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

If one person can clean a house in 5 hours and second person can clean the same house in 4 hours, how long will it take to clean the house if they work together?
a) 9 hours
b) 4.5 hours
c) 22/9 hours
d) 1 hour

Simplify the expression. Which of the following is the answer as a fraction in lowest terms?
$\frac{(3/4\times <!--\; \times \; -->7/8)}{14/15}$

Solve the equation: $5x-<!--\; -\; -->2(x+3)=3(x-<!--\; -\; -->7)$

abx^2=bc

Find the number k such that the given equation has exactly one real solution $x^2-<!--\; -\; -->kx+64=0$

Estimate each quotient:
121.6 divided by 43.5
69.1 divided by 10.7
38.9 divided by 13.1
435.8 divided by 88.6
52.7 divided by 9.2
75.6 divided by 15.3

Rebecca goes to the store and spends $129 on food and $76 on non-food items.
The local sales tax rate in her town is 3% on food items and 6% on non-food items. The state sales tax rate is 3% on food items and 5% on non-food items.
What is the total cost of her purchase (including taxes)?

Find at least five ordered pairs that satisfy the following equation and graph function through them.
$y=|x-<!--\; -\; -->2|+3$

The bacteria E. coli often causes illness among people who eat the infected food. Suppose a single E. coli bacterium in a batch of ground beef begins doubling every 10 minutes.
a. How many bacteria will there be after 10, 20, 30, 40, and 50 minutes have elapsed? Assume no bacteria die.
b. Write two rules that can be used to calculate the number of bacteria in the food after any number of 10-minute periods-one using NOW and NEXT, and aother begin "y = ... ."
c. Use your rules to make a table showing the number of E. coli bacteria in the batch of ground beef at the end of each 10-minute period over 2 hours. Then describe the pattern of change in the number of bacteria from each time period to the next.
d. Find the pblackicted number of bacteria after 4, 5, and 6 hours.

The storage of a lake is $5.2\times <!--\; \times \; -->{10}^7$ liters of water. Precipitation adds $5.2\times <!--\; \times \; -->{10}^6$ liters per day and evaporation removes $5.2\times <!--\; \times \; -->{10}^6$ liters of water per day. If the net flux is zero, what is the residence time for a literof water in the take?

Suppose 24 H in a D means 24 hours in a day
find?
23 P of C in the H B......?

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 2800 pounds on Planet​ A, find the​ elephant's weight on Planet B.
The​ elephant's weight on Planet B is ?

Find the domain of the function.
$f(x)=\sqrt{5x-<!--\; -\; -->40}$
The domain is ?

So far i have $x+3\ln <!--\; \; -->10=7-<!--\; -\; -->x\ln <!--\; \; -->5e$ , does the e cancle out when I log both sides to get $\frac{1}{2}=2x-<!--\; -\; -->4$ ?
equation: ${10}^{x+3}=5e^{7-<!--\; -\; -->x}$

Given $f(x)=x^2+4$ and $g(x)=\sqrt{x-<!--\; -\; -->2}$.
a) Determine (1)$(f\circ <!--\; \circ \; -->g)x.$
b) Domain of f(x)
c) Domain of g(x)
d) Domain of $(f\circ <!--\; \circ \; -->g)x$

Solve triangle ABC.
$a=52,b=63,\mathrm{\angle <!--\; \angle \; -->}A={58}^{\circ <!--\; \circ \; -->}$
$$\begin{gathered} \mathrm{\angle <!--\; \angle \; -->}B=? \\ \mathrm{\angle <!--\; \angle \; -->}C=? \\ c=? \end{gathered}$$

Problem 1
i) Determine the (x, y) coordinates of the points of intersection for the curves described by the following equations.
$$\begin{gathered} y_1=x^2-<!--\; -\; -->4x+3 \\ {y}_2=x^2+2x+3 \end{gathered}$$
ii) Set up a definite integral to give the area of the region bounded by the two curves
iii) Evaluate the definite integral to give the area
Proble 2
Same as i, ii, iii in problem 1 above for following equations:
$$\begin{gathered} y_1=x^2 \\ {y}_2=x^3 \end{gathered}$$
Problem 3
Same as i, ii, iii in problem 1 above for following equations:
$$\begin{gathered} x=4-<!--\; -\; -->y^2 \\ x=y-<!--\; -\; -->2 \end{gathered}$$
Problem 4
Same as i, ii, iii in problem 3 above for the following equations:
$$\begin{gathered} y=x^2 \\ y=6-<!--\; -\; -->x \end{gathered}$$

$6^x-<!--\; -\; -->28\times <!--\; \times \; -->6^{-<!--\; -\; -->x}=3$

Solve the inequality and sketch solution on number line.
1. 3(4-5x which is absolute value not prentheses)less than or equal to 9.

Write the expression as the sine, cosine, or tangent of adouble angle. Then find the exact value of the expression.
${\cos }^2<!--\; \; -->15-<!--\; -\; -->{\sin }^2<!--\; \; -->15$