Answer:
A rational number is a number that can be expressed as a fraction (ratio). This includes whole numbers, square roots that can be solved evenly, negatives, decimals, and repeating decimals that can be solved with a fraction. 
 ↔  .5 ↔  .5
- 5  ↔ 5.0
 ↔ 2.0 ↔ 2.0
- -13  ↔  -13.0
- 0.38462... ( ) )
An irrational number is a number that is NOT rational. It's the complete opposite!
- π  ↔  3.14159
- .13133133...
 ↔  0.86603... ↔  0.86603...
- - ↔  -2.23607... ↔  -2.23607...
 ↔   2.23607... ↔   2.23607...
Hope this helps!!!
 
        
             
        
        
        
Step-by-step explanation:
Dilation changes the size of the shape and is not a rigid motion.
 
        
                    
             
        
        
        
Answer:
The correct option is;
D. x = -1.38 and 0.82
Please find attached the combined function chart
Step-by-step explanation:
The given equation is x³ + 3 = -x⁴ + 4
Plotting the equation using Excel, we have;
f(x) = x³ + 3, h(x) = -x⁴ + 4
x                                             f(x)                                       h(x)
-1.4                                         0.256                                   0.1584
-1.39                                       0.314381                              0.26699
-1.38                                       0.371928                             0.373261
-1.37                                       0.428647                             0.477246
-1.36                                       0.484544                             0.57898
Which shows an intersection at the point around -1.38
x                                          f(x)                                     h(x)
0.77                                    3.456533                         3.64847
0.78                                    3.474552                         3.629849
0.79                                    3.493039                          3.610499
0.8                                         3.512                                3.5904
0.81                                      3.531441                           3.569533
0.82                                       3.551368                          3.547878
0.83                                       3.571787                            3.525417
Which shows the intersection point around 0.82
Therefore, the correct option is x = -1.38 and 0.82
From the graphing calculator the intersection point is given as 
x = -1.3802775691 and 0.81917251339.