🧮 algebra

1. **State the problem:** Solve the system of linear equations: $$x + 3y = 7$$

1. **State the problem:** We want to find how many real roots the equation $ax + \cos x = b$ has, given that $a,b$ are constants and $a > 1$. 2. **Rewrite the equation:** Define a

1. Stating the problem: Simplify the expression $$(5y+5)-(4y+1)$$. 2. Remove the parentheses by distributing the minus sign to the second group:

1. समस्या: 2820 को 60% पर विभाजित करना है। 2. 60% का अर्थ है 60 को 100 से विभाजित करना, यानी 0.60।

1. The problem is to simplify the expression $\frac{2860}{60}$.\n\n2. To simplify, divide the numerator and denominator by their greatest common divisor (GCD).\n\n3. Find the GCD o

1. **State the problem:** Find the highest common factor (HCF) of 170 and 238 using the prime factorization method. 2. **Prime factorize 170:**

1. **State the problem:** Find the highest common factor (HCF) of 312, 260, and 156 using the prime factorization method. 2. **Prime factorize each number:**

1. The problem asks for the zeros of the given function, which are the x-values where the graph crosses the x-axis. 2. From the graph description, the parabola crosses the x-axis a

1. The problem has two parts: first, solve for $x$ in the expression $$x = \frac{3}{7} : \frac{3}{4} \div \frac{5}{21}$$ and second, understand the given equations $2r + \frac{1}{2

1. The problem asks for the zeros of the function, which are the x-values where the graph intersects the x-axis. 2. From the graph description, the parabola intersects the x-axis a

1. **State the problem:** Find the highest common factor (HCF) of 490, 588, and 882 using the prime factorization method. 2. **Prime factorize each number:**

1. The problem asks for the maximum profit, which typically involves finding the maximum value of a profit function $P(x)$. 2. To find the maximum profit, we need the profit functi

1. **State the problem:** We are given the total revenue function $$R = 3x^2 + 200x$$ and the total cost function $$C = 2x^2 - 150x + 5000$$ where $x$ is the number of units sold i

1. **State the problem:** Simplify the expression $5x - 2 + 7$. 2. **Combine like terms:** The terms $-2$ and $7$ are constants and can be added together.

1. **State the problem:** Simplify the expression $5 - x - 2x$. 2. **Combine like terms:** The terms involving $x$ are $-x$ and $-2x$.

1. The problem is to simplify the expression $$-4 - 3x - 7$$. 2. First, identify like terms. The constants are $$-4$$ and $$-7$$, and the term with $$x$$ is $$-3x$$.

1. **State the problem:** We are given the total revenue function $$R = 3x^2 + 2000x$$ where $$R$$ is in thousands of Ksh and $$x$$ is the number of units sold in thousands. 2. **U

1. **State the problem:** Simplify the expression $5x + 5x - 8$. 2. **Combine like terms:** The terms $5x$ and $5x$ are like terms because they both contain the variable $x$. Add t

1. The problem is to simplify the expression $3 - 3x - 4x$. 2. Combine like terms by adding the coefficients of $x$: $-3x - 4x = -7x$.

1. Stating the problem: Simplify the expression $$\frac{2\sqrt{54}+4\sqrt{6}}{4\sqrt{8}-3\sqrt{2}}$$. 2. Simplify the radicals inside the expression:

1. Solve $11 + 3^3 - 7$: Calculate the exponent: $3^3 = 27$.