Simplify 1024/384 efficiently by recognizing powers of two. What is the simplified fraction?

Simplify 12² × 12³ by combining like bases using exponent rules and compute the numerical result.

A projectile's height is modeled by h(t) = -16t² + vt + s. If v = 64 ft/s and s = 5 ft, compute the height h(2). Use the appropriate mathematical methods.

A traveler has b dollars. They spend 120 dollars on a hotel and then use one-third of the remaining money for food. Represent the amount spent on food as an algebraic expression in terms of b.

Translate the sentence and solve the resulting quadratic: "The product of a number and the difference of seven and that number is ten."

Which of the following statements correctly explains why the equation: $a(b-c)=ab-ac$ is written in terms of treating subtraction as an addition of a negative?

Distribute and simplify this expression with fractions: (1/2)(4x - 6) - (1/3)(3x + 9).

Solve for $x$: $\frac{2}{5}x-\frac{3}{4}=\frac{1}{10}x+\frac{7}{8}$

Solve the inequality $\frac{1}{2}x-3>\frac{x}{4}+1$.

Solve the compound inequality $\{\begin{array}{c}2x+1>5\\ 3-x\ge 1\end{array}$.

Solve $\mid x+1\mid =\mid 2x-3\mid$.

Solve the compound inequality and express your answer in interval notation.

Given the equations: $p=q+4$, $r=2q-1$, and $p+r=50$. Solve for the exact values of: $q$, $p$, and $r$.

Given the formula for compound interest A = P(1 + r/n)^nt, isolate r symbolically (write r in terms of A, P, n, and t).

A jacket priced at $\$250$ is discounted by $30\%$. A $7\%$ sales tax is then applied to the discounted price. What is the final price?

Which of these setups is correct for: "Make V liters of a p% solution by mixing solutions with concentrations of a% and b%, where a < p < b"? Let x be the number of liters of a% solution.

Which of the following single choices correctly lists all the ordered pairs from the set {(5,0), (8,2), (-3,4), (2,1)} that satisfy x + 2y = 5? Use substitution reasoning for each candidate.

Given two points observed on a graph, $(2,-1)$ and $(5,8)$, derive the equation of the line in standard form $ax+by=c$ with integer coefficients.

Given intercepts (8, 0) and (0, 2), which of the following standard-form linear equations is correct for the line through those intercepts?

A wheelchair ramp must rise 2 feet for every 12 feet horizontally to meet a building entrance. Starting from ground-level point (0,0), write the slope and find the coordinates of the point at the top of a 36-foot section of ramp, then state the slope-intercept equation of the ramp line.