🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{20} = \sqrt{9\%}.$$\n\n2. **Understand the components:** The percentage $9\%$ means $\frac{9}{100} = 0.09$.\n\n3.

1. The problem asks to write an equation for the function graphed above, which is a parabola. 2. The general form of a parabola's equation is $$y = a(x - h)^2 + k$$ where $(h,k)$ i

1. **State the problem:** Simplify and evaluate the expression $$\frac{u^{\frac{2}{3} + 1}}{4^{\frac{5}{3}}} - \frac{4^{\frac{5}{3}}}{u^{\frac{2}{3} + 1}}$$. 2. **Rewrite exponents

1. The problem asks: How many zeros does the graphed polynomial function have? 2. Recall that zeros of a polynomial function are the x-values where the graph crosses or touches the

1. The problem asks for the number of zeros of the polynomial function $$y = (x - 8)(x + 3)^2$$. 2. The zeros of a polynomial are the values of $x$ that make $y=0$.

1. **State the problem:** We are given data points of engine speeds $x$ (in hundreds of RPMs) and corresponding average speeds $y$ (in miles per hour) of a pontoon boat. We want to

1. The problem asks to find a recursive formula for the sequence defined explicitly by $$a_n = 10(-4)^{n-1}$$ that depends on the previous term $$a_{n-1}$$. 2. Recall that a recurs

1. The problem is to understand the given 2x3 matrix: $$\begin{bmatrix} 12x^3 - 2 & 4 \\ 6x - 5 & 2 \end{bmatrix}$$

1. The problem states: "Twenty-nine is equal to the difference between two and one fourth of a number." We need to translate this sentence into an equation. 2. Let the number be re

1. **State the problem:** Michael has 1067.13 in his checking account. He plans to spend 510.71 on a television and the rest on speakers costing 46.00 each. We want to find the ine

1. **State the problem:** We need to graph the function $$y=\frac{7}{8}x^3$$ and plot five points: one at $$x=0$$, two with negative $$x$$ values, and two with positive $$x$$ value

1. **State the problem:** We are given the function $y = \frac{7}{8}x^3$ and want to understand its shape and behavior. 2. **Formula and rules:** This is a cubic function of the fo

1. **State the problem:** Calculate the product of the fractions $\frac{28}{1}$ and $\frac{11}{14}$. 2. **Write the formula:** The product of two fractions $\frac{a}{b}$ and $\frac

1. The problem states there is a proportional relationship between the size of Zane's garden $x$ (in square feet) and the number of carrots $y$ he can grow. 2. A proportional relat

1. **State the problem:** Isaiah and his friends are sailing, and the distance from shore $y$ (in miles) is proportional to the time $x$ (in hours) they spend sailing.

1. The problem states there is a proportional relationship between the age of Brenna's apple tree $x$ (in years) and its height $y$ (in feet). 2. In a proportional relationship, th

1. The problem states there is a proportional relationship between yards ($x$) and feet ($y$), meaning $y = kx$ where $k$ is the constant of proportionality. 2. From the graph, we

1. The problem involves identifying the equations of lines from given points and matching them to graphs. 2. Given points: (4,0), (8,-5), (12,-10), (16,-15).

1. The problem states there is a proportional relationship between the number of days Tanvi is stranded on the island, $x$, and the total number of trees she cuts down, $y$. 2. A p

1. **State the problem:** Add the two polynomials $ (5s + 8) $ and $ (4s^2 + 7s + 6) $. 2. **Recall the rule:** To add polynomials, combine like terms, which are terms with the sam

1. **Stating the problem:** We want to find a function with a lesser rate of change (slope) than the function $y = -\frac{5}{4}x + 5$.