🧮 algebra

1. **Evaluate the expression:** $$6 - 6 \times (-6)^3 \div 7$$ 2. Calculate the power: $$(-6)^3 = -216$$

1. The problem asks us to determine which inequalities among A, B, C, and D are true. 2. Evaluate each inequality:

1. The problem asks which number is located to the right of the point $-3.27$ on the number line. 2. Numbers to the right of $-3.27$ must be greater than $-3.27$.

1. Let's analyze each statement to determine if it is true or false. 2. Statement: "0 is neither a rational number nor an irrational number."

1. Let's analyze each statement to determine its truth value. 2. Statement: "0 is neither a rational number nor an irrational number."

1. **State the problem:** Simplify the expression $$|3 - 8| - \left(\frac{12}{3} + 1\right)^2$$. 2. **Calculate the absolute value:** $$|3 - 8| = |-5| = 5$$.

1. The problem asks for the opposite of 145. 2. The opposite of a number $x$ is defined as $-x$.

1. The problem states: If the absolute value of $x$ is 12, which of the following is true? 2. Recall the definition of absolute value: $|x| = 12$ means the distance of $x$ from 0 o

1. The problem asks to find the value of $|6| - |-6| - (-6)$.\n\n2. Recall that the absolute value $|x|$ is the distance of $x$ from zero on the number line, always non-negative.\n

1. **State the problem:** We want to analyze the function $$y=\frac{x^3+3x}{(x+1)(x+2)}$$ including simplification and key features. 2. **Simplify the numerator:** Factor out $x$ f

1. **Stating the problem:** Rearrange the formula $$W = \frac{h^2}{7x}$$ to make (a) $$h$$ the subject and (b) $$x$$ the subject. 2. **Rearranging for h:**

1. State the problem: Find the value of the expression $$(3x - 12) - \left(\frac{1}{2}xy - 10\right)$$ for $x=3$ and $y=6$. 2. Substitute the values of $x$ and $y$ into the express

1. **Problem statement:** We have two functions: an exponential function $f(x) = a^x + q$ with horizontal asymptote $y=3$, and a linear function $g(x) = mx + c$. They intersect at

1. The problem is to verify if the equation $$(7x+3)^2 = (7x+4)(7x-4)$$ is correct and solve for $x$ if it is. 2. First, expand both sides:

1. **State the problem:** Solve the equation $$(6x - 9)^2 - (3x - 5)^2 = (9x + 4)(3x + 2)$$ for $x$. 2. **Expand the squares using the formula $(a - b)^2 = a^2 - 2ab + b^2$:**

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. **State the problem:** We are given $Z = 2^5 \times 3^m \times 5^2$ and need to express $24Z$ as a product of powers of its prime factors. 2. **Express 24 as prime factors:**

1. The problem asks us to write the number $N = 33 \times 30$ as a product of its prime factors. 2. First, find the prime factorization of each number separately.

1. The problem asks us to write the number 126 as a product of its prime factors. 2. Start by finding the smallest prime number that divides 126. Since 126 is even, it is divisible

1. The problem asks us to write the number 28 as the product of its prime factors. 2. Start by finding the smallest prime number that divides 28. Since 28 is even, it is divisible

1. The problem asks us to write 124 as a product of its prime factors. 2. Start by dividing 124 by the smallest prime number 2: $$124 \div 2 = 62$$.