🧮 algebra

1. **State the problem:** Solve the equation $6x^2 + 25 = 79$ for $x$. 2. **Isolate the quadratic term:** Subtract 25 from both sides to get

1. **State the problem:** Solve the equation $x^2 - 12 = 37$ for $x$. 2. **Add 12 to both sides** to isolate the squared term:

1. The problem involves calculating percentages and understanding their values relative to given numbers. 2. To find a percentage of a number, use the formula: $$\text{Percentage v

1. **State the problem:** Find the slope of the line passing through the points $(-2, 9)$ and $(8, 34)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. Problem: Describe the transformations from $f(x)$ to $r(x)$ or $g(x)$ for each given function. 2. Recall the transformation rules:

1. **State the problem:** Rosa wants to exercise a total of 175 minutes. She has already walked 110 minutes. She can do jumping jacks for 1 minute at a time and jog for 10 minutes

1. **State the problem:** Evaluate the expression $$2[3(4^2 + 1)] - 2^3$$ and find its value. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplicat

1. Identify the parent function and describe the transformation for $f(x) = (x + 4)^2$. - Parent function: $y = x^2$ (quadratic function).

1. **State the problem:** We need to express each fraction as the sum of two or three equal fractional parts and rewrite each as a multiplication equation. For part (a), we will al

1. **State the problem:** We are given the equation of a circle in the form $$x^2 + y^2 - 12x + 10y + 61 = 0$$ and need to find its center and radius. 2. **Formula and rules:** The

1. **State the problem:** Calculate the value of $1.0101001101011 \times 10^5$. 2. **Formula used:** Multiplying a decimal number by $10^n$ shifts the decimal point $n$ places to t

1. Problem: Solve the equation $\frac{1}{2}x - 3 = 1$. 2. Formula and rules: Use inverse operations to isolate the variable.

1. Állítsuk fel a feladatot: összevonjuk az azonos betűs tagokat, majd behelyettesítjük $a=-2$ és $b=1$ értékeket. 2. (1) kifejezés: $$4a + 3b - 2ab + 5a - 7b - 8ab$$

1. The problem asks to find the values of $a$ and $b$. 2. To solve for $a$ and $b$, we need the equations or context where these variables appear.

1. **State the problem:** Expand and fully simplify the expression $$y(3y + 6) + 3(3y + 4)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the

1. The problem is to subtract the repeating decimals $0.6\overline{6}$ and $0.3\overline{3}$.\n\n2. Recall that a repeating decimal like $0.6\overline{6}$ can be expressed as a fra

1. **State the problem:** Calculate the difference between the repeating decimals $0.6\overline{6}$ and $0.3\overline{3}$. 2. **Recall the formula for converting repeating decimals

1. **State the problem:** We are given a table with two columns, X and Y, where X is constant at -3 and Y takes values 8, 11, 14, 17, and 20. We need to determine if this table rep

1. **State the problem:** Determine if the relation given by the table with points $(-4,7)$, $(-1,7)$, $(2,7)$, $(5,7)$, and $(8,7)$ is a function. 2. **Recall the definition of a

1. **State the problem:** Determine if the given set of points \((X, Y)\) represents a function. 2. **Recall the definition of a function:** A relation is a function if every input

1. **State the problem:** We are given a set of points with coordinates $(X, Y)$: $(-3,8)$, $(-1,9)$, $(1,10)$, $(3,9)$, and $(5,8)$. We need to determine if this set represents a