🧮 algebra

1. **State the problem:** Solve the proportion $1,11 = \frac{1}{x}$ for $x$. 2. **Rewrite the problem:** The comma in $1,11$ likely represents a decimal point, so the problem is $1

1. **Problem statement:** We are given a vector $r = \begin{pmatrix}80 \\ 50\end{pmatrix}$ and a vector $x = \begin{pmatrix}30 \\ 20\end{pmatrix}$. We need to analyze these vectors

1. **Problem:** Löse die Gleichung $$6x - \left(\frac{3}{5} + 2x\right) = x - \frac{3}{4}$$ 2. **Formel und Regeln:** Um Bruchgleichungen zu lösen, multiplizieren wir beide Seiten

1. **State the problem:** We are given points $A(-12,-9,k+3)$ and $B(-15,-9,3k)$, and the midpoint of segment $AB$ lies in the $xy$-plane. We need to find the value of $k$. 2. **Re

1. **State the problem:** Solve the equation \(5^{2n} \times 25^{2n-1} = 625\). 2. **Recall the rules and formulas:**

1. **Problem 9 (i): Solve the equation** $$2^{2x} - 9(2^x) + 8 = 0$$ 2. **Rewrite using substitution:** Let $$y = 2^x$$. Then $$2^{2x} = (2^x)^2 = y^2$$.

1. **State the problem:** Find the equation of the line perpendicular to the line $$y=\frac{1}{3}x$$ and passing through the point $$(2,5)$$. 2. **Recall the rule for perpendicular

1. **State the problem:** Graph the function $$y=\left(\frac{1}{2}\right)^{x-1} - 10$$ using the given table of values and identify the asymptote.

1. **State the problem:** Graph the function $$y=\left(\frac{1}{2}\right)^{x+1} - 7$$ using the given table of values and identify the horizontal asymptote.

1. **State the problem:** Solve the simultaneous equations: $$x + y + z = 16$$

1. **State the problem:** Simplify the expression $$(2x-3)(2x-3)^2$$. 2. **Understand the expression:** The expression is a product of $(2x-3)$ and $(2x-3)^2$. Using the laws of ex

1. **State the problem:** Evaluate the expression $4 + 5^3 - 3^2 + 8(27 \div 9)^2$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Divisi

1. **State the problem:** Evaluate the expression $7^3 - 3(-4)^3$ and verify if the handwritten result $535$ is correct. 2. **Recall the formulas and rules:**

1. **State the problem:** Evaluate the expression $$-7^3 - 3(-4)^3$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\left(\frac{(-4)^3}{(-2)^4}\right)^2$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$(2^4)^{t-2} \times 2^{2t} = (2^2)^{t+2}$$ for $t$. 2. **Recall exponent rules:**

1. **State the problem:** We have two functions $f$ and $g$ given by their graphs. We need to find the domain and range of $f$, evaluate expressions involving $f$ and $g$, find inv

1. **State the problem:** Sam paid a taxi fee of 25 and gave an 18% tip. We want to create a proportion to find the tip amount $x$. 2. **Set up the proportion:** The tip percentage

1. The problem is to find the vertex of the quadratic function $$x^2 + 4x + 4$$. 2. The vertex form of a quadratic function is $$y = a(x-h)^2 + k$$, where $$(h,k)$$ is the vertex.

1. **State the problem:** Find the axis of symmetry for the quadratic function $$x^2 - 7x + 14$$. 2. **Recall the formula:** The axis of symmetry for a quadratic function $$ax^2 +

1. The problem is to find the axis of symmetry of the quadratic function $$4x^2 - 2x + 10$$. 2. The formula for the axis of symmetry of a quadratic function $$ax^2 + bx + c$$ is gi