of a yogurt sundae depends on its weight $w$ in ounces, and is given by the formula: $$P = 2 + 0.5w$$

1. **State the problem:** Simplify the expression $$(4z^{-5})^3$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power sep

1. **State the problem:** Multiply and simplify the expression $ (x + 3)(2x + 5) $. 2. **Recall the distributive property (FOIL method):**

1. **State the problem:** Find the slope of the line given by the equation $$-5x - 3y = 14$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y =

1. **State the problem:** Simplify the expression $$qr^{-75}s^{66} \times q^{-5}rs \times q^{-1}r^{60}s^{28}$$. 2. **Recall the rules:** When multiplying terms with the same base,

1. **State the problem:** Multiply the binomials $ (3x - 4)(4x + 3) $ and simplify the result. 2. **Recall the formula:** To multiply two binomials, use the distributive property (

1. **State the problem:** We need to find the missing number in the equation: $$15 \frac{3}{8} - 13 \frac{7}{8} = 1 \frac{7}{8}$$

1. **State the problem:** We are given the sequence 8, 24, 72, 216, __, __ and need to find the missing terms. Then, determine if the sequence is arithmetic (A), geometric (G), or

1. **State the problem:** Solve the equation $125.4 - x = 63 + \frac{1000}{50}$ for $x$. 2. **Calculate the division on the right side:**

1. **State the problem:** Solve the equation $$\frac{2x}{3} - \frac{1}{2} = \frac{1}{4}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation.

1. **Énoncé du problème :** Calculer le déterminant de la matrice $A = \begin{pmatrix} 1 & 2 & 0 \\ 2 & 6 & -3 \\ 3 & 10 & -6 \end{pmatrix}$. 2. **Formule utilisée :** Le détermina

1. **State the problem:** Solve the equation $12 - 2m = 2m - 3$ for $m$. 2. **Add $2m$ to both sides:**

1. **State the problem:** Determine if the function $$f(x) = \frac{x^3 - 2x^2 - 49x + 98}{x - 7}$$ is discontinuous at $$x=7$$. 2. **Recall the rule for continuity:** A function is