🧮 algebra

1. **State the problem:** Eva and Dexter share sweets in the ratio 1:2. Mo and Annie share the same total number of sweets as Eva and Dexter, but in the ratio 3:5. 2. **Part a:** I

1. The problem is to analyze the function $f(x) = |x + 2|$. 2. The absolute value function outputs the distance from zero, so $f(x)$ is always non-negative.

1. The problem is to evaluate the expression $16^{\frac{3}{2}}$. 2. Recall that an exponent of the form $a^{\frac{m}{n}}$ means the $n$th root of $a$ raised to the $m$th power: $$a

1. **Problem 25:** Given the linear equation $$n = 29.6 + 1.20t$$ where $$n$$ is the number of women (in millions) aged 35 to 44 in the labor force and $$t$$ is years since 1981. 2

1. **State the problem:** Solve the system of linear equations: $$4x + 20y = -4$$

1. **State the problem:** Solve the system of inequalities: $$9 - 3x < 3$$

1. **State the problem:** Solve the system of inequalities: $$-8 \leq 5x - 7$$

1. Stating the problem: Solve the inequality $$-5x - 8 \leq 7$$. 2. Add 8 to both sides to isolate the term with $$x$$:

1. The problem is to analyze the function $y = |x - 3| - 7$. 2. This is an absolute value function, which typically forms a V-shaped graph.

1. The problem is to analyze the function $$y = -|x| + \frac{1}{2}$$ and understand its shape and key features. 2. The function involves the absolute value of $x$, which normally c

1. The problem is to solve the equation $$\left| \frac{1}{3} x \right| = 30$$ for $x$. 2. Recall that the absolute value equation $|A| = B$ means $A = B$ or $A = -B$.

1. **Énoncé du problème :** Factoriser les expressions données en utilisant le facteur 1 ou -1. 2. **Utilisation du facteur 1 :**

1. The problem is to solve the equation $2|x + 4| = 40$. 2. Start by isolating the absolute value expression:

1. The problem is to identify which of the given functions correspond to the first or second notable identities: $$\alpha^2 + 2\alpha b + b^2 = (a + b)^2$$

1. **State the problem:** Solve the equation $$\frac{3}{2} |x - 5| = 0$$. 2. **Isolate the absolute value:** Since $$\frac{3}{2}$$ is a nonzero constant, divide both sides by $$\fr

1. Problem: Calculate $\frac{3}{4} + \frac{5}{8}$. - Convert $\frac{3}{4}$ to eighths: $\frac{3}{4} = \frac{6}{8}$.

1. The problem is to find the number of solutions to the quadratic equation $$-\frac{3}{7}x^2 + x - 7 = 0$$. 2. To determine the number of solutions, we calculate the discriminant

1. The problem is to find the next three numbers in the sequence: 4, 8, 16, 32, _, _, _. 2. Observe the pattern: each number is multiplied by 2 to get the next number.

1. **State the problem:** Simplify the expression $$(2\sqrt{x} + \sqrt{y}) - (\sqrt{x} - 2\sqrt{y})$$. 2. **Remove parentheses carefully:**

1. **State the problem:** Simplify the expression $$\sqrt{\frac{25x^6y^3}{16x^2y^9}}$$ and interpret the result. 2. **Simplify inside the square root:**

1. **State the problem:** Simplify the expression $$\left(\frac{3a^{4}b^{-1}}{8a^{-2}b^{-3}}\right)^{-2}$$. 2. **Simplify inside the parentheses:**