Exponential Equations
Rewrite the following in radical notation (roots)
23/4
fourth root of 23
Find the value of y
log21/8 = y
y = -3
In triangle ABC, AB = 22m, BC = 17m, and <b = 42o.
What is the length of AC?
AC = 14,74 m
What is the center and radius of the circle:
(x + 2)2 + (y - 1)2 = 10
Center: (-2; 1)
Radius: square root 10
There are 12 people competing in a race. How many ways can we award medals to 1st, 2nd, and 3rd place?
1320 ways
Solve the following equation
33x - 5 = 81
x = 3
Simplify
16log48
64
In triangle ABC, AB = 21cm, <a=48o , and <b=61o.
What is the length of side AC?
AC = 19,4 cm
Give the equation of a line perpendicular to the line 2x - 3y = -6 and through the point P(5; -2).
3x + 2y = 11
You are rolling two di. What is the probability the sum of the numbers is prime?
0,31 or 11/36
Simplify the following expression as a fractional exponent with base 3.
fourth root of 35 divided by third root of 3
311/12
Simplify
2log105 + log108 - log102
2
Fire towers A and B are located 10 miles apart. Rangers at fire tower A spot a fire at 42o, and the rangers at fire tower B spot the same fire at 64o. How far from tower A is the fire to the nearest tenth of a mile?
9,4 miles away
Given the points (-1; 2) and (3; -6).
a) Find the midpoint
b) Find the distance
b) 4 square roots of 5 or 8,94
How many ways are there for a family of 6 to be seated in a row is the mother is always next to the father?
240 ways
3x + 3x+1 + 3x+2 = 39
x = 1
Solve the following logarithmic equation:
2log x = log 2 + log (3x - 4)
x = 2; x = 4
Find all solutions of x in terms of pi/radians:
sin2x = 1/4
x1 = pi/6; 5pi/6
x2 = -pi/5 (or 11pi/6); 7pi/6
Find the coordinates of the intersection of the straight line equations 2x + 3y = 1 and x - 4y = -5.
( -1; 1)
A teacher has 20 arithmetic and 30 geometric math problems assigned. Students have to select 5 to complete. What is the probability a student completes 2 arithmetic and 3 geometric tasks?
0,36
$15 000 is invested in an account with 5% interest growth each year. After how many years will the account have $91 221, 04?
37 years
Solve the systems of equations:
log3 x + 2log3 y = 8
log3 x - log3 y = 2
x = 81; y = 9
A plane leaves JFK International Airport and travels due west at 570 mi/hr. Another plane leaves 20 minutes later and travels 22o north east at 585 mi/hr. To the nearest mile, how far apart are they 40 minutes after the second plane leaves?
802 miles apart.
Write the equation of the tangent line to the circle at point P(-5; 2)
k: (x + 2)2 + (y - 1)2 = 10
3x - 1y = -17
The CBS TV show 60 minutes has been successful for many years. A recent poll showed that 20% of TV owning households were tuned into the show during its time slot. An Advertiser wants to verify this and surveys 10 households. What is the probability that at least one household tuned in to 60 minutes?
89% or 0,89 probability