All categories

3 years ago

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. 5x^6=30

Mathematics

1 answer:

Elina [12.6K]3 years ago

7 0

Answer:

The real solutions are

$x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35$

Step-by-step explanation:

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

To find the real solutions of the equation $5x^6=30$ :

$\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x^6}{5}=\frac{30}{5}\\\\\mathrm{Simplify}\\\\x^6=6\\\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}\\\\x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35$

You might be interested in

Find the midpoint of A and B where A has coordinates (-3,-5) and B has coordinates (4,4).

snow_lady [41]

Answer:

( $\frac{1}{2}$ , $\frac{-1}{2}$ )

Step-by-step explanation:

Use the midpoint formula to solve.

1) Given 2 points: ( $x_{1}$ , $y_1$ ) and ( $x_2$ , $y_2$ )

The midpoint formula would be ( $\frac{x_1+x_2}{2}$ , $\frac{y_1+y_2}{2}$ ).

2) Based on this, we can easily find the midpoint of AB.

-3 would be $x_1\\$
-5 would be $y_1$
4 would be $x_2$
the next 4 would be $y_2$

3) With this information, we can solve for the midpoint.

( $\frac{-3+4}{2}$ , $\frac{-5+4}{2}$ ) --> ( $\frac{1}{2}$ , $\frac{-1}{2}$ ) --> This is your answer.

8 0

3 years ago

A school cafeteria makes cheese sauce for macoroni using 15 cups of Swiss cheese and 17 cups of cheddar cheese. Perry tries to m

blondinia [14]

Yes he is because the ratio is 1:2

6 0

4 years ago

Read 2 more answers

The perimeter of a college athletic field is 96 meters and the length is 16 m more than the width. Find the length and width.

Andre45 [30]

In order to figure this out, you are going to do the math backwards. If the perimeter of the entire field is 96 meters, you will want to remove 16, which will give you 80 meters. You will then divide this by 2, giving you 40 meters. The width of the field will be 40 meters. That means that the length of the field is going to be 56 meters.

3 0

3 years ago

Sam paid $8.28 for 18 stamps.at this rate,how much would it cost Sam to buy 12 stamps

allsm [11]

Answer: It costs $5.52 to Sam to buy 12 stamps.

Step-by-step explanation:

Given: Sam paid $8.28 for 18 stamps.

Thus, the cost of 18 stamps = $8.28

Then the cost of 1 stamp= $\frac{8.28}{18}$