🧮 algebra

1. **State the problem:** Solve the inequality $$-38d - 57 \geq -19d + 76$$ for $d$. 2. **Isolate the variable terms:** Add $38d$ to both sides to move all $d$ terms to the right s

1. **Stating the problem:** Simplify the expression $$\left( \frac{a^2 b^{-3}}{a^{-1} b^{\frac{3}{2}}} \right)^{\frac{3}{2}}$$. 2. **Recall the rules:**

1. **Problem statement:** The first, seventh, and twenty-fifth terms of an arithmetic progression (A.P.) form the first three consecutive terms of a geometric progression (G.P.). T

1. **State the problem:** We are given a rectangle ABCD with sides DC and AD defined as functions of $x$: $$DC = \frac{5}{x^2 - 25}$$

1. Diberikan fungsi linear $f(x) = 6 - 10x$ dan translasi $T = \left(\frac{10}{3}\right)$. 2. Translasi fungsi linear biasanya berarti menggeser grafik fungsi secara horizontal ata

1. The problem is to understand and apply the Factor and Remainder Theorem. 2. The Factor Theorem states that if a polynomial $f(x)$ is divided by $(x - a)$, then the remainder is

1. The problem is to understand algebraic systems focusing on semigroups, monoids, and groups, including their properties, examples, and homomorphisms. 2. **Semigroups:** A semigro

1. **Problem Statement:** Understand algebraic systems focusing on semigroups, monoids, and groups, including their properties, examples, and homomorphisms. 2. **Algebraic Systems:

1. The problem is to simplify the expressions $\frac{\sqrt{2907}}{51}$ and $\frac{\sqrt{1728}}{18}$.\n\n2. Recall the property of square roots and division: $$\frac{\sqrt{a}}{b} =

1. **State the problem:** We are given the equation of a circle: $$2x^2 + 2y^2 - 8x + 5y + 10 = 0$$ and need to find its radius. 2. **Rewrite the equation:** Divide the entire equa

1. The problem is to evaluate the polynomial $2,353x^3 + 44,998x$ for the values $x=0, 1, 2, 3, 3.4$. 2. The formula is given as $f(x) = 2,353x^3 + 44,998x$.

1. პრობლემა: გეომეტრიული პროგრესიის პირველი წევრის $b_1$ და $S_6$ ჯამის გამოთვლა, თუ $b_6=96$ და საერთო თანაფარდობა $q=2$. 2. ფორმულები და წესები:

1. The problem involves evaluating or simplifying the given functions: - $f(x) = 2x - 5$

1. The problem asks for the value of the composition \( (f \circ g)(3) \), which means \( f(g(3)) \). 2. Given functions:

1. **State the problem:** We need to find the value of $k$ such that the line joining points $A(3,k)$ and $B(-2,5)$ is parallel to the line given by the equation $5y + 2x = 10$. 2.

1. **State the problem:** We need to sketch the graph of the equation $$y^2 = 1 - x$$. 2. **Rewrite the equation:** To understand the graph better, solve for $y$:

1. **State the problem:** Find the value of $x$ that satisfies the equation $$5^{2x} - 6(5^x) + 5 = 0.$$\n\n2. **Rewrite the equation:** Notice that $5^{2x} = (5^x)^2$. Let $y = 5^

1. **State the problem:** We need to find the price after a 25% discount on 5928. 2. **Formula used:** The price after discount is given by

1. The problem is to simplify both expressions given (though the expressions are not provided, we assume two algebraic expressions). 2. To simplify algebraic expressions, we combin

1. **Problem 37:** Simplify $$\left(\frac{-7a^2 b^3 c^0}{3a^3 b^4 c^3}\right)^{-4}$$. 2. **Recall the rules:**

1. **Stating the problem:** We have three people A, B, and C with cherries. Given: