Boost Your Math Skills with our Equations and Inequalities Practice Problems

Use the point-slope formula and the given slope and point to find the linear equation in slope-intercept form.

M=1 and p=(4,3)

A: y=x-1

B: y=x-2

C: y=x+2

D: y=x+4

Find the equation for the plane tangent to each surface $z=f(x,y)$ at the indicated point.
${\displaystyle \left(a\right)z=x^3+y^3-2xy,\text{at the point}(1,2,-5)}$
${\displaystyle \left(b\right)z=\left(\cos \left(x\right)\right)\left(\cos \left(y\right)\right),\text{at the point}(0,\frac{\pi }{2},0)}$
${\displaystyle \left(c\right)z=\left(\cos \left(x\right)\right)\left(\sin \left(y\right)\right),\text{at the point}(0,\frac{\pi }{2},1)}$

Prove that ${\displaystyle |\left|x\right|-|y||\le |x-y|}$
Proof of the Triangle Inequality ${\displaystyle |x+y|\le \left|x\right|+\left|y\right|}$.
Proof of the reverse triangle inequality:
${\displaystyle |\left|x\right|-|y||\le |x-y|}$.

Choose the correct letter. Which of the following functions models exponential decay?

A. $f(x)=12\ast 3^x$

B. $y=2\ast {0.8}^x$

C. $y=-3x^2$

D. $f(x)={1.8}^x$

Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data.

$\begin{array}{|cccccc|}\hline x& 0& 1& 2& 3& 4\\ y& 10089& 578& 968& 457& 8\\ \hline\end{array}$

Complete the two-way table.

$\begin{array}{|cccc|}\hline \text{ Class }& \text{ Response }& & \\ & \text{ Yes }& \text{ No }& \text{ Total }\\ \text{ Junior }& 65& & 105\\ \text{ Senior }& & 12& \\ \text{ Total }& 116& & \\ \hline\end{array}$

Let f be the function from R to R defined by ${\displaystyle f\left(x\right)=x^2}$. Find
${\displaystyle f^{-1}\left(x\mid 0<x<1\right)}$

We're given:
Determine which of the following is greater:
$2x-y;2y-x.$

A theater as a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. 
Half as many adults attended a particular screening with full attendance as there were kids and students put together.
The receipts totaled $5600. How many children attended the show?

Show that an exponential model fits the data. Then write a recursive rule that models the data. $\begin{array}{|lllllll|}\hline n& 0& 1& 2& 3& 4& 5\\ f\left(n\right)& 2& 6& 18& 54& 162& 486\\ \hline\end{array}$

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.
$5\le 3+|2x-7|$