🧮 algebra

1. **State the problem:** We start with the parent function $f(x) = \sqrt[3]{x}$. We want to find the new function $g(x)$ after three transformations: - Reflection over the x-axis

1. **Problem:** Determine if the proportion $\frac{4}{5} = \frac{20}{25}$ is true. 2. **Formula:** Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equal if $ad = bc$.

1. **State the problem:** Simplify the expression $$(10x^0)^6$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $x^2 \cdot x \cdot x^6$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same b

1. **State the problem:** We are given the polynomial function $$f(x) = -5x^3 - 30x^2 + 200x$$ and want to analyze it.

1. **State the problem:** Simplify or analyze the quadratic expression $-4x^2 + 16x + 84$. 2. **Identify the formula and rules:** This is a quadratic expression of the form $ax^2 +

1. The problem involves simplifying expressions with square roots and variables: $$4.5\sqrt{3524} - 3xyx^4 - 4hy$$ and $$5\sqrt{8xy} + xhy^3$$. 2. Recall the properties of square r

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$

1. The problem is to make the left side look like the original state of the right side. 2. To solve this, we need to identify the expressions on both sides and apply algebraic oper

1. The problem is to solve an equation or expression where the right side must remain unchanged. 2. When solving equations, the goal is to isolate the variable on one side without

1. **State the problem:** Jen has 72 flowers and arranges them equally into 6 vases. We need to find how many flowers, $v$, are in each vase. 2. **Write the equation:** Since the t

1. The problem is to convert the mixed number percentage $2 \frac{1}{2}\%$ into a decimal or fraction. 2. Recall that a percentage means "per hundred," so $x\% = \frac{x}{100}$.

1. The problem asks whether the prime factors of 99 are 9 and 11. 2. Prime factors are prime numbers that multiply together to give the original number.

1. Planteamos el problema: Dada la función cuadrática $$g(x) = -x^2 + 6x - 14$$, escribiremos la ecuación en la forma $$g(x) = a(x-h)^2 + k$$, encontraremos el eje de simetría, y d

1. **Stating the problem:** We want to find variables in a binomial equation, which typically looks like $ (a + b)^n $. 2. **Formula used:** The binomial theorem states:

1. **State the problem:** Determine if 38, 58, and 76 are all multiples of 19. 2. **Recall the definition:** A number $n$ is a multiple of another number $m$ if there exists an int

1. **State the problem:** Determine if the numbers 38, 58, and 76 are all multiples of 19. 2. **Recall the definition:** A number $n$ is a multiple of 19 if there exists an integer

1. **State the problem:** We need to express the numbers 60, 88, and 120 as products of their prime factors. 2. **Recall the prime factorization method:** Prime factorization means

1. **State the problem:** Solve the quadratic equation $$2x^2 - 5x + 3 = 0$$. 2. **Recall the factoring method:** To solve quadratic equations by factoring, we look for two binomia

1. **State the problem:** We need to find the break-even function $t(p)$ relating ticket sales $t$ to price $p$, then solve for the ticket price $p$ that meets the student attendan

1. The problem is to evaluate the expression $7 \_ 7 \frac{1}{2}$, which appears to be $7 - 7 \times \frac{1}{2}$.\n\n2. The order of operations (PEMDAS/BODMAS) tells us to do mult