Master Algebra 1 Word Problems with our Comprehensive Practice

We to explain the procedure to find $\frac{d{}_{}{}_{}{}^{2}y}{d{x}^2}$ (second order derivative) of any function $y=f(x)$.

How many times does 9 occur between 1 to 100

If 15 is rounded off to the nearest tens, we will round the number ___ to the nearest tens to get ____.

Every real number falls into one of two categories: rational or irrational. True or False

What is the cosine inverse of $0$?

Use inductive reasoning to predict the next line in this sequence of computations. Then use a calculator or pertorm the arithmetic by hand to determine whether your conjecture is correct.
$$\begin{gathered} 6\cdot <!--\; \cdot \; -->3+2=20 \\ 66\cdot <!--\; \cdot \; -->3+2=200 \\ 666\cdot <!--\; \cdot \; -->3+2=2000 \\ 6666\cdot <!--\; \cdot \; -->3+2=20000 \end{gathered}$$
Make a conjecture by predicting the correct numbers in the line below
$(?)\cdot <!--\; \cdot \; -->3+2=(?)$
Is the conjecture correct?
Yes or No

Is it true that f(n)=O(g(n)) implies g(n)=O(f(n))

BPM interacts through the ________ layer.
A data access
B presentation
C both of options
D none of the above

A plastic ball has radius 12.0 cm and floats in water with 24.0 % of its volume submerged.
What force must you apply to the ball to hold it at rest totally below the surface of the water?

To solve a system of equations, you need use substitution. $y=3x-<!--\; -\; -->2,y=2x-<!--\; -\; -->5$

How to find period of a real function f given the functional equation $\sqrt{3}f(x)=f(x-<!--\; -\; -->1)+f(x+1)$?
If a periodic function satisfies the equation $\sqrt{3}f(x)=f(x-<!--\; -\; -->1)+f(x+1)$ for all real x then prove that fundamental period of the function is 12.
Here fundamental period means the smallest positive real for which function repeats its value for all x.
I tried replacing x by $x\pm <!--\; \pm \; -->1$ then try to find f(x) in terms of other but always end up with it in terms of sum of other two arguments in the function eg $f(x+2)$ etc.
Please provide a general method and also especially do give the thought process or reasoning for all the steps ie why you are doing these particular steps or what led you to thinking that doing these steps would give you the period of f.

How do you find the general form of an equation?

A spinner is divided into 5 sections of equal size. You spin it 4 times, with the following results: 1, 5, 3, 2. Which of the following is Talse?
a The theoretical probability of a 1 is 20%.
b The expernimental probability of a 2 is 25%.
c. If you spin the spinner again and get different results, the theoretical probability will change.
d. All of the above are true

Which statement is true for the function $f(x)=\ln <!--\; \; -->(\tan <!--\; \; -->x)$ on the openinterval $\mathrm{\pi <!--\; \pi \; -->}<x<\frac{5\mathrm{\pi <!--\; \pi \; -->}}{4}$?
a. f(x) is increasing at an increasing rate.
b. f(x) is increasing at a decreasing rate.
c. f(x) has a point of symmetry in the open interval.
d. f(x) has an absolute maximum in the open interval
e. f(x) has a point of inflection in the open interval.

It is function is odd function?
$y=2x^3-<!--\; -\; -->3x^2$

The value of 5! is _____

$y=2x-<!--\; -\; -->5$ linear on nonlinear and why

$\sqrt{2}+\sqrt{3}$ over Q, find min polynomial

Solving $-<!--\; -\; -->1/3(x-15)=-4$, what is the correct sequence of operations?
1. Multiply each side by -1/3, subtract 15 from each side
2. Multiply each side by −3, add 15 to each side
3. Multiply each side by -1/3 , add 15 to each side
4. Multiply each side by 3, subtract 15 from each side

Find the exact value of the real number y if it exists. Do not use a calculator.
$y=\arccos <!--\; \; -->(\frac{\sqrt{2}}{2})$

Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. $y=\arccos <!--\; \; -->(\frac{\sqrt{2}}{2})$
B. $\arccos <!--\; \; -->(\frac{\sqrt{2}}{2})$ does not exist