Algebra Word Problem Solutions

Write an exponential growth or decay function to model each situation. initial value: 50, growth factor: 1.15

Solve the given system of equations by matrix equation.
5x-4y=4
3x-2y=3

To find: The smallest positive integer that solves the congruences
${\displaystyle x\equiv 3\left(bmod7\right),x\equiv 4\left(bmod5\right)}$

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
${\displaystyle 24a^4+10a^{3}b-4a^2{b}^2}$

Solve the equation: ${\displaystyle {\log }_3(2x+1)={\log }_3\left(5x\right)+2}$.

Use the exponential growth model, $A=A_0{e}^{kt}$. In 1975, the population of Europe was 679 million. By 2015, the population had grown to 746 million.
Solve,
a. Find an exponential growth function that models the data for 1975 through 2015.
b. By which year, to the nearest year, will the European population reach 800 million?

A quadratic function is given. ${\displaystyle f\left(x\right)=x^2+2x-5}$ (a) Express the quadratic function in standard form.

The number of users on a website has grown exponentially since its launch. After 2 months, there were 300 users. After 4 months there were 30000 users. Find the exponential function that models the number of users x months after the website was launched.

State whether the equation represents exponential growth, exponential decay, or neither.
${\displaystyle f\left(x\right)=18x^2}$

Determine the equation $8b+12=52$

Decide the factorization of the polynomial $m^2+5m+mt+5t$

2y=−22 ​

What is the solution of the system of equations?
$y=2x-3$
$5x+y=11$
$A(2,1)$
$B(1,2)$
$C(3,-4)$
$D(1,-1)$

The population of a region is growing exponentially. There were 10 million people in 1980 (when $t=0$) and 75 million people in 1990. Find an exponential model for the population (in millions of people) at any time tt, in years after 1980.
P(t)=?
What population do you predict for the year 2000?
Predicted population in the year 2000 =million people. What is the doubling time?

Integers that are not whole numbers

The incomplete dot plot shows the result of a survey in which each student was asked how many dimes were in their pockets or wallets. The results for "4 dimes" are not shown. Each dot represents one student. It is known that 12.5% of the students had one dime.
a) Find the number of students surveyed. Then complete the dot plot.

Describe any similarities and differences. Refer to the end behaviour, local maximum and local minimum points, and maximum and minimum points.
a) Sketch graphs of ${\displaystyle y=\sin x}$ and ${\displaystyle y=\cos x.}$
b) Compare the graph of a periodic function to the graph of a polynomial function.

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. State the domain and range. ${\displaystyle y=x^3-3x^2,[-2,5]by[-10,10]}$

What is the level of precision for the solution to the addition problem below? Given: The numbers are 6.339m, 0.170m and 30.4m and the operation is addition.

The condition under which we may use synthetic division to divide polynomials