🧮 algebra

1. Stating the problem: An investor invested a total amount $T$ in two ventures with the same percentage return per year. From the total amount, $\frac{3}{10}T + 600$ was invested

1. **State the problem:** Solve the rational inequality $\frac{2x - 1}{x - 2} \leq 3$.\n\n2. **Rewrite the inequality:** Move all terms to one side to have zero on the other side:\

1. Problem: After $t$ seconds, the height $h$ of an object thrown upward is given by $$h = -16t^2 + 96t.$$ Find $t$ when $h=144$ feet.

1. **State the problem:** Simplify the expression $$\frac{24r^{20}}{3r^2 \times 10r^6}$$ and also simplify $$\frac{6f^7 \times 4f^2}{8f^{14}}$$. 2. **Simplify the first expression:

1. Problem 28: A total of 35000 is invested at 4%, 5%, and 6% interest rates. The first year's interest is 1780.

1. The problem is to simplify the expression $$10y^6 \div 2y^3$$. 2. Start by rewriting the division as a fraction:

1. **State the problem:** We have a pyramid of bricks where the top brick expression equals the sum of the two bricks below it. The expressions are:

1. State the problem: Simplify the expression $$\frac{3a^3}{12a^9}$$. 2. Simplify the coefficients: $$\frac{3}{12} = \frac{1}{4}$$.

1. Problem h) Solve for $y$ in the equation $6(y - 3) - 5(y - 8) = 48 - 3(y)$. 2. Expand both sides:

1. **State the problem:** We need to find the value of $a$ given the equation $a + 345 = 700$. 2. **Isolate $a$:** Subtract 345 from both sides of the equation to get $a = 700 - 34

1. Problem: Solve for $x$ in the equation $6x^2 = 81$. Step 1: Divide both sides by 6: $x^2 = \frac{81}{6} = 13.5$.

1. Stated problem: Solve for $a$ in the equation $a + 128 = 400$.\n\n2. To isolate $a$, subtract 128 from both sides: $$a + 128 - 128 = 400 - 128$$\n\n3. Simplify both sides: $$a =

1. We are given the equation $a + 128 = 400$ and asked to solve for $a$. 2. To isolate $a$, subtract 128 from both sides of the equation:

1. Stating the problem: We want to find the sum of a geometric series. 2. Definition: A geometric series is a series of terms where each term is found by multiplying the previous t

1. Stating the problem: We want to understand how to divide one polynomial by another, similar to long division with numbers. 2. Step 1: Arrange the dividend (the polynomial to be

1. **State the problem**: Simplify the expression $x + x$. 2. **Combine like terms**: Both terms have the variable $x$, so we can add their coefficients.

1. The problem is to solve the quadratic equation $$x^2 - 10x - 9 = 0$$. 2. We will solve it by factoring or using the quadratic formula. Here, let's try to factor it first.

1. Bài toán: Giải phương trình bậc hai $ax^2 + bx + c = 0$. 2. Xác định hệ số: Cho ví dụ $x^2 - 5x + 6 = 0$ (tương ứng với $a=1$, $b=-5$, $c=6$).

1. Perform Addition $(f + g)(x)$ where: $f(x) = 4x^4 - 8x^3 + 6x^1 - 5x^1 + 9x - 8$

1. Vamos a calcular el MCD de 207 y 36 mediante el algoritmo de Euclides. 2. Primero dividimos 207 entre 36: $$207 = 36 \times 5 + 27$$, el primer residuo es 27.

1. Stating the problem: We are asked to find the original sum (principal) given that after 3 years at an interest rate of 12% per annum, the amount becomes 250005. 2. Identify the