Expert Answers to Algebra 2 Problems

decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem. If false,provide an example,illustration,or brief explanation of why the statement is false.
Q) The system of differential equations ${\displaystyle x\prime =ty+5\left(\sin t\right)y-3e^t,y\prime =t^{2}x-7xy-1}$ is a first-order linear system of differential equations.

Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. ${\displaystyle (1,2),(2,1),(3,3),(6,1)(1,2),(2,1),(3,3),(6,1)}$.

Write the first six terms of the arithmetic sequence ${\displaystyle a_n=a_{n-1}+4,a_1=-7}$

Often new technology spreads exponentially. Between 1995 and 2005, each year the number of Internet domain hosts was 1.43 times the number of hosts in the preceding year. In 1995, the number of hosts was 8.2 million.
(a) Explain why the number of hosts is an exponential function of time. The number of hosts grows by a factor of -----? each year, this is an exponential function because the number is growing by ------? decreasing constant increasing multiples.
(b) Find a formula for the exponential function that gives the number N of hosts, in millions, as a function of the time t in years since 1995.
(c) According to this model, in what year did the number of hosts reach 49 million?

A home is valued at $236,500 in 2012. In 2017, the home is worth $305,700. Assume the homes

Replace the 880-lb force acting at point A by a force-couple system at
(a) point O
and
(b) point B.

Decide if the equation represents exponential growth or decay. Explain your answer. $y=2^x/3^x$

To write:
The radical expression using exponent ${\displaystyle y^{-\frac{5}{3}}}$

Find the slope and y intercept of the line in the given equation ${\displaystyle y=-\frac{7}{10}x-2}$

Solve for x ${\displaystyle 1200{\left(1.03\right)}^x=800{\left(1.08\right)}^x}$

The following table lists the reported number of cases of infants born in the United States with HIV in recent years because their mother was infected.
Source:
Centers for Disease Control and Prevention.
$\begin{array}{|cc|}\hline \text{Year}& \text{Cases}\\ 1995& 295\\ 1997& 166\\ 1999& 109\\ 2001& 115\\ 2003& 94\\ 2005& 107\\ 2007& 79\\ \hline\end{array}$
a) Plot the data on a graphing calculator, letting ${\displaystyle t=0}$ correspond to the year 1995.
b) Using the regression feature on your calculator, find a quadratic, a cubic, and an exponential function that models this data.
c) Plot the three functions with the data on the same coordinate axes. Which function or functions best capture the behavior of the data over the years plotted?
d) Find the number of cases predicted by all three functions for 20152015. Which of these are realistic? Explain.

Need to calculate:The factorization of the polynomial, $3x^2-2x+3x-2$.

Solve the following systems of equations by using the addition (elimination) method.
x+2y=2 and -3x-6y=-6

Use the linear factorization theorem to construct a polynomial function with the given condition.
n=3 with real coefficients, zeros = -4, 2+3i.

Determine whether the ordered pair is a solution to the given system of linear equations.
3.(-1,7) ${\displaystyle \{\begin{array}{c}4x+y=3\\ 2x-3=y\end{array}\}}$

Directions: Define 2 variables, write 2 equations, and solve the system of equations.
The North Ridgeville Football team played a game against Avon last week. A total of 125 points were scored by both teams. The teams scored a total of 22 six-point touchdowns and three-point field goals. In additon, there were 4 two-point safeties and 12 one-point kids scored. How many touchdowns and field goals were scored by the teams during the game?

Suppose that a nonhomogeneous system with 10 linear equations in 8 unknowns has a solution with 2 free variables. Is it possible to change some constants on the equations’ right hand side to make the new system inconsistent?

Use the Rational Zero Theorem to list all possible rational zeros for the function $f(x)=x^3+x^2-4x-4$.

Consider the polynomial Division $\frac{x^3+5x^2-7x-4}{x-2}$
The correct Answer is: hint the answers contains $x^2$, x, and it has a remainder.

Find the sum of the first n terms of the arithmetic sequence.$-9+(-12)+(-15)+...$ (to 10 terms) Find the sum of the first 100 terms of an arithmetic sequence with 15th term of 86 and first term of 2.