Rational Reasoning
Identify the excluded value(s):
(x-4)/((x+3)(x-4))
x = -3 and x = 4
Simplify so the radical contains the smallest integer possible.
sqrt(243)
9sqrt(3)
Is the following sequence geometric, or arithmetic, or neither?
2, 4, 6, 8, 10, 12, ...
Arithmetic
If my bank account grows by 3% in a year, what value should I multiply my starting amount of money by to represent that growth?
1.03
Solve for x:
log_3 81 = x
x=4
Simplify the expression.
(n+8)/(n^2+3n-40)
1/(n-5)
Convert to radical form and simplify:
4^(3/2)
8
Construct an explicit formula for the following sequence:
1, 3, 9, 27, 81, ...
a_n=3^(n-1)
Solve for x:
4^x=8^(x-2)
x=6
Solve for x, round to the nearest ten-thousands place (3 decimal places).
10^x+5=30
x=1.398
Simplify the expression:
(9n^2-90n)/(n+10)*(n+10)/(9n)
n-10
Solve for x:
-6=sqrt(24-2x)-8
x=-10
Find the 5th term of the following sequence:
a_n=3a_(n-1)+4; a_1=1
241
Solve for r:
36^(r-2)*216^(3r)=216
r=7/11
Expand the log out fully so that every log contains only a single variable.
log((5x^3sqrt(y))/(z^2))
log(5)+3log(x)+1/2log(y)-2log(z)
Simplify the expression:
5/(n+2)-(6n)/(5n+5)
(6n^2+13n+25)/(5(n+1)(n+2))
Simplify:
2n^-2*n^(-5/4)*2n^(-1/3)
(4n^(5/12))/n^4
Given the following terms, construct an explicit formula for the sequence.
a_6=30, a_7=41, a_8 = 52
a_n=-25+11(n-1)
A company releases a new smartphone model every month. Each model's battery life will be 6% longer than the previous model's. If the current model's battery life is 702.0 minutes, what will the latest model's battery life be 2 years from now?
2842.35 minutes
Solve for x:
ln8+ln2x^2=4
x=+-1.847
Solve the equation.
1/(x^2+10x+24)-4/(x+6)=1/(x+4)
x=-21/5
Solve for x:
0=-8+(2m-52)^(3/2)
28
Find the summation of the following series. Note that the series has 10 terms.
5+10+20+40+80+...2560
5115
A country pledges to reduce its annual CO2 emissions by a constant percentage per year. In 2022, the country emitted 3,390 Mt (Megatons) of CO2. In 2042, they emitted 1,071 Mt. What is the percentage the country pledged to reduce emissions by per year?
5.6% per year.
Solve for x:
7^(x+1)=2^(x+3)
x=0.107