🧮 algebra

1. **Solve the equation** $\frac{4p - 2}{5} = \frac{p + 1}{5} - 3$. 2. Multiply both sides by 5 to clear the denominators:

1. The problem is to graph the circle given by the equation $$(x + 2)^2 + (y - 6)^2 = 9.$$\n\n2. This equation is in the standard form of a circle's equation: $$(x - h)^2 + (y - k)

1. **Problem statement:** Graph the circle given by the equation $$(x + 1)^2 + y^2 = 81$$. 2. **Identify the center and radius:** This is the equation of a circle in standard form

1. The problem is to find the missing value in the proportion $43:14::54:x$. 2. By definition of proportion, the ratios are equal: $$\frac{43}{14} = \frac{54}{x}$$

1. The problem is to determine if the boolean expression representing the equality $4! = 4 + 0j$ is true or false. 2. Calculate $4!$ (4 factorial):

1. The problem is to understand the expression $5x^2$. 2. Here, $5x^2$ means $5$ times $x$ squared.

1. The problem is to simplify the expression $5\frac{a}{b}\sqrt{x}20$. 2. First, rewrite the expression for clarity: $5 \times \frac{a}{b} \times \sqrt{x} \times 20$.

1. **State the problem:** Solve the equation $$3 - \frac{3 - 7p}{4} = \frac{5p}{2}$$ for $p$. 2. **Rewrite the equation:** Move terms to isolate fractions and simplify.

1. **State the problem:** Compare the cost per kilogram of potatoes in London and Dublin to determine which city offers better value for money. 2. **Given information:**

1. The problem is to simplify the expression $$7^{-8} \times 7^{-7} \div 7^{-4}$$ leaving the answer with indices (exponents). 2. Use the law of indices for multiplication: $$a^m \

1. The problem is to simplify the expression $$14^{-3} \div 14^{-11} \times 14^{-19}$$ and leave the answer in indices form. 2. Recall the properties of exponents: $$a^m \div a^n =

1. State the problem: Simplify the expression $$6^{-2} \times 6^{4} \div 6^{-8}$$ leaving the answer in indices. 2. Use the laws of indices for multiplication and division: When mu

1. **State the problem:** We need to calculate the mean (average) of the given volumes: 25 cm^3, 27 cm^3, 28 cm^3, 21 cm^3, and 25 cm^3. 2. **Add all the volumes:**

1. The user provided several expressions: $32\pi$, $64$, $64\pi$, and $16$. 2. We will analyze these numbers to find their relationships or simplify them.

1. Solve $d = rt$ for $r$. Start with the equation:

1. Problem: Determine if $4xy + 2y = 9$ is a linear equation. Step 1: A linear equation in two variables $x$ and $y$ must be of the form $Ax + By = C$ where $A$, $B$, and $C$ are c

1. Find the x- and y-intercepts for the linear equations given. 2. For equation 7: \(y-4=0\)

1. The problem states an irregular polygon with sides labeled as $x-2$, $x$, $x-7$, $x-1$, and $x-3$, and the total perimeter is 52 inches. 2. To find $x$, we set up an equation: t

1. The problem asks to analyze and graph the line given by the equation $y = 3x - 6$. 2. First, identify the slope and the y-intercept.

1. **State the problem:** Simplify the expression $$\frac{1 + \sin\theta + i \cos\theta}{1 + \sin\theta - i \cos\theta}$$. 2. **Multiply numerator and denominator by the conjugate

1. Stating the problem: We have the function $$f(x) = \frac{1 + x^{8}}{5x}$$ and we want to understand its properties and simplify it if possible. 2. Simplify the function: The num