🧮 algebra

1. The problem is to solve the equation $$6x\15 = 4(x-1)\-30$$. 2. First, rewrite the equation correctly by interpreting the slashes as division: $$\frac{6x}{15} = \frac{4(x-1)}{-3

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to find 7.25% of 44. 2. To find a percentage of a number, convert the percentage to a decimal by dividing by 100: $$7.25\% = \frac{7.25}{100} = 0.0725$$

1. **State the problem:** Solve the system of equations: $$6y - 2x = 1$$

1. The problem is to find the function $f$ defined as $f = A - B$. 2. This means for any input $x$, the function $f(x)$ is the difference between the values of functions $A(x)$ and

1. **State the problem:** X, Y, and Z share 68 units such that for every 1 unit Z gets, Y gets 2 units, and for every 3 units Y gets, X gets 4 units. We need to find how much Y get

1. The problem asks to find the total price of sneakers including a sales tax of 3.75% on a $20 price. 2. First, convert the sales tax percentage to a decimal: 3.75% = \frac{3.75}{

1. The problem is to find the solution for the system of equations. However, the system of equations is not provided in the question. 2. Please provide the system of equations so I

1. **State the problem:** Taub bought pants priced at 36. The sales tax rate is 9%. We need to find the total price including tax, rounded to the nearest cent. 2. **Calculate the a

1. **State the problem:** Taub bought pants priced at 36 with a sales tax of 9%. We need to find the total price including tax, rounded to the nearest cent. 2. **Calculate the amou

1. Stwierdźmy problem: mamy wyrażenie $-3n^2 + 2n$ i chcemy je przekształcić tak, aby znajdowało się w mianowniku, ale już poza pierwiastkiem. 2. Załóżmy, że pierwiastek jest z jak

1. Stwierdźmy problem: mamy wyrażenie z \(-3n^2 + 2n\) w mianowniku, ale chcemy, aby było ono poza pierwiastkiem kwadratowym. 2. Załóżmy, że mamy wyrażenie w postaci \(\frac{1}{\sq

1. **State the problem:** We are given the equation of a line in the Cartesian plane: $$2 - y = 5 - x$$ and a point on the line with an x-coordinate of $$x = -3$$. We need to find

1. The problem asks for the nth term of the sequence denoted as $s_n$. 2. To find the nth term, we need the explicit formula or pattern of the sequence $s_n$.

1. **State the problem:** Evaluate $\log 2 \sqrt[3]{2}$. 2. **Rewrite the expression:** Note that $\sqrt[3]{2} = 2^{\frac{1}{3}}$, so the expression inside the logarithm is:

1. Let's analyze the problem: We are looking for a number that is less than 2 and not divisible by 2. 2. Since the number is less than 2, possible candidates are numbers less than

1. **State the problem:** Solve the equation $$\frac{2x - 1}{3} - \frac{3 - x}{2} = \frac{x}{4}$$ for $x$. 2. **Find a common denominator:** The denominators are 3, 2, and 4. The l

1. The problem is to convert the binary number $101101_2$ to its decimal (base 10) equivalent. 2. Each digit in a binary number represents a power of 2, starting from the rightmost

1. The problem states that the quadratic equation $y = x^2 + bx + c$ has roots $m$ and $n$. 2. By definition, if $m$ and $n$ are roots of the quadratic, the factorization of the qu

1. **State the problem:** Simplify the expression $$\sqrt{\frac{9}{9}} + \frac{3}{2} \times \left(\frac{3}{2}\right)^2$$. 2. **Simplify the square root:** Since $$\frac{9}{9} = 1$$

1. نبدأ بتحديد قيمة $m$ بحيث يكون العدد 2 جذرًا لكثير الحدود $P(x) = 2x^3 + mx^2 - 11x - 6$. هذا يعني أن $P(2) = 0$. 2. نحسب $P(2)$: