🧮 algebra

1. **State the problem:** Determine whether the function $y=5x^5 - x^3 + 1$ is even, odd, or neither. 2. **Recall definitions:**

1. The problem is to understand and use the point-slope form of a linear equation, which is given by the formula: $$y - y_1 = m(x - x_1)$$

1. **Problem Statement:** We need to find the slopes of the missing line segments to complete the Christmas tree shape, which extends up to $y=23$. We will use the point-slope form

1. Problem: Find the x-intercept and y-intercept of the equation $4y = 2x - 1$. - To find the x-intercept, set $y=0$ and solve for $x$.

1. **State the problem:** Simplify the expression $$3(x - 5)^2 - 2(x - 5) + 4$$ by distributing and writing it as a polynomial in standard form. 2. **Recall the formula:** The squa

1. **State the problem:** We need to subtract the expression $$(x - 5)^2$$ from $$4x^2 - 7$$ and simplify the result into a polynomial in standard form. 2. **Recall the formula:**

1. **State the problem:** We need to find the result when the polynomial $(2x - 6)^2$ is subtracted from $8x$. 2. **Write the expression:** The expression is $$8x - (2x - 6)^2$$

1. **State the problem:** We need to find the result when the expression $$(x + 8)^2$$ is subtracted from $$(x + 7)$$ and write the answer as a simplified polynomial in standard fo

1. **State the problem:** We need to subtract the polynomial $(x - 3)^2$ from $7x^2$ and write the result as a simplified polynomial in standard form. 2. **Recall the formula:** Th

1. **State the problem:** Determine if the table shows a proportional relationship and find the value of $y$ when $x=\frac{3}{5}$.\n\n2. **Check proportionality:** A relationship i

1. **State the problem:** Evaluate the division of fractions $\frac{5}{4} \div \frac{3}{5}$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its

1. **Problem Statement:** Suppose a square and an equilateral triangle have the same perimeter. Each side of the equilateral triangle is 6 centimeters longer than each side of the

1. Diberikan persamaan kuadrat $$3x^2 - 2x + 10 = 0$$ dengan akar-akar $$x_1$$ dan $$x_2$$. 2. Kita gunakan rumus jumlah dan hasil kali akar persamaan kuadrat:

1. **State the problem:** We need to find the rate of change in cost per visitor for a tour given two data points: 3 visitors cost 31 and 10 visitors cost 80. 2. **Formula used:**

1. **State the problem:** Solve the equation $$\frac{2x - 4}{3} = \frac{4x - 2}{5}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by th

1. **Problem 1:** Two airplanes leave St. Louis at the same time and fly in opposite directions. One travels at 500 km/h, the other at 600 km/h. Find the time $t$ when they are 192

1. **State the problem:** We need to find which two fractions from the list $\frac{1}{4}$, $\frac{6}{23}$, $\frac{2}{7}$, $\frac{3}{5}$, and $\frac{9}{8}$ multiply together to give

1. نبدأ بحل التعبير $5\sqrt{0.0003}$. 2. نعرف أن الجذر التربيعي لـ $0.0003$ يمكن كتابته كـ $\sqrt{3 \times 10^{-4}}$.

1. **State the problem:** Solve for $x \in \mathbb{R}$ in the equation $$2^{3x+1} - 3 \cdot 2^{2x} + 2^{x+1} = 2^x.$$\n\n2. **Rewrite the equation using properties of exponents:**

1. **State the problem:** Solve the equation $$2^{3x+1} - 3 \cdot 2^{2x} + 2^{x+1} = 2x$$ for $x$. 2. **Rewrite terms using properties of exponents:**

1. **State the problem:** Simplify the expression $$\frac{3q^5rt^2}{24q^7t}$$. 2. **Write the expression:** $$\frac{3q^5rt^2}{24q^7t}$$.