Mathematics: Could someone explain and answer these? you!

Could someone explain and answer these? you!

Ответ:

goreimani9

11.03.2022

Mathematics

Question 1/ First image

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

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

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.

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