🧮 algebra

1. **State the problem:** We need to subtract $-25$ from $-18$, which means calculating $-18 - (-25)$. 2. **Recall the subtraction rule:** Subtracting a negative number is the same

1. **State the problem:** Multiply the mixed numbers $1\frac{1}{5}$, $\frac{3}{4}$, and $2\frac{1}{2}$.\n\n2. **Convert mixed numbers to improper fractions:**\n- $1\frac{1}{5} = \f

1. The problem is to evaluate the expression $\frac{2}{0}$.\n\n2. Division by zero is undefined in mathematics because there is no number that you can multiply by 0 to get a non-ze

1. **Problem 4: Representing the triangle angles as a system of linear equations** The problem states:

1. **State the problem:** Solve the inequality $9x + 4 > 10$ for $x$. 2. **Recall the rule:** To solve inequalities, isolate the variable on one side. When dividing or multiplying

1. The problem states that the height $h$ of a person should not be less than 3.8 ft to ride the roller coaster. 2. This means the height must be at least 3.8 ft.

1. The problem states that Adam's average marks in subjects A, B, C, D, and E are more than 85. 2. To express the average, we sum the marks of all five subjects and divide by 5.

1. **State the problem:** We need to find the values of $p$ for which the inequality $$\frac{2}{3} - \frac{p}{4} \geq \frac{7}{6}$$ holds true. 2. **Write down the inequality:** $$

1. **Stating the problem:** We are given an arithmetic sequence with the formula for the $n$-th term: $$U_n = 12 - 5n$$

1. **State the problem:** We have three purchases with total costs and want to find the cost of one t-shirt ($t$), one video ($v$), and one stuffed animal ($s$).

1. **State the problem:** We need to find the number of adult ($x$), student ($y$), and child ($z$) tickets sold given:

1. **State the problem:** We need to draw the prime factor tree for 90 and then use it along with the prime factorization of 252 to find the highest common factor (HCF) of 90 and 2

1. **State the problem:** We have a bag with green, red, and blue marbles. The number of marbles for each color is given by expressions involving $x$ and $y$: - Green: $4x - y + 3$

1. **Problem 1:** Solve the equation $4^3 = 4(2x + 3)$. - Calculate $4^3 = 64$.

1. **State the problem:** Simplify and solve the given expressions and equations step-by-step. 2. **Simplify the first expression:**

1. The problem is to plot the graph of a function. 2. Since no specific function was given, let's consider a general exponential function for demonstration: $$y = a^x$$ where $a >

1. **Problem Statement:** Solve for $x$ given the departments' workers and their total: Department K = $x + 2^1$, Department L = $x$, Department M = $x - 10$, and their sum is 40.

1. El problema es expandir la expresión $4(x-5)(x-2)$ usando la propiedad distributiva. 2. La propiedad distributiva dice que $a(b+c) = ab + ac$. Aquí la aplicaremos dos veces porq

1. **State the problem:** We have a parabolic curve representing the bridge arch given by the function $f(x) = px^2 + \frac{1}{4}x + 91$. The length of the base $AB$ is 144 m, and

1. **State the problem:** Solve the equation $$2^2 (-y + 1) = \frac{3}{4} y$$ for $y$. 2. **Rewrite the equation:** Since $2^2 = 4$, the equation becomes $$4(-y + 1) = \frac{3}{4}

1. **State the problem:** We need to find all vertical and horizontal asymptotes of the rational function $$f(x) = \frac{3x^2 - 6x - 9}{2x^2 + 7}$$. 2. **Vertical asymptotes:** The