What is the solution set for the inequalities x^3<0 or 4x^4>x^2?

  (x < 0) ∪ (x > 1/2)

Step-by-step explanation:

First inequality:

  x^3 < 0

  x < 0 . . . . . take the cube root

Second inequality:

4x^4 > x^2

4x^4 -x^2 > 0

x^2(4x^2 -1) > 0

Any non-zero x will make the first factor positive. The product will be positive only when the second factor is positive, for x^2 > 1/4

  x^2 > 1/4

  |x| > 1/2 . . . . . take the square root

  x < -1/2   or   x > 1/2

The first part of this solution is already covered by the solution to the first inequality. Hence the solution set for the system of inequalities is ...

  (x < 0) ∪ (x > 1/2)

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.