Answer:
d) ![7^{14}](https://tex.z-dn.net/?f=7%5E%7B14%7D)
Step-by-step explanation:
we simplify
by doing 7 x 2 = 14
so it is now
![7^{14}](https://tex.z-dn.net/?f=7%5E%7B14%7D)
to check, we can use a calculator.
7 to the power of 14 = 678223072849
and
7 to the power of 7, squared also = 678223072849
Hope this helps!
Answer:
2<x<4/3
Step-by-step explanation:
Given the equation of a graph to be y = |3x− 5|, if the equation is one unit to the right, this can be expressed as |3x-5| > 1.
Solving the resulting equation
|3x-5| > 1.
Since the function 3x-5 is in a modulus sign, this means that the function can take both negative and positive values.
For positive value of the function;
+(3x-5) > 1
3x > 1+5
3x>6
x>6/3
x>2 ... (1)
For the negative value of the function;
-(3x-5) > 1
On expansion
-3x+5 > 1
-3x > 1-5
-3x > -4
Multiplying through by -1 will also change the inequality sign
x < -4/-3
x < 4/3...(2)
Combining equation 1 and 2, we have;
2<x<4/3
The shortcut is the hypotenuse of a right triangle with legs 6 and 8, so 6²+8²=c²
36+64=c
100=c²
c=10.
so he traveled 6+8+10=24km
Given:
second term = 18
fifth term = 144
The nth term of a geometric sequence is:
![\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_n%5Ctext%7B%20%3D%20ar%7D%5E%7Bn-1%7D%20%5C%5C%20Where%5Ctext%7B%20a%20is%20the%20first%20term%7D%20%5C%5C%20r%5Ctext%7B%20is%20the%20common%20ratio%7D%20%5Cend%7Bgathered%7D)
Hence, we have:
![\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bar%7D%5E%7B2-1%7D%5Ctext%7B%20%3D%2018%7D%20%5C%5C%20ar%5Ctext%7B%20%3D%2018%7D%20%5C%5C%20%20%5C%5C%20ar%5E%7B5-1%7D%3D%5Ctext%7B%20144%7D%20%5C%5C%20ar%5E4%5Ctext%7B%20%3D144%7D%20%5Cend%7Bgathered%7D)
Divide the expression for the fifth term by the expression for the second term:
![\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bar%5E4%7D%7Bar%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B144%7D%7B18%7D%20%5C%5C%20r%5E3%5Ctext%7B%20%3D%20%7D%5Cfrac%7B144%7D%7B18%7D%20%5C%5C%20r%5Ctext%7B%20%3D%202%7D%20%5Cend%7Bgathered%7D)
Substituting the value of r into any of the expression:
![\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20ar%5Ctext%7B%20%3D%20%2018%7D%20%5C%5C%20a%5Ctext%7B%20%7D%5Ctimes%5Ctext%7B%202%20%3D%20%2018%7D%20%5C%5C%20Divide%5Ctext%7B%20both%20sides%20by%202%7D%20%5C%5C%20%5Cfrac%7B2a%7D%7B2%7D%5Ctext%7B%20%3D%7D%5Cfrac%7B18%7D%7B2%7D%20%5C%5C%20a%5Ctext%7B%20%3D%209%7D%20%5Cend%7Bgathered%7D)
Hence, the explicit rule for the sequence is: