Equations, Expressions, and Inequalities Q&A: Get Expert Help and Learn from Real-World Examples

Create a linear relationship (equation) that you would use or rely on in your field or everyday life and explain what it is and how it is used. Identify the initial condition, such as your starting weight, and the rate of change. For a linear equation, the rate of change (slope) needs to be constant.

Simplify the exponential expression.
$\frac{(6a^5{b}^6{)}^2}{(3a{b}^2{)}^3}$

Three friends are raising money through a raffle for a weekend to go a spa. The according of them got twice as much money than the first, and the third got the triple money than the second. If they gathered a total of $1440, the he turned each?

Solve the following equations: $3^x=8,e^{2x}-<!--\; -\; -->2e^x-<!--\; -\; -->5=0,\ln <!--\; \; -->(4x+1)=20$

All has $20 to spend each week and he can allocate that money between bus tickets for getting to work and the burger he eats for lunch. Burgers cost $4 each, and bus tickects are $1 each.
1. What’s the equation of the budget constraint
2. Find the slope of the budget constraint
3. Interpret the slope of the budget constraint
4 Suppose Al’s town drops the price of bus tickets by half and the price of burgers also drops by half but his weekly spending money remains the same. What’s the equation of the new budget constraint ? How is the slope of the budget constraint affected by these two changes ?

Blood contains three types of​ cells: red blood​ cells, white blood​ cells, and platelets. For approximately every 267 red blood cells in healthy​ humans, there are 86 ​platelets, and 17 white blood cells. Write the ratio of red blood cells to platelets as a fraction in simplest form.

Solve the equation. (Find only the real solutions. Enter your answers as a comma-separated list.)
$10x^2+20x+9=0$

Solve:
1) $-<!--\; -\; -->6-<!--\; -\; -->2n=-<!--\; -\; -->(1+3n)$
2) $-<!--\; -\; -->5+6(-<!--\; -\; -->3n+5)=-<!--\; -\; -->9-<!--\; -\; -->n$
3) $3(6+5n)=-<!--\; -\; -->n-<!--\; -\; -->30$
4) $10-<!--\; -\; -->x=-<!--\; -\; -->4(x-<!--\; -\; -->2)+2$
5) $4p+5(1-<!--\; -\; -->2p)=20-<!--\; -\; -->3p$
6) $15+2v=5(5v+37)$ -<!--\; -\; -->3(5a+4)=-<!--\; -\; -->6a+6$$

What is x: $\frac{0.460+2(x{)}^2(0.230-<!--\; -\; -->x)}{0.460+2(x{)}^2}$

How can i change $1-<!--\; -\; -->x^2$ to a form where it is $(x^2)$ first then one. In the form $(x^2-<!--\; -\; -->a)$? Do i just mulitply by -1 and that switches the order of the $x^2$ and 1 ?

Solve the inequality. Write your answer in interval notation and graph the solution set on a number line: $3\le <!--\; \le \; -->2x-<!--\; -\; -->15<9$

You operate a gaming website, where users must pay a small fee to log on. When you charged $4 the demand was 540 log-ons per month. When you lowered the price to $3.50, the demand increased to 810 log-ons per month.
a) Construct a linear a linear demand function for your website and hence obtain the monthly revenue R as a function of the log-on fee x.
$R(x)=?$
b) Your internet provider charges you a monthly fee of $10 to maintain your site. Express your monthly profit P as a function of the log-on fee x.
$P(x)=?$
Determine the log-on fee you should charge to obtain the largest possible monthly profit.
$x=\$?$
What is the largest possible monthly profit?
$\$?$

Solve each equation $x^{2/5}=16$

A certain recipe calls for $\frac{22}{3}$ cups of sugar, how much sugar is needed to make $\frac{1}{3}$ of the recipe?

five points for f(x)=4

Solve by using substitution method
$\{\begin{array}{l}-<!--\; -\; -->4x+y=-<!--\; -\; -->11\\ 2x-<!--\; -\; -->3y=5\end{array}$

The mailman leaves the post office and first makes a delivery to Hannah, then picks up a package from George, and finally delivers the package to Frank before returning to the post office. How far did the mailman travel? ​Hannah: 6 1/5, George: -6.2, Frank: 10/4, Post Office: -10

1) Evaluate without using a calculator.
$\sec <!--\; \; -->(-<!--\; -\; -->\frac{\mathrm{\pi <!--\; \pi \; -->}}{3})-<!--\; -\; -->\cot <!--\; \; -->(-<!--\; -\; -->\frac{5\mathrm{\pi <!--\; \pi \; -->}}{4})$
2) Evaluate without using a calculator.
$\cos <!--\; \; -->\frac{\mathrm{\pi <!--\; \pi \; -->}}{2}-<!--\; -\; -->\csc <!--\; \; -->(-<!--\; -\; -->\frac{\mathrm{\pi <!--\; \pi \; -->}}{2})$
3) Simplify the expression:
$\tan <!--\; \; -->\mathrm{\beta <!--\; \beta \; -->}\cot <!--\; \; -->\mathrm{\beta <!--\; \beta \; -->}$
4) Evaluate without using a calculator.
${\sin }^2<!--\; \; -->{20}^{\circ <!--\; \circ \; -->}+\frac{1}{{\sec }^2<!--\; \; -->{20}^{\circ <!--\; \circ \; -->}}$
5) Evaluate without using a calculator.
$\frac{\sin <!--\; \; -->(-<!--\; -\; -->{40}^{\circ <!--\; \circ \; -->})}{\cos <!--\; \; -->{50}^{\circ <!--\; \circ \; -->}}$
6) Evaluate without using a calculator.
$\sin <!--\; \; -->{400}^{\circ <!--\; \circ \; -->}\sec <!--\; \; -->(-<!--\; -\; -->{50}^{\circ <!--\; \circ \; -->})$
7) Find the exact value of all remaining trig functions
$\sin <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=\frac{4}{5},\mathrm{\theta <!--\; \theta \; -->}$ is acute

the base of an isosceles triangle is 2mm more than one third the length of the equal sides. if the perimeter is 6mm, find the length of each side

Use Addition Method:
2x - 3y = -13
5x - 12 y = -46