🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x-4}{x^2+8x+15} \div \frac{x^2-16}{2x^2+7x+3}$$ and state the restrictions on $x$. 2. **Rewrite the division as multiplica

1. **State the problem:** Simplify the expression $$\left(\frac{x^2 - 4x - 5}{x^2 - 3x - 10}\right)\left(\frac{9x + 3x^2}{x^2 - 9}\right)$$ and state the restrictions on $x$. 2. **

1. **State the problem:** Solve the equation $3(y + 4) = 8y + 37$ for $y$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** Solve the equation $6u - 28 = 4(u - 6)$.\n\n2. **Apply the distributive property:** Expand the right side: $4(u - 6) = 4u - 24$. So the equation becomes:\

1. **State the problem:** Solve the equation $-9y + 46 = -2(y - 2)$ for $y$. 2. **Apply the distributive property:** Expand the right side:

1. **State the problem:** Solve the equation $-4(u - 6) = -6u + 28$ for $u$. 2. **Apply the distributive property:** Multiply $-4$ by each term inside the parentheses.

1. **State the problem:** Find the inverse function $f^{-1}(x)$ for the function $$y = -\frac{10}{1 + x^2}, \quad x \geq 0.$$\n\n2. **Rewrite the function:** We have $$y = -\frac{1

1. The problem asks to find the concentration of the drug 1 hour after ingestion by evaluating the function $$f(x) = \frac{10}{1+x^2}$$ at $$x=1$$. 2. The formula for the concentra

1. The problem involves simplifying the expression $4\pi r^2 + 4\pi rh + 2\pi rh$. 2. We start by identifying like terms. The terms $4\pi rh$ and $2\pi rh$ are like terms because t

1. **State the problem:** Simplify the expression $3(x + 1)(5x + 3) - (2x + 4)(6x - 2)$. 2. **Use the distributive property (FOIL) to expand each product:**

1. **State the problem:** Simplify the expression $$3(x+1)(5x+3) - (2x + 4)(6x - 2)$$. 2. **Use the distributive property (FOIL) to expand each product:**

1. **State the problem:** Simplify the expression $$3(x+1)(5x+3) - (2x+4)(6x-2)$$ and verify the expanded form. 2. **Recall the distributive property and FOIL method:**

1. The problem is to expand and simplify the expression $(2x^2 - 5x + 4)(x^2 + 3x - 7)$. 2. Use the distributive property (FOIL for polynomials) to multiply each term in the first

1. **State the problem:** Solve the inequality $|5 - x| \geq -6$. 2. **Recall the property of absolute values:** The absolute value of any real number is always non-negative, meani

1. The problem asks which equation corresponds to the shaded parts of a 10 by 10 grid model representing multiplication. 2. The grid has 100 small squares total, representing 1 who

1. **State the problem:** Simplify the rational expression $$\frac{y^2 - 3y - 28}{y^2 + 12y + 32}$$ and find all values of $y$ that must be excluded from the domain. 2. **Factor nu

1. **State the problem:** Simplify the expression $$\frac{x^2 + 8x + 16}{x^2 - x - 20}$$ and state any restrictions on the variable. 2. **Factor numerator and denominator:**

1. **State the problem:** We have an element with an initial mass of 640 grams that decays by 7.3% per minute. We want to find how much of the element remains after 8 minutes, roun

1. **State the problem:** Simplify the expression $$\frac{50x^6 y^2}{30x^3 y^5}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{5x^7 y^7}{25x^7 y^2}$$. 2. **Recall the rules:**

1. **State the problem:** Expand and simplify the expression $-3(x - 2)^2$. 2. **Recall the formula:** The square of a binomial $(a - b)^2$ is expanded as $$ (a - b)^2 = a^2 - 2ab