🧮 algebra

1. **State the problem:** We have three variables representing numbers of tank cars: $x_1 = 8 + 2t$, $x_2 = 33 - 3t$, and $x_3 = t$. Each corresponds to tank cars with capacities 7

1. The problem asks to express the decimal number 0.14 as a percentage. 2. To convert a decimal to a percentage, multiply the decimal by 100.

1. The problem is to solve the equation $\sqrt{v} \left(\frac{2}{5}\right)^x = \frac{32}{3125}^{-1}$.\n\n2. First, simplify the right side. Since $\frac{32}{3125}^{-1} = \frac{3125

1. Probleem 4: 'n Motor se petroltenk hou 45 liter brandstof en gebruik 8,5 liter petrol per 100 km. Die reis is 350 km lank. Hoeveel petrol is oor aan die einde van die reis? 2. B

1. Masalah: Kita akan menyelesaikan soal matematika yang cocok untuk anak SMP kelas 8. 2. Misalnya, kita ingin menyelesaikan persamaan linear sederhana: $$2x + 3 = 11$$

1. The problem is to find the equation of the line passing through the points $(1,2)$ and $(3,8)$.\n\n2. First, calculate the slope $m$ of the line using the formula $$m=\frac{y_2-

1. The problem is to combine the constant terms by finding a common denominator and express the polynomial in standard form. 2. Given the fractions $\frac{4}{3}$ and $\frac{12}{3}$

1. To help you with steps 4 to 6, I need to know the specific problem or the previous steps you are referring to. 2. Please provide the problem statement or the earlier steps so I

1. Stating the problem: We need to factorize the equation $$4(u - y)^3 = (x - y)$$. 2. Rewrite the equation: The equation is already simplified as $$4(u - y)^3 = x - y$$.

1. The problem is to find the number that should replace the gap in the equation: $$16 \times 21 = (16 \times 3) \times \square$$

1. **State the problem:** Evaluate the expressions given the values $x = -2$, $y = -3$, and $z = -2$. 2. **Part a) Calculate $xyz$:**

1. **State the problem:** Factorize the quadratic expression $6x^2 + 19x + 15$. 2. **Identify coefficients:** Here, $a=6$, $b=19$, and $c=15$.

1. The problem is to convert the expression $$(x+2)^2 - \frac{4}{3}$$ into standard form. 2. Start by expanding the squared term using the formula $$(a+b)^2 = a^2 + 2ab + b^2$$:

1. **State the problem:** We have four digits 3, 5, 7, 8 to fill in the missing places in two decimal numbers on a number line between 7 and 9. The numbers are of the form $[\_].7[

1. The problem is to find the square root of 1538, written as $\sqrt{1538}$.\n\n2. First, estimate the value by finding perfect squares near 1538.\n\n3. Note that $39^2 = 1521$ and

1. **State the problem:** We have the value of an antique sewing table given by the function $$V = 1200(1.06)^t$$ where $V$ is the value in dollars and $t$ is the time in years. We

1. The problem is to find the square root of 1539, written as $\sqrt{1539}$.\n\n2. First, check if 1539 is a perfect square by finding factors or estimating.\n\n3. Estimate: $39^2

1. Let's start by stating the problem clearly: you want to solve an equation using an algebraic formula. 2. Since you did not specify the exact equation, I will demonstrate solving

1. The problem is to solve a quadratic equation without using the algebraic formula (quadratic formula). 2. Instead, we can use factoring, completing the square, or graphing method

1. **Problem statement:** Find the products of the expressions: i) $ (a - 1)(a^2 + a + 1) $

1. **State the problem:** We need to show that $$-11100 \times 134 \equiv -1 \pmod{13}$$ without using a calculator. 2. **Reduce each number modulo 13:**