🧮 algebra

1. We start with the equation to solve for $x$: $$16^{3x - 2} = \left(\frac{1}{4}\right)^{5 - x}$$

1. **State the problem:** We need to find the binomial expansion of the function $$\sqrt{1 + x}$$ up to the $$x^4$$ term. 2. **Recall the binomial series formula:** For any real nu

1. Let's assume the problem you refer to involved calculating or deriving the number 2,754,000. 2. To understand how this number was obtained, we need to examine the final step or

1. The problem asks us to describe what raising a number to a power means and explain the difference between $-7^2$ and $(-7)^2$. 2. Raising a number to a power means multiplying t

1. State the problem: We need to find how many peanuts are required to make 5.1 kg of peanut butter, given that 540 peanuts make 340 g of peanut butter. 2. Convert 5.1 kg to grams

1. The problem is to solve the equation $4^{x^2-\frac{5x}{7}}=16^{\frac{1}{7}}$ for $x$. 2. Rewrite the bases as powers of 2: $4=2^2$ and $16=2^4$, so the equation becomes

1. **Calculer:** 1) $\sqrt{2} \sqrt{64} = \sqrt{2 \times 64} = \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2}$.

1. **State the problem:** We are asked to find the first four terms of the sequence given by $$u_n = 2 + (-1)^n$$ for $$n = 1, 2, 3, 4$$. 2. **Recall the sequence formula:** $$u_n

1. The problem asks for the first four terms of a sequence, with four given options: A (1, -3, 1, -3), B (3, 1, 3, 1), C (1, 3, 1, 3), and D (-1, 3, -1, 3). 2. To determine the cor

1. Stating the problem: Solve the equation $$\left(\frac{1}{2}\right)^x \cdot 8 - 4^{x-1} = 0$$ for $x$. 2. Rewrite the terms with base 2:

1. Let's clarify the method being discussed, likely completing the square. 2. The standard form of a quadratic equation is $ax^2 + bx + c = 0$.

1. Solve the quadratic equation $ax^2 + bx + c = 0$ by completing the square. Step 1: Divide all terms by $a$ (assuming $a \neq 0$) to get $x^2 + \frac{b}{a}x + \frac{c}{a} = 0$.

1. Let's clarify what "adding and subtracting half of the coefficient" usually refers to. It often comes up in the process of completing the square in algebra. 2. Consider a quadra

1. **Enunciado:** Dado o sistema com incógnitas $x,y,z$ e parâmetros reais $a,b$: $$\begin{cases} x - 4y + 3z = 2b \\ ay + z = b \\ x - y + (a+1)z = -b \end{cases}$$

1. **أوجد ناتج التعبير التالي في صيغة ترميز علمي:** المطلوب جمع العددين $98.6 \times 10^4$ و $7.24 \times 10^5$ بصيغة علمية.

1. **أوجد ناتج التعبير في صيغة ترميز علمي:** المعطى: $$ (98.6 \times 10^4) + (7.24 \times 10^5) $$

1. The problem is to complete the square for a quadratic expression such as $ax^2 + bx + c$. 2. Start with the quadratic expression in the form $x^2 + bx + c$ (assume $a=1$ for sim

1. **সমস্যা বর্ণনা**: g(t) = $\frac{t^4 + t^2 + 1}{t^2}$ এবং আমাদের $g(-3^{-1})$ নির্ণয় করতে হবে। 2. প্রথমে $-3^{-1}$ মানে $-\frac{1}{3}$, অর্থাৎ আমরা $t = -\frac{1}{3}$ বসাব।

1. Stating the problem: Simplify the expression $$\frac{12 w^{12}}{2 w^2}$$. 2. Simplify the numeric coefficients: $$\frac{12}{2} = 6$$.

1. State the problem: Evaluate the function $$f(x) = \frac{1 - x}{(x + 1)^2}$$ at $$a = -1$$. 2. Substitute $$x = -1$$ into the function:

1. Given the equation $5^x = 27$, we want to find the value of $k$ and the equation of the variation. 2. Taking the natural logarithm on both sides to solve for $x$, we get: