Master Algebra 1 Word Problems with our Comprehensive Practice

Ina recipe for tomato sauce, the ratio of fluid ounces of water to fluid ounc. of tomato paste is 3 : 4. You plan to make 35 fluid ounces of tomato sauce. Tow many fluid ounces of tomato paste do you need?

Need to calculate:The value of g(5) from the function $g(x)=\{\begin{array}{l}x-5ifx\le 5\\ 3xifx>5\end{array}$

f​ increased by 45 is equal to 88

Let G be a group. Show that ${\displaystyle G\ne qH\cup KG=H\cup K}$ for any two subgroups ${\displaystyle H\le GH\le G\text{and}K\le GK\le G}$.

A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio $x_1$
(in $) and the amount spent advertising in the newspaper $x_2$ (in $) according to $y=a{x}_1+b{x}_2+c$
The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.
$\begin{array}{|ccc|}\hline \text{ Advertising, }{x}_1& \text{ Advertising, }{x}_2& \text{sales, y}\\ \$2400& \$800& \$36,000\\ \$2000& \$500& \$30,000\\ \$3000& \$1000& \$44,000\\ \hline\end{array}$
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 monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

Graph the solution set for the system of linear inequalities
${\displaystyle x\ge 3}$
${\displaystyle y\ge -1}$

Given linear equation y = 0.5x – 2
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.

Given linear equation y = -0.75x-5
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z, cannot contain an equation in the form y = mx + b.

n(n - 4) = 7

$(2\sin \alpha +3\cos \alpha {)}^2+(3\sin \alpha -2\cos \alpha {)}^2=13$

An outdoor furniture manufacturer has fixed costs of $14,000 per month and average variable costs of $12.75 per units manufactured. The company has $110,000 available to cover the monthly costs. How many units can the company manufacture? (Fixed costs are those that occur regardless of the level of production. Variable costs depend on the level of production.)

Solve the equations and inequalities. ${\displaystyle a.a^2+12a+36=0}$
${\displaystyle b.a^2+12a+36<0}$
${\displaystyle c.a^2+12a+36\le 0}$
${\displaystyle d.a^2+12a+36>0}$
${\displaystyle e.a^2+12a+36\ge 0}$

Express each of the following pairs of signed numbers as absolute values and subtract the smaller absolute value from the larger absolute value.
c.-6,+6

Identify each value is equivalent to ${\displaystyle \frac{1}{2}}$.
A. Absolute value of -2.
B. Absolute value of ${\displaystyle \frac{1}{4}}$.
C. Absolute value of ${\displaystyle \frac{1}{2}}$.
D. Absolute value of 2.
E. Absolute value of ${\displaystyle -\frac{1}{2}}$.

Reduce the system of linear equations to upper triangular form and
$2x+3y=5$
Solve
$-y=-2+\frac{2}{3}x$

Consider the function ${\displaystyle f\left(x\right)=x^4-72x^2+9,-5\le x\le 13}$.
This function has an absolute minimum value =?
and an absolute maximum value =?

Graph the solution set for the of linear inequalities
${\displaystyle y<\frac{1}{3}x+1}$
${\displaystyle y\ge \frac{1}{3}x-2}$