🧮 algebra

1. The problem asks for the coordinates of point R on the Cartesian plane. 2. The x-coordinate is the horizontal position, and the y-coordinate is the vertical position.

1. The problem is to expand the expression $5(x + \Delta x)^2$. 2. Recall the formula for the square of a binomial: $ (a + b)^2 = a^2 + 2ab + b^2 $.

1. Factor $9x^2 - 144z^2$ completely. Step 1: Recognize this as a difference of squares: $a^2 - b^2 = (a-b)(a+b)$.

1. The problem is to analyze the linear function $y = -3x + 9$. 2. This is a straight line with slope $-3$ and y-intercept $9$.

1) Écrire chacun des nombres suivants sous la forme d'une puissance. A = 3 \times 3 \times 3 = 3^3

1. The problem is to find the determinant of the matrix $$\begin{vmatrix} 1 & 1 & 1 \\ x & y & n \\ x^3 & y^3 & z^3 \end{vmatrix}$$

1. נתחיל מהגדרת פונקציה קבועה: פונקציה קבועה היא פונקציה שבה כל הערכים של $y$ הם אותו מספר, ללא תלות ב-$x$. 2. בשאלה הראשונה, "סְרִיָּת השׁוֹאָה הָיְשָׁר שֶׁלָאוֹרֶךְ הַתְּּבִיעָה

1. The problem is to identify the coordinates of the given point on the Cartesian plane. 2. The point is given as $(-2, -4)$, where $-2$ is the x-coordinate and $-4$ is the y-coord

1. Stating the problem: Solve the equation $$\frac{3x}{6} = 2 + \frac{x}{3}$$ for $x$. 2. Simplify the fractions: $$\frac{3x}{6} = \frac{x}{2}$$, so the equation becomes $$\frac{x}

1. The problem is to evaluate the expression $8 \times \frac{5}{10} \div 2 + 6$. 2. First, calculate $8 \times \frac{5}{10}$.

1. Stating the problem: Solve the equation $$\frac{3x}{6} = 2 + \frac{x}{3}$$ for $x$. 2. Simplify the fractions: $$\frac{3x}{6} = \frac{x}{2}$$, so the equation becomes $$\frac{x}

1. Stating the problem: Solve the equation $$\frac{3x}{6} = 2x$$ for $x$. 2. Simplify the left side: $$\frac{3x}{6} = \frac{3}{6}x = \frac{1}{2}x$$.

1. The problem is to simplify the expression $\frac{6x}{3}$.\n\n2. We start by recognizing that both the numerator and denominator have a common factor of 3.\n\n3. Divide the numer

1. **State the problem:** Solve the equation $$2T^2t^2 + t^4 = 9T^4$$ for $t$ in terms of $T$. 2. **Rewrite the equation:**

1. **State the problem:** We have three pipes A, B, and C that fill a tank in different times: Pipe A in 2 hours, Pipe B in 1 hour 30 minutes, and Pipe C in 2 hours 30 minutes. We

1. The problem states the equation $9C = 9(F - 32)$ and asks to find the value of $F$ when $C = 100$. 2. Substitute $C = 100$ into the equation:

1. **State the problem:** We need to find the principal amount invested in the bank to get a profit (simple interest) of 3500 at an interest rate of 7% per annum for 4 years. 2. **

1. **State the problem:** Abdullah gave 60 to Umar, and Umar gave 90 to Ahmed. After these transactions, all three have the same amount of money. We need to find how much more Umar

1. The problem states that the sale price of a book is 855 with a loss of 5%. We need to find the cost price (CP) of the book. 2. Loss percent is given by the formula:

1. **Problem statement:** The population of a town decreased by 8% in 2077 B.S., then decreased by 10% in 2078 B.S. and onward. At the beginning of 2080 B.S., the population is 556

1. **Reflecting the graph of** $f(x) = \log_{10} \left( \frac{3}{4} (x+2) \right) - 4$ **in the x-axis:** Reflecting in the x-axis changes $y$ to $-y$, so the new function is: