Master Algebra 1 Word Problems with our Comprehensive Practice

Q: Let ${\displaystyle \{\begin{array}{cc}{x}^m\sin \frac{1}{x};& x\ne 0\\ 0;& x=0\end{array}}$
Find the set of values of m for which
(i) ${\displaystyle f\left(x\right)}$ is continuous at ${\displaystyle x=0}$
(ii) ${\displaystyle f\left(x\right)}$ is differentiable at ${\displaystyle x=0}$
(iii) ${\displaystyle f\left(x\right)}$ is continuous but not differentiable at ${\displaystyle x=0}$.

Given the following statements:
I. The function ${\displaystyle f\left(x\right)=x^2{\sin }^{2}x}$ is an odd function.
II. The function ${\displaystyle f\left(x\right)=e^{-x}\sin x}$ is a neither function.
III. The function ${\displaystyle f\left(x\right)=\cos \left(5x\right){\sin }^{2}x}$ is an even function
IV. The function ${\displaystyle f\left(x\right)=(x-5)e^{2x}}$ is an even function.

How do you graph the inequality ${\displaystyle y<2x-1}$?

Use the point-slope formula and the given slope and point to find the linear equation in slope-intercept form.

M=1 and p=(4,3)

A: y=x-1

B: y=x-2

C: y=x+2

D: y=x+4

 

Simplify ${\displaystyle 8^{-1}}$

Sketch the graph of the following function
${\displaystyle f\left(x\right)=-5x}$
Use the graphing tool to graph the function

Clearly draw quadratics on a graph that matches the information given.
Discriminant of 6 and ${\displaystyle a=-2}$

Solve each equation by completing the square.
a) ${\displaystyle x^2+16x+45=-10}$

How can I graph ${\displaystyle y=2x-1}$ by plotting points?

Find a solution of ${\displaystyle x\frac{dy}{dx}=y^2-y}$ that passes through the indicated points.
a. ${\displaystyle (0,0)}$
b. ${\displaystyle (\frac{1}{4},\frac{1}{4})}$
c. ${\displaystyle (6,\frac{1}{8})}$

Which digit is in the ten thousands place in 782,341,693?

Explain how to find the vertex of a parabola in standard form.

How do you find the square root of 81?

A person on an assembly line produces P items per day after t days of training, 400 where ${\displaystyle P\left(t\right)=}$ How many days of training will it take for a person to ${\displaystyle 1+23e}$ produce 340 items? (Find algebraically.)

Three cousins have ages that are consecutive integers. The product of the two older cousins

You had $10,000 to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression ${\displaystyle 0.05x+0.12(10,000-x)}$.
a. Simplify the algebraic expression.
b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested $6000 in the safe, government-insured certificate of deposit.

Solve the equation algebraically. Verify your results using a graphing utility.
${\displaystyle x(1+2x)=(2x-1)(x-2)}$

Solve the following equation algebraically. Round to 2 decimal places. Show all work.
${\displaystyle 5e^{x+2}-8=14}$

A community college offers courses in Applied Algebra, Business Calculus, and Statistics. Each section of Applied Algebra has 50 students and earns the college $20,000 in revenue. Each section of Business Calculus has 20 students and earns the college $50,000 in revenue. Each section of Statistics has 30 students and earns the college $60.000 in revenue. Assuming the college wishes to offer a total of 7 sections, accommodate 230 students, and bring in $320,000 in revenue, how many sections of each course should they offer?
? sections of Applied Algebra
? sections of Business Calculus
? sections of Statistics

Find the value of the given expressions
a) ${\displaystyle {(2+3)}^2;}$
${\displaystyle 2^2+3^2}$
b) ${\displaystyle {(8+10)}^2;}$
${\displaystyle 8^2+{10}^2}$
c) Check whether the given statement is true or false:
${\displaystyle Thegiven\exp ressionsarePSK{(a+b)}^2=a^2+b^2}$