Master Algebra 1 Word Problems with our Comprehensive Practice

Write a quadratic equation with the given solutions. -1 and -6

A coffee merchant sells three blends of coffee. A bag of houseblend contains 300 grams of Colombian beans, 50 grams of Kenyanbeans, and 150 grams of French roast beans. A bag of specialblend contains 200 grams of Colombian beans, 200 grams of Kenyanbeans, and 100 grams of French roast beans. A bag of Gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyanbeans and 50 grams of French roast beans. Merchant has on hand 30kg of Colombian beans, 15 kg of Kenyan beans and 15 kg of French roast beans. One bag of the house blend produces profit of $0.50 , onebag of the Special blend produces a profit of $1.50, and one bag ofthe gourmet blend produces a profit of $2.00. How many bags of eachtype should the merchant prepare if he wants to use up all of thebeans and maximize his profit? What is the maximum profit?

${\displaystyle \frac{3}{2x+3}-1(2x-3)=\frac{4}{4x^2-9}}$

Find the value of x that satisfies the inequality.
${\displaystyle \left|\frac{x-1}{2}\right|\le 1}$

Write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3

1. The graph of a linear equation in two variables is a _____________________line.
2. The general form of linear equation in two variables is _______________________.
3. Linear equations in three variables are expressed as _________________________.
4. The number of variables in is __________________________.
5. The solution of a linear equation always ________________________ the equation.

Looking around in your own country, discuss one practical application in which “piecewise functions” are used either explicitly or implicitly.
Example to be used- A paid parking lot based on length of time stayed, up to half an hour cost $1, over half an hour up to an hour cost $2.50 and over an hour and up to 15 hours cost $20.

Radical and Exponents Simplify the expression $(\frac{a{b}^2{c}^{-3}}{2a^3{b}^{-4}}{)}^{-2}$

Graph the solution set of each system if inequalities.
X is greater than or = 0
X+Y is less than or equal to 4
2x+y is less than or equal to 5

Determine whether the orderred pair is a solution to the system of inequlities
x+y<4
${\displaystyle y\le 2x+1}$
a. (0,1)
b. (3,1)
c. (2,0)
d. (1,4)

Linear equations of first order.
Solve the initial-value problem on the specified interval $y^{\prime }+y\tan x=\sin 2xon(-\frac{1}{2}\pi ,\frac{1}{2}\pi )\text{with}y=2\text{when}x=0$.

Solve the quadratic by using the quadratic formula $x^2=7x+9$

Graphing systems of linear equations
find the solution for the following equations by graphing.
${\displaystyle Y=6-\frac{2}{3x}}$
${\displaystyle Y=x+1}$

The number of units N of a finished product produced by a particular automobile company where x units of labor and y units of capital are used is approximated by ${\displaystyle N=50x^{\frac{1}{2}}{y}^{\frac{1}{2}}}$
Estimate how many units will be produced using 256 units of labour and 144 units of capital.

Describe a sequence of translations that can be used to show that Figures A and A

${\displaystyle 310=3x^2-x}$

A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each. One day they sold 6 more squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many pumpkins and quash they sold?

Write a definition of Piecewise-Defined functions

Show that the inverse of any linear function $f(x)=mx+b$, where $m\ne 0$, is also a linear function. Give the slope and y-intercept of the graph of f-1 in terms ofm and b.