Linear Equations
Solve -x+1+5x=21 for x
x=5
Solve 12+4/x=2 for x
x = -2/5
Solve x2-12x+20=0 for x
x = 10, 2
Solve x4/3=-6561 for x
No solution
A rock is thrown directly upward with an initial velocity of 102 feet per second from a cliff 277 feet above a beach. The height of the rock above the beach h after t seconds, is given by the equation h=−16t2+102t+277
When will the rock hit the beach?
0 = −16t2+102t+277
x = 8.43
Solve 2x/9+10=5-3x/8 for x
-360/43
Solve (3-4x)/(-3+x) = 5 for x
x = 2
Solve (8x+15)2-1=0 for x
x = -2, -7/4
Solve sqrt(-3x+4) = x for x
x = 1
On average, Mary can do her homework assignments in 70 minutes. It takes Frank about 3 hours to complete a given assignment. How long (in minutes) will it take the two of them working together to complete an assignment? (Round your answer to two decimal places.)
1/70 + 1/180 = 1/x
x = 50.40 minutes
Solve x+7/5=3x/2+7/3+9/8 for x
-247/60
Solve (8x+2)/(9x-3) = (8x-8)/(9x+3)
x = 3/23
Solve 5x2=5x-10 for x
No solution
Solve x3/5=-343 for x
x = -3435/3 or -16807
Two trains leave a station at 8:00 am. One train travels north at a rate (speed) of 64 mph and another travels east at a rate (speed) of 120 mph. Assuming that the trains do not stop, at what time will the trains be 238 miles apart?
(64t)2 + (120t)2 = (238)2
x = 1.75
time = 9:45 am
Solve -8(5+3x/8)-8(5-5x/8)=5+x-4(8-x) for x
x = -53/3
Solve 3/(x+6) - 9/(x2-36) = 7/(x-6) for x
x = -69/4
Solve (2x+4)(x+7)=15 for x
x = -(sqrt(55)+9)/2, (sqrt(55)-9)/2
Solve 28x4-96x3-36x2=0 for x
x = 3, 3/7,0
A family plans to have the hardwood floors in their square dining room re-finished, and new baseboards installed. The cost of re-finishing the hardwood floors is $1.75 per square foot and the cost of purchasing and installing the new baseboard is $11 per linear foot. If the family paid $1152, what is the width of the dining room?
width = 16
Solve 4-(7+(4x-4)/5)=4/7(x-10)-3+x/5 for x
x = 228/55
Solve -1/(x-4) - (x+9)/(x2-16)= -3/(x+4) for x
x = 25
Solve 4x/(x2+8x+16) = x/(x+4) - 4/(x+4) for x
x = 2-2*sqrt(5), 2+2*sqrt(5)
Solve 3x-4-16x-2+1=0 for x
x = +-sqrt(+-sqrt(61)+8)
The blueprints for a new bathroom show a raised, rectangular bathtub with an area of 28 ft2. The blueprints show that the raised tub will be surrounded by tile on all four sides; 11-foot of tile on each side of the rectangular tub as well as at the bottom of the rectangle, and 22-feet of tile at the top of the rectangle (as shown in the diagram below). The total length (the vertical dimension) of the raised tub including the tile will be twice the total width (the horizontal dimension). Find the length of the bathtub only.
(x-2)(2x-3)=28
length = 8