Question 1/ First image
Answer:
G,[tex]a=\sqrt{7}[/tex]
Step-by-step explanation:
To get to the correct solution we have to perform a series of manipulations on the equation we are given.
Step 1
We divide both side by [tex]3\sqrt{7}[/tex] to get the equation,
[tex]\frac{1}{a\sqrt{7} } =\frac{1}{7}. \\[/tex]
Step 2
In this step , we multiply both sides by [tex]a\sqrt{7}[/tex] to yield the result shown below,
[tex](a\sqrt{7})\times \frac{1}{a\sqrt{7} } =(a\sqrt{7})\times\frac{1}{7} \\\\\implies 1=\frac{a\sqrt{7} }{7} \\\implies 7= a\sqrt{7} \\\implies a=\frac{7}{\sqrt{7} }. \\[/tex]
Step 3
The next step is to multiply both numerator and denominator by [tex]\sqrt{7}[/tex] to yield the result below,
[tex]a=\frac{7\sqrt{7} }{\sqrt{7} \sqrt{7} } \\\\\implies a= \frac{7\sqrt{7} }{7} \\\implies a= \sqrt{7}.[/tex]
Clearly, the correct answer is [tex]a=\sqrt{7}.[/tex]
Question 2/Image 2
Answer:
The correct answer is G. $12,167.
Step-by-step explanation:
The way to solve this problem is to substitute the values of [tex]P=10\,000, n=5, r=\frac{4}{100}=0.04[/tex] in to the equation [tex]A=P(1+r)^n[/tex] and then round up the value. This calculation is shown below,
[tex]A=P(1+r)^n\\A=10\,000(1+0.04)^5\\A=12\,166.529024\\A\approx 12\,167.[/tex]
The correct answer is G.$12,167.
Question 3/Image 3
Answer: The correct Answer is H. [tex]4x^2-7[/tex]
Step-by-step explanation:
The way to compute the correct result is to realize that we are dealing with composition of functions. In this case, the function [tex]f(x)[/tex] sees [tex]g(x)[/tex] as it's input. The calculation that yields the correct result is shown below,
[tex]f(g(x))=4(x^2-2)+1\\f(g(x))=4x^2-8+1\\f(g(x))=4x^2-7.[/tex]
The correct answer is H. [tex]4x^2-7.[/tex]
