🧮 algebra

1. **State the problem:** Compare the decimal number 1.20 with the fraction \(\frac{6}{5}\) to determine if 1.20 is greater than, less than, or equal to \(\frac{6}{5}\). 2. **Conve

1. **State the problem:** Add the fractions $\frac{1}{8}$ and $\frac{3}{4}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The sum is given by $\

1. **State the problem:** Order the rational numbers 0.40, \frac{3}{7}, 0.4510, and \frac{5}{12} from smallest to largest. 2. **Convert all numbers to decimals for easy comparison:

1. **State the problem:** We are given the speed function of a model car as $$v(t) = 16 - 10t^2$$ for $$0 \leq t \leq 6$$ seconds. We need to fill in the missing values in the tabl

1. **State the problem:** Solve the equation $$6 - \frac{3y}{7} = \frac{y + 20}{9}$$ for $y$. 2. **Write down the equation:**

1. **Problem:** Determine the equation of the axis of symmetry for the parabola passing through points (8, -11) and (-3, -11). 2. **Understanding the axis of symmetry:** The axis o

1. **State the problem:** Half of Robert's wire equals two-thirds of Maria's wire, and together their wires total 10 feet. We need to find how much longer Robert's wire is than Mar

1. **State the problem:** We are given that the sum of Al's age and Bob's age is 93. 2. **Write the equation:** Let Al's age be $A$ and Bob's age be $B$. The problem states:

1. **State the problem:** Simplify the expression $$\frac{\frac{u}{5}}{\frac{25}{u-5} + \frac{u-5}{25}}$$. 2. **Rewrite the denominator:** The denominator is a sum of two fractions

1. **Problem:** Find the x- and y-intercepts of the equation $4x + y = 5$. 2. **Formula and rules:**

1. The problem is to find the value of $x$ in the proportion setup: $$\frac{13}{55} = \frac{100}{x}$$ 2. The formula for solving proportions is to cross multiply: $$a/b = c/d \impl

1. **State the problem:** Find the domain and range of the exponential function described. 2. **Recall the general form and properties:** An exponential function typically has the

1. **State the problem:** Find the domain and range of the exponential function described. 2. **Recall the general form and properties:** An exponential function typically has the

1. **State the problem:** Cho pays 3 to rent shoes and 5.10 for each game of bowling. We want to write an equation for the total cost $C$ based on the number of games $g$ played.

1. **Problem:** Solve the equation $x + b = a$ for $x$. 2. **Formula:** To isolate $x$, subtract $b$ from both sides.

1. The problem is to find the value of $y$ in the equation $9^2 + 5^2 = y^2$. 2. This is a Pythagorean theorem problem where $a^2 + b^2 = c^2$ for a right triangle.

1. The problem is to evaluate $\log \frac{1}{2}$.\n\n2. Recall the logarithm rule: $\log \frac{a}{b} = \log a - \log b$.\n\n3. Applying this rule, we get: $$\log \frac{1}{2} = \log

1. **State the problem:** Solve the inequality $$6 \geq -\frac{8}{3} v$$ for $$v$$. 2. **Recall the rule:** When multiplying or dividing both sides of an inequality by a negative n

1. The problem is to solve the system of linear equations: $$6x - 5y = 9$$

1. **State the problem:** We have a number $x$ with a partial prime factorization shown in a tree diagram. We want to find the minimum value of $x$ if $x$ is a perfect cube. 2. **A

1. **State the problem:** Simplify the expression $$\frac{\left(-\frac{2}{5}\right) + \left(\frac{1}{-2}\right)}{\left(\frac{5}{-8}\right) - \left(-\frac{1}{2}\right)}$$. 2. **Rewr