Question

Could someone please explain and answer these? Thank you!

Answer 1

Question 1/ First image

Answer:

G,
`a=√(7)`

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
`3√(7)` to get the equation,

`(1)/(a√(7) ) =(1)/(7). \\`

Step 2

In this step , we multiply both sides by
`a√(7)` to yield the result shown below,

`(a√(7))* (1)/(a√(7) ) =(a√(7))*(1)/(7) \\\\\implies 1=(a√(7) )/(7) \\\implies 7= a√(7) \\\implies a=(7)/(√(7) ). \\`

Step 3

The next step is to multiply both numerator and denominator by
`√(7)` to yield the result below,

`a=(7√(7) )/(√(7) √(7) ) \\\\\implies a= (7√(7) )/(7) \\\implies a= √(7).`

Clearly, the correct answer is
`a=√(7).`

Question 2/Image 2

Answer:

The correct answer is G. $12,167.

Explanation:

The way to solve this problem is to substitute the values of
`P=10\,000, n=5, r=(4)/(100)=0.04` in to the equation
`A=P(1+r)^n` and then round up the value. This calculation is shown below,

`A=P(1+r)^n\\A=10\,000(1+0.04)^5\\A=12\,166.529024\\A\approx 12\,167.`

The correct answer is G.$12,167.

Question 3/Image 3

Answer: The correct Answer is H.
`4x^2-7`

Explanation:

The way to compute the correct result is to realize that we are dealing with composition of functions. In this case, the function
`f(x)` sees
`g(x)` as it's input. The calculation that yields the correct result is shown below,

`f(g(x))=4(x^2-2)+1\\f(g(x))=4x^2-8+1\\f(g(x))=4x^2-7.`

The correct answer is H.
`4x^2-7.`