Radical Equations
Solve the equation.
sqrt(x) = 9
x = 81
Solve the equation below.
x^(3/4) = 8
x = 16
x^2 + 2x + 1 = 0
x = -1
Find the equation for the line with a y-intercept of (0, 9) that passes through the point (1, 2).
y = 2x + 9
Micaela is selling tickets for the school play. On the first day of ticket sales, she sells 3 adult tickets and 5 student tickets for a total of $51. On the second day, she sells 1 adult ticket and 4 student tickets for a total of $31. How much does each ticket cost.
Student: $6
Adult: $7
Solve the equation.
sqrt(2x + 1) = 5
x = 12
Solve the equation.
x^(4/3) = 256
x = 64 and -64
Solve the equation.
x^2 + 5x + 6 = 0
x = -2 and -3
Find the equation of the line that passes through the points (2, 4) and (-1, 3).
y = 1/3x + 10/3
John has $4,000 to invest and he must choose between a CD earning 4% and a mutual fund earning 7%. If he aims to return $200 in interest per year, how much should he invest in each?
CD: $2666.66
Mutual Fund: $1333.33
Solve the equation.
-4 + sqrt(6v + 15) = v
v = -1
Solve the equation.
-76 = 5 - r^(4/3)
r = 27 and -27
Solve the equation.
x^2 + 2x + 7 = 0
x = -1 + sqrt(-6) and -1 - sqrt(-6)
Find the equation of the line that passes through the point (2, 7) and is parallel to the line y = 4x + 1.
y = 4x - 1
A boat travelled 330 kilometers each way downstream and back. The trip downstream took 11 hours and the trip back took 33 hours. What is the speed of the boat in still water? What is the speed of the current?
Boat: 20 km/h
Current: 10 km/h
Solve the equation.
sqrt(-4x) = x - 1
No solution
Solve the equation.
(15 - x)^(-5/3) = 1/243
x = -12
Solve the equation.
x^2 + 8x + 6 = 0
x = -4 + sqrt(10) and -4 - sqrt(10)
Find the equation that passes through the point (1, 1) and is perpendicular to y = 4x + 2
y = 1/4x + 3/4
How many quarts of 30% sugar solution must be mixed with 2 quarts of 10% sugar solution to mix a 25% sugar solution?
6 quarts
Solve the equation.
2 = sqrt(7a - 3) - sqrt(3a - 3)
a = 4 and 1
Solve the equation.
3(a - 3)^(-1/2) = 1/3
a = 84
Solve the equation by completing the square.
x^2 + 4x + 1 = 0
x = -2 + sqrt(3) and -2 - sqrt(3)
A business sells TVs and is modeling their profits. When the business sells 8 TVs, they make a profit of $350. When they sell 14 TVs, they make a profit of $590. Write an equation to model the profits per TV sold for this business.
y = 40x + 30
The sum of the digits of a certain number is 5. When you reverse the digits, you decrease the number by 27. Find the number.
41