Expert Answers to Algebra 2 Problems

The amount required to be paid today.
Given: The total amount in account after 5 years is $10000.
The rate of compound interest of ${\displaystyle 15\mathrm{\%}}$.

To find:
The number of mini-marshmallows in one serving of Swiss Miss Chocolate box using the expression ${\displaystyle 3+2\times 4÷2-3\times 7-4+47.}$

The equivalent interest rate.
Given: The nominal interest rate is ${\displaystyle 1.5\mathrm{\%}}$ per month.

The time taken to settle a debt of $705, repaid in monthly instalments of $25 at the end of each month, with interest rate of 15% compounded monthly.

${\displaystyle f\left(x\right)=100{\left(1.25\right)}^x}$
Is it true or false, the growth factor is 25%? If not, what is and what is 25%?

Write an equation for the nth term of the arithmetic sequence.

Arithmetic Sequence? Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form ${\displaystyle a_n=a+(n-1)d}$
${\displaystyle a_n=4+2^n}$

Simplify the given:
${\displaystyle (x-y)(x+y)(2x+y)}$

Simplify the expression:
${\displaystyle \frac{x^3-5x^2+3x-2}{x}+1}$

If ${\log }_2(6x+6)=5$, then x = ___

Fill the following
A base e logarithm is called a natural/common logarithm, and a base 10 logarithm is called a natural/common logarithm.

Please, write the logarithm as a ratio of common logarithms and natural logarithms.
${\displaystyle {\log }_9\left(69\right)}$
a) common logarithms
b) natural logarithms

Multiplicative Inverse of a Complex Number The multiplicative inverse of a complex number z is a complex number zm such that ${\displaystyle z\times zm=1}$. Find the multiplicative inverse of complex number.
${\displaystyle z=3-i}$

To find:
The percent of moisture in the central Sierra Nevada (a mountain range in California), to the nearest tenth that falls as snow at each altitude (a) 3000 ft (b) 4000 ft (c) 7000 ft using the model ${\displaystyle f\left(x\right)=86.3Inx-680}$, where x is altitude in feet and f(x) is the percent of moisture that falls as snow.

${\displaystyle (\frac{2}{7},-1)\text{and}9+\frac{1}{3i}}$ are zeros.
Find a polynomial function with real coefficients.

To solve:
The equation ${\displaystyle E=IZ}$ for given ${\displaystyle I=10+4i,E=88+128i}$

To find:
a) radiative force R when the carbon dioxide level is double the preindustrial amount of carbon dioxide in watts per square meter by using ${\displaystyle R=6.3In\frac{C}{C_0}}$.
b) the global temperature increase T by using ${\displaystyle T\left(R\right)=1.03R}$

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. ${\displaystyle (1,3),(2,6),(3,12),(4,24)}$
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work.
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.

To solve: The problem by modeling and solving a system of linear equations.