🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{5}{2} - 40$$. 2. **Recall the rules:** When subtracting a whole number from a fraction, convert the whole number to a frac

1. **Problem statement:** We are given four functions and need to analyze or simplify them as needed. 2. **Function a:** $f(x) = x^6 + 2x - 1$

1. Ges.: Bestimme eine mögliche Funktionsgleichung für die gegebenen Graphen. 1.a) Der Graph hat Nullstellen bei $x=-1$ und $x=1$ und zeigt ein lokales Maximum bei etwa $x=-1.5$. D

1. **Problemstellung:** Untersuche die Funktionen $f(x) = 1{,}5^x$, $g(x) = 3 \cdot 1{,}5^x$, $h(x) = -3 \cdot 1{,}5^x$ und $f(x) = 0{,}25^x$, $g(x) = 2 \cdot 0{,}25^x$, $h(x) = -2

1. The user asks for a simpler form, but no specific expression or equation is provided. 2. To simplify an expression, you typically combine like terms, factor where possible, and

1. **State the problem:** We are given the function $f(x) = 4x^4 - 8$ and want to understand its properties. 2. **Formula and rules:** This is a quartic polynomial function of the

1. The problem is to find the values to put into each of the 8 specific boxes. 2. Since the user did not provide the exact problem or the expressions for the boxes, I cannot determ

1. **Plantear el problema:** Resolver la ecuación $$(x-4)^2 + (x+2)^2 = 20$$. 2. **Recordar la fórmula del cuadrado de un binomio:**

1. **State the problem:** Simplify the expression $(x-4)x^2$. 2. **Recall the distributive property:** To simplify expressions like this, multiply each term inside the parentheses

1. **State the problem:** Ravi is 11 years old, Devi is 5 years older than Ravi, so Devi is $11 + 5 = 16$ years old. 2. We want to find how many years later their total age will be

1. The problem is to find the points where two functions intersect, which means finding the points where their values are equal. 2. To find intersection points, set the two functio

1. **State the problem:** We need to find the slope $m$ of the line passing through the points $(-7, -7)$ and $(7, 7)$. 2. **Recall the formula for slope:** The slope $m$ of a line

1. The problem is to simplify the expression $$\left( \frac{3^2}{4^3} \right)^2$$. 2. The formula used here is the power of a quotient rule: $$\left( \frac{a}{b} \right)^n = \frac{

1. **State the problem:** Solve the quadratic equation $$7x^2 + 17x + 52 = 6x^2 + 35x - 28$$. 2. **Bring all terms to one side:** Subtract $$6x^2 + 35x - 28$$ from both sides to se

1. **State the problem:** We are given the function $f(x) = 2x - 4$ and need to find the values of $x$ for which $f(x) \geq x$. 2. **Write the inequality:**

1. Il problema chiede di determinare se i sistemi lineari della forma $AX = B$ hanno soluzioni e, se sì, di trovarle. 2. Per verificare se un sistema ha soluzioni, si confrontano i

1. **Stating the problem:** We are given a system of three linear equations with three variables $A$, $B$, and $C$:

1. **State the problem:** We are given the function $f(x) = 2x - 4$ and need to find the values of $x$ for which $f(x) \leq 3x$. 2. **Write the inequality:**

1. **State the problem:** We have a table with variables $x$, $y$, $u_1$, $u_2$, and a value $z$ to find in the last row. The table is: | $x$ | $y$ | $u_1$ | $u_2$ | Value |

1. 문제를 이해합니다: 다항식 $$x^3 + ax^2 + (a-1)x + 1 = 0.01$$ 에서 최고차항의 계수가 1이고, 일차식으로 인수분해될 때 모든 해가 정수인 경우를 찾습니다. 2. 문제에서 주어진 다항식을 정리합니다. 우선 우변의 0.01은 좌변으로 옮겨서 0으로 만듭니다:

1. The problem is to evaluate the expression $Ne^2$. 2. Here, $N$ is a variable or constant, and $e$ is the mathematical constant approximately equal to 2.71828.