Question

Could someone please explain and answer these? Thank you!

Answer 1

Question 1/ First image

Answer:

G,$a=\sqrt{7}$

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 $3\sqrt{7}$ to get the equation,

$\frac{1}{a\sqrt{7} } =\frac{1}{7}.$

Step 2

In this step , we multiply both sides by $a\sqrt{7}$ to yield the result shown below,

$(a\sqrt{7})\times \frac{1}{a\sqrt{7} } =(a\sqrt{7})\times\frac{1}{7} \\\\\implies 1=\frac{a\sqrt{7} }{7} \\\implies 7= a\sqrt{7} \\\implies a=\frac{7}{\sqrt{7} }.$

Step 3

The next step is to multiply both numerator and denominator by $\sqrt{7}$ to yield the result below,

$a=\frac{7\sqrt{7} }{\sqrt{7} \sqrt{7} } \\\\\implies a= \frac{7\sqrt{7} }{7} \\\implies a= \sqrt{7}.$

Clearly, the correct answer is $a=\sqrt{7}.$

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 $P=10\,000, n=5, r=\frac{4}{100}=0.04$ 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. $4x^2-7$

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 $f(x)$ 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. $4x^2-7.$