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

1) Evaluate the function at the indicated values.
$g(t)=\frac{t+6}{t-<!--\; -\; -->6};g(-<!--\; -\; -->6),g(6),g(0),g(a),g(a^2-<!--\; -\; -->6),g(a+1)$
$$\begin{gathered} g(-<!--\; -\; -->6)=? \\ g(6)=? \\ g(0)=? \\ g(a)=? \\ g(a^2-<!--\; -\; -->6)=? \\ g(a+1)=? \end{gathered}$$
2) Evaluate the piecewise defined function at the indicated values.
$$\begin{gathered} f(-<!--\; -\; -->3)=? \\ f(-<!--\; -\; -->2)=? \\ f(0)=? \\ f(2)=? \\ f(3)=? \end{gathered}$$

Find at least three ordered pairs that satisfy the following equation and graph the line through them.
$3x+5y=12$

Compute the sum $\underset{k=1}{\overset{10000}{\sum <!--\; \sum \; -->}}\frac{1}{k}$ and $\underset{k=1}{\overset{100000}{\sum <!--\; \sum \; -->}}\frac{1}{k}$. Are there any differences?
Compute the sum $\underset{k=1}{\overset{100000}{\sum <!--\; \sum \; -->}}\frac{1}{k^2}$ and $\underset{k=1}{\overset{1000000}{\sum <!--\; \sum \; -->}}\frac{1}{k^2}$. Are there any differences?

The Sugar Sweet Company is going to transport its sugar to market. It will cost $7500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 17 tons of sugar.
Equation ________
total cost to transport 17 tons$ _______

Negate the following statement. Also decide whether the given statement or its negation is true:
For all $x,y\in <!--\; \in \; -->R$ such that $xy\ne <!--\; \ne \; -->0$ we have that
$\frac{1}{x}+\frac{1}{y}=\frac{1}{x+y}$

what is the value of (9/4)^-1/2

Solve the inequality and graph the solution:
$\frac{4}{5}x-<!--\; -\; -->1<\frac{5}{6}x+2$

State the degree of the given polynomia: $7x^8-<!--\; -\; -->8x^7-<!--\; -\; -->4x-<!--\; -\; -->4$

A knitting shop orders yarn from three suppliers in​ Toronto, Montreal, and Ottawa. One month the shop ordeblack a total of 103 units of yarn from these suppliers. The delivery costs were ​$80​,​$54​, and ​$60 per unit for the orders from​ Toronto, Montreal, and​ Ottawa, respectively, with total delivery costs of ​$6330. The shop ordeblack the same amount from Toronto and Ottawa. How many units were ordeblack from each​ supplier? (Hint:​ "The shop ordeblack the same amount from Toronto and​ Ottawa." After getting an equation that describes this​ relationship, get all the variables to the same side of the​ equation.)
___ units ordeblack from Toronto
___ units ordeblack from Montreal
___ units ordeblack from Ottawa

Solve the inequality.
$x^4(x-<!--\; -\; -->3)\le <!--\; \le \; -->0$

$\mathrm{△<!--\; △\; -->}X=V_{0}T+1/2a{T}^2$
$-<!--\; -\; -->45m=10m/sT-<!--\; -\; -->4.90m/s^2{T}^2$

Find the sample variance and standard deviation. 20, 16​, 2​, 7​, 12

In country​ A, about six times as many cars are manufactured per day than in country B. If the total number of these cars manufactured per day is 46,242 find the number manufactured in country B and the number manufactured in country A.
In country​ A ? cars are manufactured per day
In country​ B ? cars are manufactured per day.

A function of the form f (x) = mx +b is commonly called

Solve:
1) $m-<!--\; -\; -->4=2m$
2) $6.7x=5.2x+12.3$
3) $12(2w-<!--\; -\; -->3)=6w$
4) $2(4z-<!--\; -\; -->1)=3(z+2)$
5) $\frac{1}{6}d+\frac{2}{3}=\frac{1}{4}(d-<!--\; -\; -->2)$
6) $4x-<!--\; -\; -->9=3.5x-<!--\; -\; -->9$
7) $x+6+x$
8) $3x+15=3(x+5)$
9) $5x-<!--\; -\; -->7=4x-<!--\; -\; -->1$
10) $5.5-<!--\; -\; -->x+-<!--\; -\; -->4.5-<!--\; -\; -->x$
11) $-<!--\; -\; -->3(2x-<!--\; -\; -->3)=-<!--\; -\; -->6x+9$

Simplify the following expressions: $e^{\ln <!--\; \; -->4+\ln <!--\; \; -->5},e^{2\ln <!--\; \; -->5},{\log }_5<!--\; \; -->4+{\log }_5<!--\; \; -->60-<!--\; -\; -->{\log }_5<!--\; \; -->7$

Use the rules of exponents to simplify the expression.
$2x^2\ast <!--\; \ast \; -->5x^{-<!--\; -\; -->5}$

Help please
A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $31,100. The anticipated profit for the end of the fourth year is $74,600. The ratio of change in time to change in profit is constant. Let x be years and y be profit.

Medication is prescribed in 7 out of every 10 hospital emergency room visits that involve an injury. If a large urban hospital had 860 emergency room visits involving an injury in the past​ month, how many of these visits would you expect included a prescription for​ medication?

Suppose a certain item increased in price by 18% a total of 5 times and then decreased in price by 10% a total of 2 times. By what overall percent did the price increase?