Find the equation for this table please?

Which statement is true?

love history [14]

<h2>Hello!</h2>

The answer is:

The second option,

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

Discarding each given option in order to find the correct one, we have:

<h2>First option,</h2>

$\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}$

<h2>Second option,</h2>

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

The statement is true, we can prove it by using the following properties of exponents:

$(a^{b})^{c}=a^{bc}$

$\sqrt[n]{x^{m} }=x^{\frac{m}{n} }$

We are given the expression:

$(\sqrt[m]{x^{a} } )^{b}$

So, applying the properties, we have:

$(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }$

Hence,

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

<h2>Third option,</h2>

$a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}$

<h2>Fourth option,</h2>

$\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }$

Hence, the answer is, the statement that is true is the second statement:

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

Have a nice day!

6 0

3 years ago

Suppose that F(x) = x3 and G(x) = -4x3-5. Which statement best compares the graph of G(x) with the graph of F(x)?

lara31 [8.8K]

Answer:

Answer is B

Step-by-step explanation:

F(x) is first stretched by factor 4 from '4x³';

It is then reflected in the x-axis, since it is '-4x³';

Lastly, it is shifted down 5 units, because of the '-5'.

5 0

3 years ago

I really Need help solving this problem!

Paraphin [41]

Answer:

Hello,

Answer A : 11.2 ≤ X ≤ 29.2

Step-by-step explanation:

$Z=\dfrac{X-20.2}{4.5} \\\\X=4.5*Z+20.2\\\\For\ Z=-2, \ X=4.5*(-2)+20.2=11.2\\For\ Z=2, \ X=4.5*2+20.2=29.2\\$

8 0

3 years ago

What is the area of a triangle whose sides are 12 6 and 20 meters long

aleksley [76]

38 meters long is the answer

3 0

3 years ago

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

Rama09 [41]

Answer:

The simple interest rate is 5%.

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

We have that $P = 4200, E = 630, t = 3$ . We have to find I.

$E = P*I*t$

$630 = 4200*I*3$

$I = \frac{630}{4200*3}$

$I = 0.05$

The simple interest rate is 5%.

Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of return of 6%?

We have to find T when $P = 4200, t = 4, I = 0.06$

So

$E = P*I*t$

$E = 4200*0.06*4$

$E = 1008$

$T = E + P = 4200 + 1008 = 5208$

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

7 0

2 years ago