🧮 algebra

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

1. The problem asks to find 15% of £50. 2. To find a percentage of a value, convert the percentage to a decimal and multiply by the value.

1. The problem asks us to find the lower and upper bounds for a number $r$ which, when rounded to the nearest integer, equals 28. 2. When rounding to the nearest integer, values ar

1. The problem is to understand the concept of composition of functions. 2. Composition of functions means applying one function to the result of another function.

1. Problem (a): Simplify $$y = 9 - 15x + 4^3 - \frac{7x^5}{x^4}$$ Step 1: Calculate powers and simplify fractions