🧮 algebra

1. **State the problem:** We are given that 3 ladybugs equal 90, and we need to find the value of a ladybug with a ladybug subscript (which we interpret as a single ladybug). 2. **

1. **State the problem:** We need to solve the equation $$a^{3/4} = 125$$ for $a$. 2. **Recall the formula and rules:** To solve for $a$, we want to isolate it by raising both side

1. **State the problem:** We need to solve the system of equations using substitution: $$y = 9x - 9$$

1. **State the problem:** Solve the system of equations using substitution: $$x + 4y = 9$$

1. **State the problem:** We need to solve the system of equations using substitution: $$y = 3x + 4$$

1. **State the problem:** We need to solve the system of equations using substitution: $$y = 4x + 2$$

1. **State the problem:** We need to solve the system of equations using substitution: $$y = -7x - 8$$

1. The problem is to simplify the expression by combining like terms. 2. Like terms are terms that have the same variable raised to the same power.

1. **State the problem:** We need to solve for $a$ in the equation $$5 = a(-2 - \sqrt{5})(-2 + \sqrt{5}).$$ 2. **Recall the formula:** The product of conjugates $$(x - y)(x + y) =

1. **State the problem:** Solve the system of equations: $$\begin{cases} 3x + 3y + z = -4 \\ x - 3y + 2z = -6 \\ 8x - 2y + 3z = -30 \end{cases}$$

1. **State the problem:** A motel clerk has a total of $63$ bills consisting of $1$-dollar and $10$-dollar bills. The total amount of money is $225$. We need to find how many bills

1. **State the problem:** Simplify the expression $$8 - (-12) + 20 - 13 + (-15)$$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterp

1. The problem is to analyze the set $\left\{-\frac{15}{7},-\sqrt{2},\frac{2}{3},1,\sqrt{3},3.25\right\}$ and understand its elements. 2. This set contains six numbers: two negativ

1. **State the problem:** We want to compare the total cost of ordering $t$ tacos from Taco Trek and Burrito Bus and find when their costs are equal.

1. **State the problem:** We need to find Juma's age given that Juma is 6 years older than Joseph and the sum of their ages is 38.

1. **State the problem:** Roseline earns $68000$ per month and pays $18\frac{1}{2}\%$ of her salary as income tax. We need to find the amount she pays as income tax. 2. **Formula u

1. **State the problem:** Factor the quadratic expression $$x^2 + 14x + 49$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, if it can be factor

**Problem:** Evaluate $\sum_{j=2}^{6}(j^3-1)$. 1. A summation adds the expression for every integer from the lower limit to the upper limit, including both endpoints.

1. **State the problem:** Calculate the summation $$\sum_{j=2}^{6}(j^3-1)$$ which means we sum the values of the expression $$j^3 - 1$$ for $$j$$ from 2 to 6 inclusive. 2. **Formul

1. Problem: evaluate $\sum_{j=2}^{6} (j^3-1)$. 2. Use the sum by substituting each value of $j$ from $2$ to $6$.

1. **State the problem:** Factor the quadratic expression $$6x^2 - 5x - 4$$ into the product of two binomials. 2. **Recall the factoring method:** For a quadratic $$ax^2 + bx + c$$