🧮 algebra

1. Задача: определить количество решений системы уравнений \[

1. **Stating the problem:** We are given points on a graph representing Corey’s earnings over weeks worked. We need to determine which statements about these points correctly descr

1. **State the problem:** We need to find the length of Yui's zen garden given that the perimeter is 32 meters and the length is 3 times the width. 2. **Write the formula for the p

1. The cancellation in math is based on the property that if you multiply or divide both numerator and denominator of a fraction by the same nonzero number, the value of the fracti

1. **State the problem:** There are 23 players on a soccer team. Each player bought either a short sleeve jersey or a long sleeve jersey. A long sleeve jersey costs 50 and a short

1. **State the problem:** We have a ticket sale where students pay 2 each and faculty pay 4 each. A total of 120 tickets were sold and total revenue was 380.

1. **State the problem:** We are given that $a - b = b - c = 2$ and need to find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}.$$

1. The problem asks to find the cube root of 64, written as $\sqrt[3]{64}$. 2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.

1. **State the problem:** Josie wants to make lemonade servings using syrup, lemon juice, and water. Each serving requires 3/4 ounces of syrup, 2 1/4 ounces of lemon juice, and 5 o

1. **State the problem:** Solve the system of equations by graphing: $$y = x + 3$$

1. **State the problem:** Solve the system of equations by graphing: $$x + y = 2$$

1. **State the problem:** Given the function $h(x) = \sqrt{x - 1} + 2$, we need to find its domain and range, identify the end node, find the inverse function $h^{-1}(x)$ along wit

1. **Problem:** Simplify the algebraic fraction $$\frac{4}{3x-1} - \frac{3}{2x+1}$$ 2. **Formula and rules:** To subtract fractions, find a common denominator and combine the numer

1. **State the problem:** We need to graph the logarithmic function $$g(x) = \log_{\frac{1}{5}} x$$ and identify which graph (A, B, C, or D) correctly represents it. 2. **Recall th

1. **Planteamiento del problema:** Se nos dan las matrices

1. **State the problem:** Solve the equation $$x^2 - 9 = 0$$ by factoring. 2. **Formula and rules:** To solve quadratic equations by factoring, we rewrite the equation in the form

1. **State the problem:** Solve the inequality $$-6x - 3 \geq 9$$ and graph the solution on a number line. 2. **Write the inequality:** $$-6x - 3 \geq 9$$

1. **State the problem:** Solve the inequality $$3q - 9 \leq 8q + 10$$ for $q$ and write the answer in simplest form. 2. **Write the inequality:** $$3q - 9 \leq 8q + 10$$

1. **Problem:** Given $a=2$, $b=-3$, $c=4$, find: i) $ab - bc$

1. **State the problem:** Simplify the expression $$\frac{9\sqrt{432p^5} - 7\sqrt{27p^5}}{\sqrt{33p^4}}, p > 0.$$\n\n2. **Recall the formula and rules:** \n- The square root of a p

1. **State the problem:** Factor each quadratic expression given. 2. **Recall the factoring formulas and rules:**