Algebra Word Problem Solutions

When writing a system of equations or inequalities from a situation, how do you know that you have possibly written the system correctly?

What is the square root of -98?

To simplify:
The given expression ${\displaystyle \left(2\sqrt{a}\right)\left(\sqrt{3}\left\{a^2\right\}\right)}$

Last Saturday, 1,750 people attended an event at Farway Gardens. The admission fee was $3.50 for children and $8.00 for adults. If the total amount of money collected at the event was $9,860, how many children and how many adults attended the event?

Condense them to the same base before solving for x ${\displaystyle \log 16\left(x\right)+\log 4\left(x\right)+\log 2\left(x\right)=7}$

If $y=(x+3{)}^2$, then $(-2x-6{)}^2$ must equal which of the following?

Use your results to write the complete factorization of f(x). Function ${\displaystyle f\left(x\right)=2x^3-x^2-10x+5}$ Factors ${\displaystyle (2x-1),(x+\sqrt{5})}$

Lisa spends 3 hours driving to and from work each work day. What percent of her day does she spend driving to and from work, each work day?

How do i get the equation ${\displaystyle x²-16x-8y+80=0}$ into a standard parabolic equation?

Write the equation in point-slope form of the line that passes through the given point with the given slope.
(3,1), m=2

${\displaystyle 7x^2-24x+9=0}$

Simplify the rational expression: ${\displaystyle 8\frac{x}{6y}}$

At a price of $3.20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2.95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. Find a price–supply equation of the form p = mx + b. p is in dollars, and x is in million bushels.

${\displaystyle \log (x+5)-\log (x-3)=\log 2}$

The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer $x_1$ (in $1000) and on the square footage of the home $x_2(\text{ in }100f{t}^2)$ according to $y=a{x}_1+b{x}_2+c$
The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a) Use the data to write a system of linear equations to solve for a, b, and c.
b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.
c) Write the model $y=a{x}_1+b{x}_2+c$
d) Predict the purchase price for a buyer who makes $100000 per year and wants a $2500f{t}^2$ home.

Solve the Numercial Method Explain how Newton`s interpolation formula better tha the Lagrange formula

Show all steps to solve the system of equations:
y = 2x + 3
2x + 4y = -8

Solve the following linear and quadratic systems of equations:
$y+3x=-2or3x+2=y$
$y=x^2$
a. Show all work in solving your system of equations algebraically.
b. Graph your system of equations and show the solution graphically to verify your solution.

Find the exact value of each of the following.
$\cos {195}^{\circ }$

A nut wholesaler sells a mix of peanuts and cashews.
The wholesaler charges $2.80 per pound for peanuts and $5.30 per pound for cashews.
The mix is to sell for $3.30 per pound.
How many pounds of peanuts and how many pounds of cashews should be used to make 100 pounds of the mix?