🧮 algebra

1. The problem states that for a quadratic equation of the form $$ax^2 + bx + c = 0$$, the sum and product of the roots are given by the formulas $$-\frac{b}{a}$$ and $$\frac{c}{a}

1. **State the problem:** We need to find a number such that when it is increased by 12, the result is 25. 2. **Set up the equation:** Let the number be $x$. The problem states:

1. **State the problem:** We are given the quadratic equation $$3x^2 - 6(2a - b)x + ab = 0$$ with the sum of the roots equal to 4 and the product of the roots equal to 8. We need t

1. **State the problem:** Simplify the expression using De Morgan's Laws and describe the solution set for $$\sim(x < -2 \text{ or } x \geq 5)$$. 2. **Recall De Morgan's Laws:**

1. **State the problem:** Simplify the expression using De Morgan's Laws and describe the solution set for $$\sim(x < -2 \text{ or } x \geq 5)$$. 2. **Recall De Morgan's Laws:**

1. **State the problem:** Solve the equation $4x^2 - 8 = 0$ using common monomial factoring. 2. **Identify the common factor:** Both terms $4x^2$ and $-8$ have a common factor of 4

1. **State the problem:** Solve the equation $4x^2 - 8 = 0$ using common monomial factoring. 2. **Identify the common factor:** Both terms $4x^2$ and $-8$ have a common factor of 4

1. **State the problem:** Simplify the expression $$\frac{2^{2x+4} - 2^{2x+3}}{2^{2x-2} + 2^{2x-4}}$$. 2. **Recall the properties of exponents:**

1. **Problem 1:** Find the value of the expression $p^2 + 10p + 21$ when $p = 8$. 2. **Step 1:** Substitute $p = 8$ into the expression:

1. Masala: Tengsizliklarni qo'shing: $3 < 9$ va $9{,}4 > 0{,}1$. 2. Qoidalar: Sonlarni solishtirishda agar birinchi son kichik bo'lsa, tengsizlik $<$ belgisi bilan ifodalanadi va a

1. Muammo: Tengsizliklarni qo'shish: $3 < 9$ va $9.4 > 0.1$. 2. Tengsizliklarni qo'shishda, har bir tengsizlik alohida tekshiriladi va ular birgalikda "va" (kon'yunktiv) bilan bog'

1. Muammo: Tengsizliklarni qo'shish. 2. Berilgan tengsizliklar: $14 < 18$ va $7,4 > 0,6$.

1. **Problem statement:** A networking technician has an initial annual salary of 40000. The salary increases by 2% of the initial salary every year. We need to find:

1. Let's start by understanding what indices (or exponents) are. An index tells us how many times to multiply a number by itself. For example, $a^n$ means multiply $a$ by itself $n

1. **State the problem:** Solve the exponential equation $$8 \cdot 0.25^{2x - 3} = 2^{x - 1}$$ for $x$. 2. **Rewrite the bases as powers of 2:** Note that $0.25 = \frac{1}{4} = 2^{

1. The problem is to simplify the expression without including the term $-\lg 100$. 2. Recall that $\lg$ denotes the base-10 logarithm, so $\lg 100 = 2$ because $100 = 10^2$.

1. **State the problem:** Simplify and analyze the expression $$\frac{a}{b} \cdot \frac{1}{x^2 + 2x - 8}$$. 2. **Identify the formula and rules:** We are multiplying a constant fra

1. **State the problem:** Simplify the expression $2 \lg 5 + 0.5 \lg 16 - \lg 100$. 2. **Recall logarithm properties:**

1. The problem is to graph a function and find its domain and range. 2. The domain of a function is the set of all possible input values (x-values) for which the function is define

1. **Problem statement:** A hard drive initially contains 1500 megabytes of data and loses 5 megabytes every hour due to corruption. 2. **Formula:** The amount of data left after $

1. **State the problem:** Solve the exponential equation $$2^{4x-9} = \left(\frac{1}{8}\right)^{x-4}$$. 2. **Rewrite the bases:** Note that $$\frac{1}{8} = 8^{-1}$$ and $$8 = 2^3$$