🧮 algebra

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.

1. Énoncé du problème : Nous voulons effectuer la division euclidienne de $$n^2 + 7n + 18$$ par $$n + 2$$. 2. Dividende : $$n^2 + 7n + 18$$.

1. **Exercice 1 : Périmètre et aire maximale** Un fermier a 200 mètres de clôture pour délimiter un terrain rectangulaire.

1. The problem is to explain how to use the inverse function to graph $f(x)=\log_6 x$. 2. Recall that the logarithm function $f(x) = \log_6 x$ is the inverse of the exponential fun

1. Let's analyze the given information: the graph of $g(x)$ is a smooth continuous curve with oscillations, passing near points $(1,1)$ and $(1.5,1.5)$. 2. The curve starts near $y

1. Problem statement: Sketch the graph and make a sign table for the polynomial $Q(x)=-(x-1)^3(x+2)^2$. 2. Factorization and roots: The factorization is given as $Q(x)=-(x-1)^3(x+2

1. Let's say the problem is to simplify an expression or solve an equation. To keep it easy, we will break it down into just a few steps. 2. Identify what you need to find or simpl

1. The problem is to simplify the expression $2\sqrt{284}$.\n\n2. First, factorize 284 to find perfect squares inside the square root.\n284 can be broken down as $284 = 4 \times 71

1. **State the problem:** We have a language school where 39 7/12 % learn Chinese, 31 1/4 % learn German, and the remaining 210 learn Japanese.

1. The problem asks which values of $n$ make $f(x) = x^n$ a polynomial function. A polynomial function has non-negative integer exponents. So: