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By setting up and solving an appropriate algebraic equation.
How long will it take $700 to triple itself at 5% simple interest?

Multiply the algebraic expression using a Special Product Formula, and simplify.
${\displaystyle (5-y)(5+y)}$

Write an algebraic expression for the verbal description. The total revenue obtained by selling x units at $10.74 per unit $?

Which expression is equal to ${\displaystyle 9\times \frac{3}{2}}$?

Write an algebraic formula that models the given quantity.
The average A of two numbers a and b.

Write an algebraic expression to represent each verbal expression. Fifteen less than the cube of a number.

Andy and Ena opened separate bank accounts that earn compound interest. Andy's account can be modeled by the function ${\displaystyle f\left(x\right)=275{\left(1.06\right)}^x}$. Ena's account can be modeled by the function ${\displaystyle f\left(x\right)=115{\left(1.09\right)}^x}$. Which statement about the functions is true?
F. The beginhing balances cannot be determined, but Andy's account earns a higher annual interest rate than Ena's account.
G. The beginning balances cannot be determined, but Ena's account earns a higher annual interest rate than Andy's account.
H. Andy's account has a higher beginning balance, but Ena's account earns a higher annual interest rate of 9%.
J. Andy's account has a higher beginning balance, but Ena's account earns a higher annual interest rate of 1.09%.

(a) Find the area of the triangle having vertices A(1, 0, 1), B(0, 2, 3), and C (2, 1, 0).
(b) Use the result of part (a) to find the length of the altitude from vertex C to side AB.

For c|| ${\displaystyle n\in N\sum _{i=0}^n(4i+3)=2n^3+5n+3}$ prove

Identify a variable, write an equation and solve algebraically. Answer in a sentence. The length of a rectangular garden is 8 meters less that three times the width. If the garden's perimeter is 56 meters, what are the dimensions of the garden?

If A is ${\displaystyle 3\times 3}$ with rank ${\displaystyle A=2}$, show that the dimension of the null space of A is l.

Solve ${\displaystyle x^3+5x^2=4x+20}$ algebraically.

What is the 4th partial sum for the geometric sequence where ${\displaystyle a_1=18\text{and}r=2}$
a) ${\displaystyle S_4=-18}$
b) ${\displaystyle S_4=288}$
c) ${\displaystyle S_4=152}$
d) ${\displaystyle S_4=270}$

Simplify the algebraic expressions by combining similar terms.
${\displaystyle 5x-8x+x}$

Evaluate ${\displaystyle {\log }_{2}185}$ to four decimal places. Show algebraic processes.

Write a verbal expression for each algebraic expression.
1. 23f
2. ${\displaystyle 7^3}$

Solve the following system of equations algebraically, and check:
${\displaystyle x+2y=4}$
${\displaystyle y=2x+7}$
Answer: ${\displaystyle x=?,y=?}$

Show the work steps for finding the roots of ${\displaystyle x^4-13x^2+36}$ algebraically.