What are the rational routes of 8x^3+2x^2-5x+1=0 ?

By using synthetic division we can write:
8x^3+2x^2-5x+1=(x+1)(8x^2-6x+1)
then by the quadratic equation, factoring, or some other method we get
8x^3+2x^2-5x+1=(x+1)(2x-1)(4x-1)
The roots are: {-1, 1/2 1/4}

A machine can pump 7 gallons of water in 12 minutes. How many gallons can the machine pump in 2 hours?

12min=1/5hr, so 2hr is 10 times as long as 12min and so it will pump 70 gallons

Simplify: sqrt(-27x^5)

If log 94.3 is 1.9745 then log 0.0943 =

Recall that  and since 0.0943=94.3/100, we can write 

find an equation of a hyperbola with vertices (+4,0), (-4,0) and foci (6,0), (-6,0)

refer to a text for details, but...
,  

so that 

 

and thus... 

y=x^2+2x+1 what is the range of the parabola?

so the range is [0,oo)

Solve the equation 3x^3+x^2-8x+4=0

by synthetic division we can determine that

then by some other method we can see that


therefore the solution is:
{ 1, 2/3, -2}

solve: −6x<−24 and x+6>3

 and 

so that
 and 

both are true for

The sum of two consecutive integers is -45. Write an equation that models this situation and find the values of these two integers.

n + n+1 = -45
2n = -46
n=-23
so the integers are -22 and -23

Pump a can fill a tank in 12 minutes. Pump b can fill a tank in 20 minutes. How long to fill a tank with pump a and b together?

Rates add linearly, so together they are...

so 7 minutes, 30 seconds

The 4th and 15th term of an arithmetic progression are -30 and 10 respectively. find the arithmetic progression and it's 20th term.

We can use the typical equations for arithmetic sequences, with some "twists" 

 
Common difference works like slope, so...
 

Now we can find the first term...
 
so that 
 
and so 

Find the sum: (-2)+0+2+...+76. Show all steps.

solving the arithmetic equation  for n yields

A sequence has a third term of 18, and a common ratio of 3. What is the fifth term?

Which of the points a. (0,1), b. (-1,2), c.(-3,2), d. (1,0) is a solution of 3x+4y < 2?

We test each ordered pair by checking if it results in a true statement when substituted into the inequality: 

a) 0+4 < 2, false
b) -3+8 < 2, False
c) -9+8 < 2, True
d) 3+0 < 2, False 

c. is correct

Solve the system: {A+B=140, B+C=160, C+D=130, D+A=110}

Writing in matrix form we get the augmented matrix:

After row operations the system can be transformed to:
 

using t we can write:

A=110-t
B=t+30
C=130-t
D=t

The first and last term of the arithmetic progression are 3 and 21 respectively and the sum of the series is 240. Find the number of terms.

how do you simplify (5-2i)/(-4+i) ?

 

simplifying...

Solve for x : 15^(2x)=36

if the three sides of a triangle are 2, 5, and x units and area of triangle is x sq. units, what is the value of x ?

I used Heron's formula for the area and after some algebra we can see that there is no real solution for x:

What is the slope of a line that is perpendicular to the line that passes through (-2,-2) and (1,3)?

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