🧮 algebra

1. The problem is to solve the equation $108 \div y = 18$ for $y$. 2. The formula used here is to isolate $y$ by multiplying both sides of the equation by $y$ and then dividing bot

1. **State the problem:** Determine if $b=6$ is a solution for each equation. 2. **Equation a: $8b=48$**

1. **State the problem:** Complete the square for the quadratic function $$f(x) = 4x^2 - x + 2$$ and find the vertex coordinates, maximum or minimum value, and its nature. 2. **Rec

1. **State the problem:** We are given the function $g(x) = x^2 + 6$ and need to find $g(0)$, $g(-2)$, and $g(\sqrt{3})$. 2. **Recall the formula:** The function is $g(x) = x^2 + 6

1. **State the problem:** Solve the quadratic equation $$x^2 - 10x + 22 = 0$$. 2. **Identify coefficients:** Here, $$a = 1$$, $$b = -10$$, and $$c = 22$$.

1. **State the problem:** We are given the function $g(x) = x^2 + 6$ and need to find $g(-2)$, $g(0)$, and $g(3)$. 2. **Recall the formula:** The function is $g(x) = x^2 + 6$. To f

1. **Problem:** Use set notation to specify the domain and range of each relation. 2. **Relation a:** $5x + 2y = 2$

1. **State the problem:** A restaurant charges a delivery fee plus the price of pizzas. One customer pays 25 for 2 pizzas, another pays 58 for 5 pizzas. Find how many pizzas a cust

1. **State the problem:** We need to find the value of $A$ that satisfies the equation $$2 \frac{1}{A} = \frac{19}{A}.$$ 2. **Rewrite the mixed fraction:** The mixed fraction $2 \f

1. The problem asks to convert 73.6% to a decimal. 2. Recall that percent means per hundred, so 73.6% means 73.6 out of 100.

1. **State the problem:** Solve the equation $$\log_2 \left( \log_2 (7x - 10) \times \log_x 16 \right) = 3$$ and find the sum of all solutions. 2. **Recall properties and formulas:

1. **State the problem:** We know that 19.9% of all registered doctors were female, and the number of female doctors is 41,300. We need to find the total number of registered docto

1. **State the problem:** We know that 39,700 copies sold represent 9.4% of the total copies sold to date. We need to find the total number of copies sold, denoted as $T$. 2. **Wri

1. The problem asks to solve the equations 1 and 2. 2. Since these are just numbers, the solution to equation 1 is simply 1.

1. Problem: Determine if the statement $(3x^2)^3 = 9x^6$ is TRUE or FALSE. Step 1: Use the power of a product rule: $(ab)^m = a^m b^m$.

1. **State the problem:** Solve for $n$ in the equation $$9^{2n-1} = 27^{n+2}.$$ 2. **Rewrite bases as powers of the same base:** Both 9 and 27 can be written as powers of 3:

1. The problem asks for the 5th root of $7^{10}$. 2. The formula for the $n$th root of a number $a^m$ is $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$.

1. The problem asks for the cube root of $5^{15}$. 2. Recall the property of exponents and roots: the $n$th root of $a^m$ is $a^{\frac{m}{n}}$.

1. **State the problem:** Find the 4th root of $3^{12}$. 2. **Recall the formula for roots and exponents:** The $n$th root of $a^m$ can be written as $$\sqrt[n]{a^m} = a^{\frac{m}{

1. **State the problem:** Simplify the expression $$\left(\frac{x^3}{x^{\frac{1}{2}}}\right) \times \left(\frac{x^{\frac{3}{2}}}{x^0}\right) \times x^7$$. 2. **Recall the laws of e

1. **State the problem:** We need to find the wind speed $s$ when the tornado traveled a distance $d=27.1$ miles using the model: $$s = 93\log(d) + 65$$