🧮 algebra

1. **State the problem:** Bonaficio sells thingamabobs and whosie-whats-its. He sold 12 thingamabobs and 10 whosie-whats-its for 111.20, and another shipment of 10 thingamabobs and

1. The problem asks to write equations of cubic functions with given zeros and belonging to the same family of functions. 2. For cubic functions with zeros $r_1$, $r_2$, and $r_3$,

1. **State the problem:** Chris sold 180 cookies and cupcakes. Cupcakes cost $0.50 each, cookies cost $0.25 each, and total sales were $66. Find how many of each were sold. 2. **Id

1. The problem is to understand what a decimal number is and how to work with it. 2. A decimal number is a number that has a whole part and a fractional part separated by a decimal

1. **Identify the variables for problem 12:** - Let $x$ be the amount invested at 5.5% interest.

1. **State the problem:** The Sears Tower's total height including the antenna is 1729 feet.

1. **State the problem:** Teerasiole is a rectangle where the length is 5 inches longer than the width. The perimeter is 34 inches. We need to find the dimensions (length and width

1. **State the problem:** Michaela's mom wants to find the number of hours at which two plumber companies charge the same total amount.

1. The problem is to find the expression for $3n+2$. 2. This is a linear algebraic expression where $n$ is a variable.

1. **State the problem:** Solve the system of equations using the addition-subtraction method: $$3x - y = 1$$

1. **Problem:** Determine whether the point (3, -2) is a solution to the system of equations: $$y = 2x - 8$$

1. **State the problem:** Runners D, E, and F ran a sprint with a combined time of 72 seconds. Runner D's time is half of E's time and one-third of F's time. We need to find how lo

1. **State the problem:** Simplify the expression $\frac{1}{x} + 2 - \frac{1}{x}$. 2. **Identify like terms:** Notice that $\frac{1}{x}$ and $-\frac{1}{x}$ are additive inverses.

1. **State the problem:** We have multiple lawn sections with given algebraic dimensions and know their areas are equal. We need to find the dimensions of each section. 2. **Identi

1. **Problem statement:** Given that $a > b$ and both $a$ and $b$ are positive numbers, prove that for any natural number $n$, the inequality $\frac{n}{a} < \frac{n}{b}$ holds. 2.

1. The problem states: If $7^m = t$, find an expression for $7^{m+3}$ in terms of $t$. 2. Recall the exponent rule: $a^{x+y} = a^x \times a^y$.

1. **State the problem:** Simplify the expression $$-\sqrt[3]{2x^{2}y^{2}} \cdot 2\sqrt[3]{15x^{5}y}$$. 2. **Recall the property of cube roots:** The product of cube roots can be c

1. The problem is to simplify the expression $6 \sqrt{13}$. 2. Recall that $\sqrt{a}$ represents the square root of $a$, and it cannot be simplified further if $a$ is not a perfect

1. **State the problem:** Simplify the expression $$\sqrt[5]{32y^{25}}$$. 2. **Recall the formula:** The fifth root of a product is the product of the fifth roots: $$\sqrt[5]{ab} =

1. The problem is to simplify the expression $14) -\sqrt{81c^{48}d^{64}}$. 2. First, note that the square root of a product is the product of the square roots: $$\sqrt{81c^{48}d^{6

1. The problem asks to write the given numbers as powers of ten. 2. Recall that any number can be written as $10^n$ where $n$ is the exponent representing how many times 10 is mult