🧮 algebra

1. **Stating the problem:** Solve the inequality $$3^{x-2} < \frac{3}{9^{\frac{1}{x}}}$$.

1. Išspręskime lygčių sistemą: \[

1. **State the problem:** Solve the inequality $$3^{x-2} < \frac{3}{9^{1/x}}.$$\n\n2. **Rewrite the right-hand side:** Note that $$9 = 3^2,$$ so $$9^{1/x} = (3^2)^{1/x} = 3^{2/x}.$

1. **State the problem:** Solve the inequality $$3^{x-2} < \frac{3}{9^{1/x}}.$$\n\n2. **Rewrite terms with the same base:** Note that $9 = 3^2$, so rewrite \(9^{1/x}\) as \((3^2)^{

1. Let's start with a simple problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. Subtract 3 from both sides to isolate the term with $x$: $$2x + 3 - 3 = 7 - 3$$ which simplifie

1. Problem: A line passes through points $(-2, \rho)$ and $(1, 5)$ with slope $4$. Find $\rho$. Step 1: Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

1. Problem a): Bestäm linjens riktningskoefficient (k). Riktningskoefficienten mellan punkterna $(-2,p)$ och $(1,5)$ ges av $$k = \frac{5 - p}{1 - (-2)} = \frac{5 - p}{3}.$$ Enligt

1. مسئله را بیان کنیم: تفاوت بین قضیه فاکتور و قضیه باقیمانده چیست؟ 2. قضیه فاکتور می‌گوید اگر چندجمله‌ای $f(x)$ را بر $(x - a)$ تقسیم کنیم و باقیمانده صفر باشد، آنگاه $(x - a)$ یک

1. The problem: Understand and apply the Factor Theorem which states that for a polynomial $f(x)$, if $f(c)=0$ for some constant $c$, then $(x-c)$ is a factor of $f(x)$. 2. Step 1:

1. Problem: Sketch the graph of the quadratic function $f(x) = x^2 + 2x$. 2. Step 1: Understand the function.

1. Let's first understand Jade's journey and the distances at given times. 2. She travels from home to the gym in 20 minutes at a constant speed, so at 20 minutes she is at the gym

1. Problem: Find the Least Common Multiple (LCM) of 105 and 637 using their prime factor trees. 2. Prime factorization:

1. **Stating the problem:** Find the lowest common multiple (LCM) of 42 and 66 using their prime factor trees. 2. **Prime factorization of 42:**

1. Let's denote the original price of the product as $P$. 2. The price is first increased by 25%, so the new price after the increase becomes:

1. **Beräkna 4 - 2 · 5 - 1 + 3:** Multiplicera först: $2 \cdot 5 = 10$

1. The problem is to find the linear equation of the form $C = mV + b$ that fits a straight line on a graph with given points. 2. From the description, the line passes near points

1. Stating the problem: Solve the quadratic equation $$2x^2 + 6x + 5 = 0$$ by completing the square. 2. First, divide the entire equation by 2 to simplify the coefficient of $$x^2$

1. We are given the estimation equation: $$8.41 \times 0.62 \approx \_\_ \times \_\_$$ 2. To estimate, we round each number to one significant digit:

1. Stating the problem: A number $h$ is rounded to the nearest integer and the result is 40. 2. a) Write down the error interval for $h$.

1. **State the problem:** Plot the quadratic function for the given data points:\nx: 0, 1, 2, -1.5, -2, -3, -4, -5\ny: 0, 4, 10, -2.25, -2, 0, 4, 10 2. **Analyze the data:** Let's

1. The problem states that the number $x$ is rounded to the nearest integer as 23. 2. When rounding to the nearest integer, the maximum error is half the distance between two conse