🧮 algebra

1. Let's clarify the problem: you asked "Why 10 to 30?" which seems to refer to a range or interval from 10 to 30. 2. In mathematics, when we say "from 10 to 30," it usually means

1. **State the problem:** We are given the equation $\frac{a}{3} = 10 - 7b$ and need to express $b$ in terms of $a$, assuming $a \neq 0$. 2. **Start with the given equation:**

1. **State the problem:** Simplify the expression $$\frac{(\log_3 567 - \log_3 7) + 10^{\log 6}}{7^{1+10} \cdot 7^{3 - \log_{11} \sqrt{x^{x}}}}$$. 2. **Recall logarithm and exponen

1. Problem: Solve the absolute value equations given. 2. Formula and rules: For $|A| = |B|$, solutions come from $A = B$ or $A = -B$. For $|A| = C$ with $C \geq 0$, solutions come

1. **State the problem:** Write the vertex form of the parabola given by the equation $y=2x^2+36x+170$. 2. **Recall the vertex form:** The vertex form of a parabola is given by $$y

1. Problem a: Solve the inequality $3x - 2 < 8$. Step 1: Add 2 to both sides:

1. **State the problem:** Calculate the product of $(-13\sqrt{5})$ and $(-4\sqrt{7})$. 2. **Recall the multiplication rule for radicals:** When multiplying expressions with square

1. The problem is to find the value of $\sqrt{9}$. 2. The square root function $\sqrt{x}$ gives the number which, when multiplied by itself, equals $x$.

1. **State the problem:** Jackson has $x$ dimes and $y$ nickels. The total number of coins is at least 22, the total value is at most 1.70, there are at least 4 dimes, and at most

1. **State the problem:** We need to find the cost equation $C(x)$ for producing $x$ items, given a cost per item of 9 and fixed costs of 1950. 2. **Formula used:** The linear cost

1. **Problem Statement:** We have the price-demand equation $x = -30p + 9000$ and the cost function $C(x) = 30x + 150000$, where $x$ is the number of tables sold and $p$ is the pri

1. **Problem Statement:** Determine which graph corresponds to the function $y = (2 - x)(x + 1)^2$. 2. **Analyze the function:** The function is a product of two factors: $(2 - x)$

1. **State the problem:** We need to identify which graph corresponds to the function $$g(x) = (x + 1)(x - 2)(x + 5)$$. 2. **Recall the roots:** The roots of the polynomial are the

1. **State the problem:** Simplify the expression $$(4x^2+18x)(16x^2-32y)$$. 2. **Recall the distributive property:** To multiply two binomials, multiply each term in the first bin

1. Problemi belirtelim: $$\frac{1}{3}x - \frac{2}{4}x + \frac{3}{5}x = \frac{26}{25}$$ ifadesinde $x$ gerçel sayısını bulacağız. 2. İlk olarak kesirleri sadeleştirelim ve ortak pay

1. Problemi anlama: A mağazası telefon fiyatı 15000 TL ve her cihaz için 1000 TL indirim uygulanıyor. 2. B mağazası telefon fiyatı 16000 TL, kulaklık fiyatı ise (10 - y) TL olarak

1. Problem: Kobra, başlangıç, orta ve zor seviyedeki İngilizce kurslarını sırasıyla $a$, $b$, ve $c$ ayda tamamlıyor. Her seviyenin aylık ders saati ve saat başı ücretleri verilmiş

1. **State the problem:** Calculate the summation $$\sum_{i=3}^4 i$$ which means adding all integer values of $i$ from 3 to 4 inclusive. 2. **Formula and explanation:** The summati

1. **Problem:** Simplify each square root expression and express as mixed numbers if possible. 2. **Formula and rules:**

1. The problem is to subtract a fraction from a whole number in each case. 2. The formula for subtracting a fraction from a whole number $a - \frac{b}{c}$ is to write the whole num

1. **State the problem:** Valentina's parents buy a 6-day Fun Pass and a 30-dollar arcade pass, spending a total of 129 dollars. We need to find the daily cost of the Fun Pass. 2.