Answer:
Question 1: [tex]x=4[/tex]
Question 2: [tex]x= \pm7[/tex]
Question 5: The dimensions of one face of the container are 6 by 6 inches.
Step-by-step explanation:
Hi there!
Question 1
[tex]x^3=64[/tex]
Rewrite 64 as a power of 3:
[tex]x^3=4^3[/tex]
(We could find that 4³ = 64 through trial and error)
This above equation makes it true that x=4. If aⁿ = bⁿ, then a=b:
[tex]x=4[/tex]
Question 2
[tex]x^2=49[/tex]
Rewrite 49 as a power of 2:
[tex]x^2=7^2[/tex]
Again, we could have found this through trial and error, or by looking at our multiplication tables.
[tex]x=7[/tex]
However, remember that positive and negative numbers will all square to be a positive number. So, therefore, x can be -7 OR 7 (since both, when squared, equal 49):
[tex]x= \pm7[/tex]
Question 5
Let x be equal to the length of one edge of the cube.
Volume of a cube formula: [tex]V=x^3[/tex]
Plug in the given information, when V is the volume:
[tex]216=x^3[/tex]
Rewrite 216 as a power of 3:
[tex]6^3=x^3[/tex]
^ We could have found this through trial and error.
[tex]x=6[/tex]
Therefore, the dimensions of one face of the container are 6 by 6 inches.
I hope this helps!
