If a line has slope -3/7, find the equation in slope-intercept form of the line perpendicular to it that passes through the point (7, -1).

A small greenhouse's temperature increases linearly over four days. At day 2 the temperature was 14°C and at day 6 it was 26°C. (i) Compute the slope (rate of temperature change per day). (ii) Write the temperature in point-slope form using the day-2 data, and (iii) convert to slope-intercept form.

Given the system of constraints $x\ge 0$, $y\ge 0$, $x+2y\le 8$ and $y\ge x-1$, determine whether the point $(3,2)$ is in the feasible region that satisfies all constraints.

Find the domain of $y=\sqrt{\frac{x+1}{x-2}}$. Express your answer in interval notation.

A linear function $f$ is known to satisfy $f\left(1\right)=3$ and $f\left(3\right)=7$. Find the constants $a$ and $b$ so that $f\left(x\right)=ax+b$.

Let $f\left(x\right)=\frac{1}{x-2}$ and $g\left(x\right)=\sqrt{x}$. Find the domain of $(f\circ g)\left(x\right)$ expressed in interval notation.

Solve the system using substitution: { y = (3/4)x - 2 ; (1/2)x + (3/2)y = 6 }

Use elimination to solve the system 5x + 2y = 13 and 8x − 7y = −6 by multiplying each equation by the other's x-coefficient. What is the final solution?

A company makes two products: $A$ and $B$. Each product $A$ gives \(30 in profit and uses 2 hours of labor; each product $B$ gives \)50 in profit and uses 3 hours of labor. The weekly labor available is at most 60 hours per week. They must make at least 5 units of product $A$. There is no minimum for $B$. Set up a system of inequalities and determine which corner of the feasible region (integer or fractional that is allowed) that will maximizes the profit: $P=30A+50B$. Show all calculations.

Simplify ${\left(ab\right)}^2\times a^3\times b^{-1}$ and express the result as 'a single power of $a$' multiplied by 'a single power of $b$'.

Simplify symbolically $\frac{p^{2n+3}}{p^{n+1}}$. Express your answer in terms of $n$.

Simplify ${\left(2a^3{b}^2\right)}^2\cdot a^{4}b$.

Given the equation $(\frac{2x}{5y}{)}^3=\frac{16}{125}$ with $x$ and $y$ nonzero, find $\frac{x}{y}$.

Simplify the rational expression $\frac{3x^{-2}{y}^3}{x^{-5}{y}^{-1}}$ and express your answer with only positive exponents.

Simplify $(4a^{-2}{)}^2\cdot (3a^5)$.

Determine the degree of the polynomial $P(x,y)=x^4+2x^2{y}^3+y^6$ and justify how you found it.

Simplify $(4x^2+6x)+(-x^2+2x)$ and factor the result by pulling out the greatest common factor.

Multiply and simplify: (2x² + 3x - 1)(x² - x + 2). Provide the simplified quartic polynomial.

Factor the trinomial $16x^2-24x+9$ completely.