🧮 algebra

1. Problem: Simplify the expression $$\sqrt{6}-\sqrt{\frac{7}{2}+\frac{\sqrt{12}+\sqrt{27}}{\sqrt{300}}}$$. 2. Simplify inside the square roots:

1. El problema es expandir el binomio $$ (x+y)^5 $$ usando el teorema del Binomio de Newton. 2. El teorema del binomio nos dice que:

1. لنفترض أنه نريد تبسيط التعبير الجبري: $f(2) = 2 + x$ أو $2 - x$. 2. بدايةً، إذا كان المقصود هو دالة تعتمد على $x$ مثل $f(x) = 2 + x$ أو $f(x) = 2 - x$، فهذه دوال خطية بسيطة.

1. The problem is to simplify the expression $$\sqrt{6} - \sqrt{\frac{7}{2}} + \frac{\sqrt{12} + \sqrt{27}\sqrt{300}}{}$$. 2. Simplify each square root:

1. Stated problem: Solve for $n$ in the equation $$\frac{11}{7} = \left(\frac{101}{100}\right)^n.$$\n2. Start by taking the natural logarithm of both sides to deal with the exponen

1. We are given an estimated area of 785 m² and the block dimensions of 30 m and 26 m. We need to calculate the actual area and find the percentage error in the estimation. 2. Calc

1. State the problem: Solve for $n$ in the equation $$10^n = 7 \times 11^{n-1}$$. 2. Rewrite the right side to isolate the exponential term: $$10^n = 7 \times \frac{11^n}{11} = \fr

1. **State the problem:** Given an arithmetic sequence with the last term $a_n = 4$, common difference $d = 2$, and sum of $n$ terms $S_n = -14$, find $n$ (the number of terms) and

1. Stating the problem: Sydney and Ann invested a total of 232212 in the ratio 1:2, find how much Ann invested. 2. Let Sydney's investment be $x$.

1. The problem is to convert decimals to percents. 2. To convert a decimal to a percent, multiply it by 100 and add the percent symbol (%).

1. The problem is to simplify the expression $\frac{X}{x-6} - \frac{5}{2}$. 2. To combine the two terms, find a common denominator, which is $2(x-6)$.

1. Stated the problem: Given the function $m(x) = x^2 - 4x + 3$ with domain $x \geq p$, find the value of $p$ so that $m$ has an inverse function. Also, given $g^{-1}h(x) = 5x + 4$

1. Calculate 3% of 1,245.38. 3% means 3 out of 100, so we convert the percent to a decimal: $3\%=\frac{3}{100}=0.03$.

1. **Problem 4.1** involves understanding Moshe's constant speed from the table and answering related questions. 2. **Given table for travel:**

1. The problem is to find the expression for the graph that should be plotted on Desmos. 2. Since the user did not specify any function or equation, we will assume a generic form.

1. Problem: Complete the tables and plot the points for each given rule. 2. For (a) $y = x + 2$, substitute each $x$:

1. **Stating the problem:** We need to predict if the decimal form of each given fraction is terminating or non-terminating (repeating). 2. **Recall:** A fraction \( \frac{a}{b} \)

1. Let's start with the given equation: $y = x + 2$. 2. This is a linear function where $y$ depends on $x$ plus a constant value 2.

1. **Understanding the Problem:** We are given a pattern of relationships between pairs of letters.

1. المسألة: إثبات أن الدالتين $$h(x) = \sqrt{x + 1} - 1$$ و $$k(x) = \frac{x}{\sqrt{x + 1} + 1}$$ متساويتان على المجال $$]-1 ; +\infty[$$. 2. نبدأ بحساب تعبير $$k(x)$$ ونبسطه:

1. Problem: Expand the squares for the expressions: $$(x - 1)^2, (1 - x)^2, (x - 2)^2$$