🧮 algebra

1. **Énoncé du problème** : Nous avons plusieurs exercices concernant des endomorphismes sur \( \mathbb{R}^4 \) et \( \mathbb{C}^4 \), avec des conditions spécifiques sur \( f \) e

1. The problem is to find the zero(s) of the quadratic polynomial $$p(x)=x^2+7\times100$$. 2. First, simplify the polynomial:

1. Masalah: Temukan persamaan garis yang melewati titik $(-3, 2)$ dan (a) sejajar dengan garis $-2y + 3x + 36 = 0$.

1. The problem states that 1681 students will attend the school function, and we need to arrange chairs such that the number of students in each row equals the number in each colum

1. Masalah yang diberikan adalah untuk menggambar grafik persamaan $$3x - 5y + 30 = 0$$ dan mencari gradien (slope) dari fungsi tersebut. 2. Langkah pertama adalah menyusun persama

1. Given the system \(\begin{cases} xy = 7, \\ xy = 18; \end{cases}\) Since both equations say \(xy\) equals different values (7 and 18), there is no solution because one product c

1. The problem presents several expressions and a linear equation system: simplifying an expression, solving simple equations, and analyzing a linear equation. 2. Simplify the expr

1. Stating the problem: We are given two equations involving cubic terms: $$7x^3 - 3y^3 + 5xy - 2x - 27 = 0$$

1. Solve the equation $6x+2=24$. Step 1: Subtract 2 from both sides: $$6x=24-2$$

1. State the problem: We need to multiply the two-digit numbers 31 and 29 using the lattice multiplication method. 2. Write the numbers on the top and side of the lattice grid: Top

1. Solve the equation: $$3^{2x} - 4 \cdot 3^x - 3 = 0$$ Step 1: Let $$y = 3^x$$. Then, the equation becomes $$y^2 - 4y - 3 = 0$$.

1. The problem is to simplify and explain the properties of equality. 2. The properties of equality are fundamental rules that allow us to manipulate equations while keeping them b

1. State the problem: Find the x-intercept(s) of the function $$y = x^4 - 4x^3 + 10$$, i.e., find values of $$x$$ such that $$y=0$$. 2. Set the function equal to zero:

1. Solve the equation $10x + 3 = 32$ for $x$. Subtract 3 from both sides to isolate the term with $x$:

1. The problem states: If $p = -2$, find the value of $2p$. 2. Substitute $p = -2$ into the expression $2p$.

1. The problem states two equations: 10x + y = 32 and y = 3, and then claims that 4x + 3 = 7 follows. 2. Substitute y = 3 into 10x + y = 32 to get 10x + 3 = 32.

1. The problem gives two height functions of an archer’s arrow, in terms of horizontal distance $x$, and asks to understand the translations modeling the arrow’s paths. 2. For part

1. The original problem involved a term with -3, and now it is changed to +3. 2. Replace every occurrence of -3 in the original expression with +3.

1. Soal 35: Diketahui fungsi tinggi pohon mangga pada hari ke-$t$ adalah $$h(t) = 6 \log (t+2)$$ dan diberikan $$3 \log 2 = x$$ serta $$2 \log 5 = y$$. Tentukan tinggi pohon mangga

1. Masalah: Bagaimana cara menyelesaikan persamaan kuadrat $ax^2 + bx + c = 0$? 2. Langkah pertama adalah memahami bentuk umum persamaan kuadrat.

1. Let's start by understanding what a fraction is. 2. A fraction represents a part of a whole or any number of equal parts.