In this question ,it is given that
The penny size of a nail indicates the length of the nail. The penny size
d is given by the literal equation
[tex] d=4n-2 [/tex]
where n is the length (in inches) of the nail.
In the first part we have to solve for n .
And for that firt we add 2 to both sides
[tex] d+2 =4n [/tex]
Now we divide both sides by 4, that is
[tex] n = \frac{d+2}{4} [/tex]
Part b.
When d=3
[tex] n= \frac{3+2}{4} = Â \frac{5}{4} = 1.25 [/tex]
When d =6, we will get
[tex] n=\frac{6+2}{4}=2 [/tex]
When d =10, we will get
[tex] n = \frac{10+2}{4}= 3 [/tex]
Answer:
The simplify form of the provided equation in form of n is [tex]n=\frac{d+2}{4}[/tex]. For penny size 3, 6, and 10. the lengths of nail is 5/4, 2 and 3 respectively.
Step-by-step explanation:
Consider the provided equation.
[tex]d=4n-2[/tex]
Where n is the length (in inches) of the nail and d is the penny size.
Part(a) Solve the equation for n.
Consider the provided equation and add 2 to the both sides.
[tex]d+2=4n-2+2[/tex]
[tex]d+2=4n[/tex]
Now divide both the sides by 4.
[tex]\frac{d+2}{4}=n[/tex]
[tex]n=\frac{d+2}{4}[/tex]
The simplify form of the provided equation in form of n is [tex]n=\frac{d+2}{4}[/tex].
Part (B) To find the lengths of nails with the following penny sizes: 3, 6, and 10.
For penny size 3.
Substitute d=3 in [tex]n=\frac{d+2}{4}[/tex].
[tex]n=\frac{3+2}{4}[/tex]
[tex]n=\frac{5}{4}[/tex]
For penny size 6.
Substitute d=6 in [tex]n=\frac{d+2}{4}[/tex].
[tex]n=\frac{6+2}{4}[/tex]
[tex]n=\frac{8}{4}[/tex]
[tex]n=2[/tex]
For penny size 10.
Substitute d=10 in [tex]n=\frac{d+2}{4}[/tex].
[tex]n=\frac{10+2}{4}[/tex]
[tex]n=\frac{12}{4}[/tex]
[tex]n=3[/tex]
Hence, for penny size 3, 6, and 10. the lengths of nail is 5/4, 2 and 3 respectively.
