🧮 algebra

1. **State the problem:** We need to find the length and width of a rectangle where the length is 33 cm less than 4 times the width, and the perimeter is 74 cm. 2. **Write down the

1. **State the problem:** We are given that 7 times as many people attended the convention on Sunday as on Thursday, and the total attendance on both days combined is 4592. We need

1. **State the problem:** We need to find two positive numbers where the difference between them is 125, and one number is 6 times as large as the other. 2. **Define variables:** L

1. **State the problem:** We need to find two numbers whose sum is 178 and one number is 84 more than the other. 2. **Set variables:** Let the smaller number be $x$.

1. **State the problem:** We need to add the fractions $\frac{1}{2}$ and $\frac{1}{3}$ by finding a common denominator. 2. **Formula and rules:** To add fractions, they must have t

1. **State the problem:** Simplify the expression $$\frac{1}{4} - \frac{1}{8}$$ by finding a common denominator. 2. **Formula and rules:** To subtract fractions, they must have the

1. **State the problem:** We are given two tables showing the relationship between pages read and minutes spent reading. The first table has pages: 7, 1, 4, 15 and minutes: 14, wit

1. **State the problem:** Factor the polynomial $3x^2 + 2x - 5$ fully. 2. **Recall the factoring method for trinomials when the leading coefficient is not 1:**

1. **State the problem:** We need to determine if the points $(0, -27)$ and $(-9, 0)$ lie on the line given by the equation $$3y - 9x = 18.$$\n\n2. **Rewrite the equation in slope-

1. **State the problem:** Find the unit rate of miles per gallon given 450 miles and 15 gallons. 2. **Formula:** The unit rate is found by dividing the total miles by the total gal

1. **State the problem:** Solve the equation $$6x - \frac{2x + 3}{5} = \frac{x - 5}{4} - x$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation.

1. The problem is to find the missing numerator in the equation $$\frac{?}{10 r w^2} = \frac{2 r t}{5 w}$$. 2. To solve for the missing numerator, we use the property of equality o

1. **State the problem:** Simplify the expression by adding like terms: $$6x^2y^0 + 5x^2 + \frac{3x^3 y}{xy}$$ 2. **Recall important rules:**

1. **Stating the problem:** We want to understand why the inequality $$gd \leq (1+k) V^2$$ holds, starting from the given inequality involving $$g^2 d^2$$ and $$V^4$$. 2. **Given i

1. **State the problem:** Solve the system of linear equations: $$-2x + 6y = 6$$

1. **State the problem:** Simplify the expression $$\frac{144x^3 y^7}{-18x^5 y - 11}$$. 2. **Analyze the denominator:** The denominator is $$-18x^5 y - 11$$, which is a sum of two

1. The problem involves understanding and identifying the behavior of four exponential functions: $t(x) = 3(2)^x$, $k(x) = -(2)^x$, $m(x) = 3\left(\frac{1}{2}\right)^x$, and $g(x)

1. **Problem:** Simplify the expression $$\sqrt[3]{64x^4}$$. 2. **Formula and rules:** The cube root of a product is the product of the cube roots: $$\sqrt[3]{a \cdot b} = \sqrt[3]

1. **State the problem:** Solve for $X$ in the equation $X \times 18\% = 89654.56$. 2. **Recall the formula:** To find $X$, divide both sides of the equation by $18\%$.

1. **State the problem:** Solve for $X$ in the equation $X \times 1.18 = 89654.56$. 2. **Formula and rule:** To isolate $X$, divide both sides of the equation by $1.18$.

1. Let $x$ be the number. $4(6x + 7) = 30(-x) + 10$