🧮 algebra

1. **Problem statement:** A can complete a work in 20 days, B can complete the same work in 30 days. They work together for 5 days, then A leaves. We need to find how many more day

1. **State the problem:** Solve the quadratic inequality $$2x^2 \geq 7x + 15$$ in the set of real numbers. 2. **Rewrite the inequality:** Bring all terms to one side to set the ine

1. **State the problem:** Simplify and understand the expression and polynomial expansions given. 2. **Recall the formula for binomial expansion:**

1. The problem is to solve the quadratic inequality $$2x^2 \geq 7x + 15$$ in the set of real numbers. 2. First, rewrite the inequality in standard form by moving all terms to one s

1. **State the problem:** Find the sum of the values from 0 to 26 inclusive. 2. **Formula used:** The sum of the first $n$ natural numbers is given by the formula $$\text{Sum} = \f

1. **State the problem:** Find the domain and sketch the graph of the function $f(x) = -2 + \log_2 x$. 2. **Recall the domain rule for logarithms:** The argument of a logarithm mus

1. The problem is to find a function that has a vertical asymptote at $x=0$, an x-intercept at $(4,0)$, and passes through the points $(1,-2)$, $(2,-1)$, and $(8,1)$ with a smooth

1. **State the problem:** Find the value of $\log 3.6$ given $\log 2 = 0.3010$, $\log 3 = 0.4771$, and $\log 5 = 0.6990$. 2. **Recall the logarithm property:** For any positive num

1. **Statement of the problem:** Simplify the expression $$A = 5\sqrt{28} + \sqrt{7} - 3\sqrt{63}$$. 2. **Recall the rule:** Simplify square roots by factoring out perfect squares:

1. **State the problem:** Find the intersection point of the two lines given by the equations: $$y = -\frac{1}{2}x - 2$$

1. **Problem:** Solve the simultaneous equations: $$\log_2 x + \log_2 y = 3$$

1. المشكلة هي التحقق من صحة المعادلة: $9 \times 10 \times 298 = -1$. 2. نبدأ بحساب الضرب في الجانب الأيسر: $9 \times 10 = 90$.

1. **State the problem:** Find the turning point of the curve given by the quadratic function $$y = 2x^2 - 20x + 58$$ by completing the square. 2. **Recall the formula and method:*

1. **State the problem:** Rewrite the quadratic expression $2x^2 + 20x + 28$ in the form $a(x + b)^2 + c$, where $a$, $b$, and $c$ are integers.

1. **State the problem:** Evaluate $\log_1 2 + \log_3 8$.\n\n2. **Recall the definition of logarithm:** $\log_a b$ is the exponent to which we raise $a$ to get $b$.\n\n3. **Importa

1. **State the problem:** Multiply the mixed number $2 \frac{2}{8}$ by the fraction $\frac{2}{9}$. 2. **Convert the mixed number to an improper fraction:**

1. The problem appears to be an equation: $9 \cdot 10 \cdot 298 = -1$. 2. Let's analyze the left side: multiply $9$, $10$, and $298$.

1. The problem is to evaluate the expression $m - m + 3$ when $m = 1$. 2. The expression is $m - m + 3$.

1. The problem is to understand the number 3.25434343... which appears to be a decimal with a repeating pattern. 2. Identify the repeating part: here, the digits "43" repeat indefi

1. The problem is to convert the repeating decimal $0.666666\ldots$ into a rational number. 2. Let $x = 0.666666\ldots$.

1. **State the problem:** Simplify the expression $\left(3\sqrt{2} - 2\sqrt{3}\right)^2$. 2. **Recall the formula:** The square of a binomial $(a - b)^2 = a^2 - 2ab + b^2$.