🧮 algebra

1. **State the problem:** We need to find the age $y$ of a child given the child's dosage $D=20$ mg and the adult dosage $A=40$ mg using Young's formula: $$D = \frac{yA}{y + 12}$$

1. **State the problem:** Simplify the expression $$(p^0 \times p^6) \div p^2$$. 2. **Recall the exponent rules:**

1. **State the problem:** A number is increased by 17, then the result is tripled, and the final value is 24. 2. **Create the equation:** Let the number be $x$. Increasing it by 17

1. **Stating the problem:** Simplify and factor the expression $a(a + 1) - (a + 1)^2$. 2. **Formula and rules:** Use the distributive property $x(y + z) = xy + xz$ and factoring te

1. **Stating the problem:** Simplify and factor the expression $a(a + 1) - (a + 1)^2$. 2. **Formula and rules:** Use distributive property $x(y + z) = xy + xz$ and factoring techni

1. **State the problem:** Solve the linear equation $$\frac{2x - 6}{4} = \frac{5x + 6}{3}$$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the

1. **Stating the problem:** Simplify the expression $$\frac{(a^2 b^5 c^4)}{(ab)^2}$$ where $$a=\left(\frac{2}{9}\right)^4$$, $$b=\left(\frac{4}{27}\right)^3$$, and $$c=\left(\frac{

1. We are asked to simplify the radical expressions given in problem 8.a: $\sqrt{338a^3b^3}$. 2. Recall the rule for simplifying square roots: $\sqrt{x^2} = |x|$ and $\sqrt{xy} = \

1. The problem is to simplify the expression $8d$. 2. Here, $8d$ means $8$ multiplied by $d$.

1. **State the problem:** Solve the equation $$5x^3 - 45x = 0$$. 2. **Write down the formula and rules:** To solve polynomial equations, factor the expression and set each factor e

1. **State the problem:** We have 50 scoops of popcorn initially. Vivian fills bags with popcorn, and the number of scoops remaining decreases as more bags are filled. The graph sh

1. **State the problem:** Simplify the expression $$\frac{1}{6x-5} - \frac{1}{6x-1}$$. 2. **Formula and rules:** To subtract fractions, find a common denominator and combine the nu

1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $8x + 10y = 20$. 2. **Recall the intercept rules:**

1. **State the problem:** Solve the system of equations simultaneously: $$y = 4$$

1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$2x + 6y = -6$$ and use these intercepts to graph the line. 2. **Recall intercept

1. **State the problem:** Calculate the value of the expression $$2000\left(1 + \frac{0.0023}{4}\right)^{4.5}$$. 2. **Identify the formula:** This expression resembles the compound

1. **State the problem:** Simplify the expression $12(z+1)21(z+1)$. 2. **Rewrite the expression:** The expression can be seen as $12 \times (z+1) \times 21 \times (z+1)$.

1. **State the problem:** Carter has a total of 50 pigs and cows. The number of cows is ten less than three times the number of pigs. We need to find how many pigs Carter has. 2. *

1. **State the problem:** Doug has already saved $1200 and wants to save a total of $2800. He saves $200 each week. We need to find how many weeks it will take for him to reach $28

1. **State the problem:** There are 20 more peppermints than lifesavers in a bowl, and the total number of candies is 48. We need to find how many peppermints and lifesavers there

1. **Problem Statement:** We are given a graph of a quadratic function with a restricted domain. The vertex is at $(-1,1)$ and the parabola opens upward starting from $x=-1$ extend