🧮 algebra

1. **State the problem:** Solve the inequality $$\left(\frac{1}{2}\right)^{x - 2\sqrt{x} - 3} > 1.$$\n\n2. **Recall the properties of exponents:** For a base $0 < a < 1$, the funct

1. **State the problem:** Factor the polynomial $$x^{10} + x^5 + 1$$. 2. **Recognize the structure:** Notice that the polynomial resembles a quadratic in terms of $$x^5$$, since $$

1. **State the problem:** Use the distributive property to simplify and find the product for the expressions given. 2. **Recall the distributive property formula:**

1. **State the problem:** Solve the quadratic equation $3x^2 - 20x - 13 = -6$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Solve the quadratic equation $4x^2 - 8x = -3$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to find the value of $150!$ (150 factorial), which is the product of all positive integers from 1 to 150. 2. The factorial of a number $n$, denoted $n!$, is defin

1. O problema é resolver a equação quadrática $x^2 + 5x + 6 = 0$. 2. A fórmula para resolver equações quadráticas é a fórmula de Bhaskara: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

1. **Find the HCF of 540 and 1350** The Highest Common Factor (HCF) is the greatest number that divides both numbers exactly.

1. **State the problem:** Factorise fully the expression $$30pq^4 + 20p^2q^3 + 10q$$. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 30, 20, and 10. The

1. **State the problem:** We are given three functions: $$f(x) = 3 - 4x, \quad g(x) = \frac{1}{3}x - 2, \quad h(x) = \frac{2x - 3}{5x - 7}$$

1. **State the problem:** Calculate the value of the expression $60\left(\frac{2}{5} + \frac{7}{12}\right)$.

1. **State the problem:** A company donates 7.20 each time a social media post is shared. The post is shared 2731 times. The total donation is divided evenly among 4 charities. We

1. **State the problem:** A company donates 7.20 each time a social media post is shared. The post is shared 2731 times. The total donation is divided evenly among 4 charities. We

1. **State the problem:** We have 24 players on a baseball team. Seventh graders are \(\frac{1}{6}\) of the players. The number of seventh-grade players is about 3% of all seventh-

1. **State the problem:** Solve for $x$ in the equation $$\frac{x \cdot \tan(49.2)}{\tan(49.2)} = \frac{18}{\tan(49.2)}.$$ 2. **Simplify the left side:** Since $\tan(49.2)$ appears

1. **State the problem:** Solve the quadratic equation $$x^2 - 22 = 5x + 2$$ by factoring. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem states: Find the whole number $k$ such that $k > 3$. 2. Since $k$ is a whole number greater than 3, the smallest possible value for $k$ is 4.

1. The problem involves determining the position of a number relative to the fractions 0, \frac{1}{3}, and 1. 2. We analyze the intervals given: between 0 and \frac{1}{3}, between

1. **State the problem:** Solve the quadratic equation $$x^2 - 39 = -2x + 9$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** A company donates 7.20 each time a social media post is shared. The post is shared 2731 times. The total donation is divided evenly among 4 charities. We

1. **State the problem:** A company donates 7.20 each time a social media post is shared. The post is shared 2731 times. The total donation is divided evenly among 4 charities. We