🧮 algebra

1. The problem asks for the degree of the polynomial $$p(x) = 3x^4 - 5x^3 + 7x^2 - 2x + 1$$. 2. The degree of a polynomial is the highest power of the variable $x$ with a nonzero c

1. The problem is to multiply $\frac{20}{100}$ by 10. 2. Write the multiplication as a fraction: $\frac{20}{100} \times 10$.

1. The problem asks to find the inverse function $f^{-1}(x)$ of the function $f(x) = 2x + 3$. 2. To find the inverse, start by replacing $f(x)$ with $y$: $$y = 2x + 3$$

1. Solve $8^{4x + 2} = 64$. Express bases as powers of 2: $8 = 2^3$, $64 = 2^6$.

1. **State the problem:** A number $w$ is decreased by 6, then the result is multiplied by 4. The final result is greater than the original number $w$. We need to write and solve a

1. The problem asks for the sum of the roots of the quadratic equation $$3x^2 - 5x = 2 = 0$$. 2. First, note that the equation as written is ambiguous because of the double equals

1. **State the problem:** Solve the inequality $$2(3x - 4) > 5(5 - x)$$ for $x$. 2. **Expand both sides:**

1. The problem is to find the roots of the quadratic equation $$x^2 - 4x + 3 = 0$$. 2. To find the roots, we use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ w

1. The problem is to solve the inequality $7 \leq 2x - 5$. 2. Start by isolating $x$ on one side. Add 5 to both sides:

1. **State the problem:** Solve the inequality $$2(3d + 7) \leq 4d + 28$$. 2. **Expand the left side:** Multiply 2 by each term inside the parentheses:

1. **State the problem:** Find the number of integer values of $x$ that satisfy the inequality $$5 < 2x + 1 \leq 9.$$\n\n2. **Isolate the variable term:** Subtract 1 from all parts

1. The problem is to multiply the fraction $\frac{15}{101}$ by the number 404. 2. Write the multiplication as a single fraction: $$\frac{15}{101} \times 404 = \frac{15 \times 404}{

1. The problem is to multiply the fraction $\frac{15}{101}$ by the number 404. 2. Write the multiplication as:

1. The problem is to calculate $\frac{50}{101} \times 101$. 2. We start by writing the expression clearly: $$\frac{50}{101} \times 101$$

1. لنفترض أن قدرات الطلاب الستة متساوية، أي أن كل طالب لديه نفس القدرة على أداء مهمة معينة. 2. هذا يعني أن إذا كان لدينا مهمة أو اختبار معين، فإن كل طالب سيؤدي بنفس المستوى.

1. The problem involves understanding the relationship between Weight (x-axis) and Cost (y-axis) based on the given graph axes and labels. 2. The x-axis represents Weight values fr

Problem: Graph the rational function $f(x)=\frac{3x^2}{x^2-4}$. 1. Factor the denominator and write the function in factored form: $x^2-4=(x-2)(x+2)$.

1. Statement of the problem: The correct expression should be $x^2 - 4$. 2. Recognize the pattern: This is a difference of squares because $x^2 - 4 = x^2 - 2^2$.

1. نبدأ بتعريف المتغيرات: لنفرض أن سرعة المشي هي $x$ كم/ساعة.

1. The problem asks to find 20% of 250. 2. To find a percentage of a number, convert the percentage to a decimal by dividing by 100: $$20\% = \frac{20}{100} = 0.20$$

1. Newton's identities relate the power sums of the roots of a polynomial to its coefficients. 2. For a polynomial $x^n + a_{n-1}x^{n-1} + \cdots + a_1 x + a_0 = 0$ with roots $r_1