🧮 algebra

1. The problem is to find the equation of the line created by two given points or lines. 2. The general formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. **State the problem:** Solve the system of equations by graphing: $$y - 5x = -26$$

1. **State the problem:** Simplify the expression $$\frac{(-3u^{-3}h^{3})^{5}}{12u^{-9}h^{10}}$$ and express it with only positive exponents. 2. **Apply the power to each factor in

1. **State the problem:** Simplify the expression $$\frac{-4(r^4t^{-2})^{-1}}{4r^2t^4}$$ so that it contains only positive exponents. 2. **Recall the rules:**

1. **State the problem:** Kayleigh ran 20 miles. Charlie ran 3 times as many miles as Kayleigh, and Zion ran 2 times as many miles as Charlie. We need to find how many miles Zion r

1. The problem asks to identify the graph of the function $$h(x) = -\tan\left(\frac{1}{2}x\right)$$ from two options. 2. The parent tangent function is $$\tan(x)$$, which has verti

1. **Problem statement:** Kelly needs to rent tables for exactly 240 people using 6-person rectangular tables and 10-person round tables. The constraints are:

1. **Problem statement:** Kelly needs to rent tables for exactly 240 people using 6-person rectangular tables and 10-person round tables. The constraints are:

1. **State the problem:** Given the equation $$\frac{1}{4}x + 5 = 7$$, prove that $$x = 8$$. 2. **Review the given proof steps:**

1. **State the problem:** Karen spends money on food, hall, and DJ, then sells tickets. We need to find the percentage profit she makes. 2. **Calculate total cost:**

1. **Problem 1(a): Expand and simplify** $3(2y - 5) + 7(y + 2)$ 2. Use the distributive property: multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Solve the equation $8(x-3)-2(3-x)=2(x+2)-5(5-x)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Solve the equation $5 - 4(x - 3) = x - 2(x - 1)$ for $x$. 2. **Apply the distributive property:**

1. Vi börjar med att bestämma derivatan för funktionen $f(x) = 4x^3 - 12x$. 2. Derivatan av $x^n$ är $nx^{n-1}$, och derivatan av en konstant multiplicerad med en funktion är konst

1. **State the problem:** Rationalise the denominator of the expression $$\frac{7 - \sqrt{5}}{\sqrt{5} - 2}$$ and express the answer in the form $$a + b\sqrt{5}$$. 2. **Formula and

1. **State the problem:** Rationalise the denominator of the expression $$\frac{2\sqrt{2}}{\sqrt{5} - \sqrt{3}}$$ and express the answer in the form $$a\sqrt{10} + b\sqrt{6}$$. 2.

1. **State the problem:** Find the coordinates of points A and B given as fractions. 2. **Identify the coordinates:**

1. **Problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula:** To isolate $x$, use the subtraction property of equality: if $a + b = c$, then $a = c - b$.

1. Das Problem lautet: Löse die Gleichung $$\frac{2x+3}{4} = 5$$. 2. Die Formel, die wir verwenden, ist das Lösen von Gleichungen durch Multiplikation beider Seiten mit dem Nenner,

1. **Problemstellung:** Gegeben sind zwei Punkte $A(2,2)$ und $B(4,4.5)$, und wir sollen eine Exponentialfunktion der Form $y = a \cdot b^x$ finden, die durch diese Punkte verläuft

1. **Stating the problem:** We want to find how to get the numbers 4, 30, 36, 52, and 57 from a total of 11 using only ones and twos. 2. **Understanding the problem:** Using ones a