🧮 algebra

1. **Solve the system of equations:** Given:

1. The problem states that the cost $C$ of renting the yacht depends on the number of people $p$ in the group. 2. The cost per person is 75, and there is a fixed rental fee of 350.

1. The problem is to factorize the given equation. However, the equation itself is not provided. 2. To factorize an equation, we need the specific polynomial or expression.

1. The problem is to factor the quadratic expression $6x^2 + 14x + 15$. 2. First, identify coefficients: $a=6$, $b=14$, and $c=15$.

1. The problem asks us to identify the independent and dependent variables from the graph of the valve on the bike tire and to state the domain and range. 2. The independent variab

1. **State the problem:** We have the formula for the number of blades of grass on a fertilized lawn as $$B = 48l \pm 2$$ where $B$ is the number of blades and $l$ is the area of t

1. **State the problem:** Solve the equation $$\frac{1}{x} + \frac{1}{2x} = 3$$ for $x$. 2. **Find a common denominator:** The denominators are $x$ and $2x$. The least common denom

1. The problem is to simplify the expression: $$\frac{1}{3} \times \frac{5}{1} - 2x \times \frac{7}{1} \times \frac{1}{2}$$. 2. First, multiply the fractions in the first term:

1. The problem is to rearrange the equation $$2y = \sqrt{x + 3} + 2$$ to make $$x$$ the subject. 2. Start by isolating the square root term on one side:

1. We are asked to factor the cubic polynomial $2x^3 + 9x^2 - 6x - 5$. 2. First, try to find rational roots using the Rational Root Theorem. Possible roots are factors of the const

1. **State the problem:** Simplify or factor the cubic polynomial $2x^3 + 9x^2 - 6x - 5$. 2. **Group terms:** Group the polynomial into two pairs:

1. The problem is to simplify the expression $6 - 4\frac{3}{8} + 2\frac{1}{4}$.\n\n2. Convert the mixed numbers to improper fractions:\n\n$4\frac{3}{8} = \frac{4 \times 8 + 3}{8} =

1. Expand $3(x+2)$: $$3x + 6$$

1. **State the problem:** We have a polynomial $$P(x) = (x^2+3)(x^2-1)$$ and it is given that when $$P(x)$$ is divided by $$(x-m)$$ and $$(x-n)$$, the remainders are the same. We n

1. **State the problem:** Given the polynomial $$P(x) = (x^2+3)(x^2-1)$$ and two values $$m$$ and $$n$$ such that the remainders when $$P(x)$$ is divided by $$(x-m)$$ and $$(x-n)$$

1. **Stating the problems:** We have multiple expressions to simplify and evaluate:

1. **Problem:** Find the simplest index form of 81. Step 1: Express 81 as a power of a prime number.

1. **Simplify the expressions involving polynomials** Given:

1. State the problem: Solve the equation $24 - 6x = 4x + 7$ for $x$. 2. Move all terms involving $x$ to one side and constants to the other side:

1. **State the problem:** We are given the ratio of analysts to field agents as 3:5 and the total number of agents as 40. We need to find the number of analysts. 2. **Understand th

1. **State the problem:** Solve the equation $3n + 3 = 25 - n$ for $n$. 2. **Combine like terms:** Add $n$ to both sides to get all $n$ terms on one side: