Expert Answers to Algebra 2 Problems

Solve for x
$2x+3=5$

A company's total cost, in millions of dollars, is given by $C(t)=120-<!--\; -\; -->80e^{-<!--\; -\; -->t}$ where t= time in years. Find the marginal cost when t=2.

You conduct a test and your p-value turns out to be 0.08. what can you conclude?

Why is the expected value $E(X^2)\ne <!--\; \ne \; -->E(X{)}^2$?

The product of two even numbers is always even.
A)True
B)False

What Does M Mean In Maths?

Identify the domain of the graph of $y=-<!--\; -\; -->x^2-<!--\; -\; -->6x-<!--\; -\; -->13$

What is two numbers that multiply to 24 but add to 25?

We need to find a solution to the logarithm $\frac{1}{2}{\log }_2<!--\; \; -->x-<!--\; -\; -->\frac{1}{{\log }_2<!--\; \; -->x}=\frac{7}{6}$

Which function has two x-intercepts, one at (0,0) and one at (4,0)?
Of(x) = x(x - 4)
O f(x) = x(x + 4)
O f(x) = (x - 4)(x-4)
Of(x) = (x + 4)(x + 4)

How do you find the cost per ounce of a mixture of 200 oz of a cologne that costs $5.50 per ounce and 500 oz of a cologne that costs $2.00 per ounce?

Write the point slope form of the equation given (-8,2) and m=-3/4

Give an example of a cubic polynomial

The smallest natural number is?

Which of the following is true regarding the solutions to the logarithmic equation below?
$2{\log }_6<!--\; \; -->(x)=2$
$$\begin{gathered} {\log }_6<!--\; \; -->(x^2)=2 \\ {x}^2=6^2 \\ {x}^2=36 \\ x=6,-<!--\; -\; -->6 \end{gathered}$$
x=6 and x=-6 are true solutions
x=6 and x=-6 are extraneous solutions
x=6 is a true solution and x=-6 is an extraneous solution
x=6 is an extraneous solution and x=-6 is a true solution

For the equations given below, which statement is true?
$$\begin{gathered} -<!--\; -\; -->3x-<!--\; -\; -->8=19 \\ -<!--\; -\; -->3x-<!--\; -\; -->2=25 \end{gathered}$$
The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation
The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation.

Show that $\frac{1}{{\log }_2<!--\; \; -->x}+\frac{1}{{\log }_3<!--\; \; -->x}+\cdots <!--\; \cdots \; -->+\frac{1}{{\log }_{43}<!--\; \; -->x}=\frac{1}{{\log }_{43!}<!--\; \; -->x}$.I am just not able to get it.please help.

Converting a polynomial ring to a numerical ring (transport of structure)
One may be curious why one wishes to convert a polynomial ring to a numerical ring. But as one of the most natural number system is integers, and many properties of rings can be easily understood in parallel to ring of integers, I think converting a polynomial ring to a numerical (i.e. integer) ring is useful.
What I mean by converting to a numerical ring is: in the standard ring of integers, + and ⋅ are defined as in usual arithmetic. But is there universal way of converting any polynomial/monomial rings such that each object in the ring gets converted to an integer, and + and ⋅ can be defined differently from standard integer + and ⋅? This definition would be based on integer arithmetic, though.

Modular operation on polynomial rings
I originally started modular arithmetic by the following:
1mod2
1/2 is 0.5
0 times 2 is 0
$1-<!--\; -\; -->0=1$
1 equals 1mod2.
Is it the same way to compute a quotient of a polynomial ring such as ${\displaystyle \frac{\mathbb{C}[x_1,\dots <!--\; \dots \; -->,x_n]}{x^2+y^2-<!--\; -\; -->z^2}}$
$x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+xmod{x}^2+y^2-<!--\; -\; -->z^2$
${\displaystyle \frac{x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+x}{x^2+y^2-<!--\; -\; -->z^2}}$
${\displaystyle \frac{(x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+x)\times <!--\; \times \; -->(x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+x)}{(x^2+y^2-<!--\; -\; -->z^2)}}$
$x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+x-<!--\; -\; -->{\displaystyle \frac{(x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+x)\times <!--\; \times \; -->(x^3+2x{y}^2-<!--\; -\; -->2x{z}^2+x)}{x^2+y^2-<!--\; -\; -->z^2}}$

Solve x in logarithm equation
I am trying to solve $x$ for $2lo{g}_{10}(x-<!--\; -\; -->4)-<!--\; -\; -->lo{g}_{10}4(x-<!--\; -\; -->1)=0$
I have the key with the answer 10 and have confirmed this is correct using Wolfram Alpha but which steps should I take to reach that answer?