🧮 algebra

1. **State the problem:** Solve the linear equation $$-9 = \frac{2}{7}x + 5$$ for $x$. 2. **Isolate the term with $x$:** Subtract 5 from both sides to get

1. The problem asks to determine the vertex of a parabola given its graph. 2. The vertex of a parabola in the form $y = ax^2 + bx + c$ is given by the formula for the x-coordinate:

1. **State the problem:** A family spends 15 per person for zoo tickets and 5.50 for parking each day. They visit for two days, and the total cost is 191. We need to find the numbe

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 3 to eliminate the d

1. **Problem:** Solve the proportion $$\frac{3}{8} = \frac{15}{x}$$ 2. **Formula:** Cross multiply to solve proportions: $$a/b = c/d \implies ad = bc$$

1. **State the problem:** A town has a population of 7000 and grows at 4% every year. We need to find the population after 13 years, rounded to the nearest whole number. 2. **Formu

1. **State the problem:** Sarah says, "If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35." We need to write an equation based on t

1. The problem is to simplify the expression where all "x" symbols represent multiplication. 2. Since "x" means multiplication, replace all "x" with the multiplication operator \(\

1. **State the problem:** Simplify the expression using exponent laws. The expression appears to be \(\frac{4a^1 g h x - 3^{2} 2^{2} 2}{6^{9} 2^{h} 2} \times x g h x\). 2. **Rewrit

1. **State the problem:** We have a function represented by a table with Speed (mi/hr) as the independent variable and Stopping Distance (ft) as the dependent variable. We need to

1. **State the problem:** We want to find the value of a car after 5 years, given it depreciates at 5.75% per year from an initial value of 16500.

1. **State the problem:** An element with an initial mass of 670 grams decays by 21.8% per minute. We want to find how much of the element remains after 15 minutes, rounded to the

1. **State the problem:** Solve the inequality $$99 - b < 8$$ for $b$. 2. **Isolate the variable $b$:** To solve for $b$, we want to get $b$ alone on one side of the inequality.

1. **State the problem:** Solve the inequality $$82 \geq 21 - t$$ for the variable $t$. 2. **Understand the inequality:** The symbol $\geq$ means "greater than or equal to." We wan

1. **State the problem:** We need to find which expression is equivalent to $38(251m - 45)$. 2. **Use the distributive property:** The distributive property states that $a(b - c) =

1. **State the problem:** We need to find which expression is NOT equivalent to $$\frac{1}{2} \cdot (x - 6)$$. 2. **Recall the distributive property:** $$a(b - c) = ab - ac$$.

1. The problem asks to identify which two values correspond to the points shown on the number line between 0 and 1. 2. The number line shows two points: one exactly at $\frac{1}{2}

1. The problem involves understanding the expression $x_i \frac{\left|x\right|}{ }$, which appears incomplete as the denominator is missing. 2. Typically, expressions like $x_i \fr

1. **State the problem:** Find the vertex, y-intercept, and x-intercepts of the quadratic function $$y = 4x^2 - 8x - 5$$. 2. **Rewrite the quadratic in vertex form:**

1. The problem states that line e has a slope of $-\frac{34}{43}$ and line f is perpendicular to line e. We need to find the slope of line f. 2. Recall the rule for slopes of perpe

1. **State the problem:** We are given two lines, line c with slope $\frac{85}{82}$ and line d with slope $-\frac{82}{85}$. We need to determine if these lines are parallel, perpen