Mathematics College

express 15 x^1/3y^1/5 using a radical

Answers

Answer 1
in short, to convert two fractions to have the same denominator, we simply multiply one by the denominator of the other, so in this case, we'll multiply 1/3 by 5, top and bottom, and 1/5 by 3, top and bottom, thus

[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------[/tex]

[tex]\bf \cfrac{15x^{\frac{1}{3}}}{y^{\frac{1}{5}}}\qquad \begin{cases} \frac{1}{3}=\frac{1\cdot 5}{3\cdot 5}\\ \qquad \frac{5}{15}\\\\ \frac{1}{5}=\frac{1\cdot 3}{5\cdot 3}\\ \qquad \frac{3}{15} \end{cases}\implies \cfrac{15x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{\sqrt[15]{x^5}}{\sqrt[15]{y^3}} \\\\\\ 15\sqrt[15]{\frac{x^5}{y^3}}[/tex]
Answer 2

Answer:

[tex]15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}[/tex]

Step-by-step explanation:

We have been given an expression [tex]15x^{\frac{1}{3}}y^{\frac{1}{5}[/tex]. We are asked to express our given expression using a radical.

Using fractional exponent rule [tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex], we can write terms of our given expression as:

[tex]15\cdot\sqrt[3]{x^1}\cdot \sqrt[5]{y^1}[/tex]

[tex]15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}[/tex]

Therefore, our required expression would be [tex]15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}[/tex].

Related Questions

An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?

Answers

I made several boxes with different sized square bases, such as 1x1, 2x2, 3x3, 4x4, 5x5, and 6x6. I calculated the heights of all of them, being 120, 30, 13.333, 7.5, 4.8, and 3.333 respectively. By using the $2/sq. in. for the sides and $3/sq. in. for the square base, I found that the box with the dimensions: 5x5x4.8 produced the most minimal cost at $267:

(5x4.8)x4 = 96 sq. in. x 2 = $192
5x5 = 25 sq. in. x 3 =$75

$192 + $75 = $267

for every 5 serves Gabby makes tanning makes 3 at volleyball practice Tammy makes 21 serves how many serves did Gabby make show your answer will mark brainiest

Answers

tammy made 21, and every 3 she makes Gabby makes 5
 divide 21 by 3 ( 21/3 = 7)
 no multiply 7 by 5 ( 7 x 5 = 35)

 Gabby made 35 serves


The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground

Answers

Given that height of the object can be found using the function h(t)=-12t²+36t, the time taken for the object to hit the ground is calculated as follows:
At the time the object hits the ground, height h(t)=0. Substituting this value in the equation we get:
0=-12t²+36t
solving for t we obtain.
12t²=36t
12t=36
hence
t=4
thus the time taken for the object to hit the ground is 4 seconds

Mary has been $50 to spend on T-shirts from an online store. there is $10 shipping and handling fee and each t-shirt cost $5 which inequality represents the number of t-shirts s Mary can buy the answer choices are 5S + 10 greater than equal to 50, 5S + 10 less than equal to 50, 10s + 5 greater than equal to 50, 10s - 5 greater than equal to 50, 5S - 10 greater than equal to 50

Answers

Hello there!
The inequality that represents this situation is 5S + 10 is less than or equal to 50.
The $10 is just a fee, and you don't have to multiply it by anything. However, when the problem says each it means that you have to multiply the given number.
Hope this helped!

a disk jockey wants to select five songs from a new CD that contains 12 songs. How many ways can a disc jockey choose 5 songs

Answers

Well this is a permutation/combination problem. If the order that the four songs is in does not matter then it will be a combination, if the order does matter it will be a permutation. 

The formula for combinations is: n!/r!(n-r)! where n is the total number possible options and r is the number taken at a time. For this problem n = 12 and r = 5 

12!/5!7! = 792 different possible combinations. 

The formula for a permutation is n!/(n-r)! where n and r represent the same things as above. 

12!/7! = 95,040 different possible permutations 

The reason for more permutation than combinations is because if you have 12 songs think of them as 1,2,3,4,5,6,7,8,9,10,11,12. Under a combination songs 1,3,6,9 and 3,6,1,9 are the same, but in a permutation the order matters so these are both different possible outcomes. 
[tex]\text {Number of ways} = C(12, 5) = \dfrac{12 \times 11 \times 10 \times 9 \times 8}{1 \times 2 \times 3 \times 4 \times 5} = 792[/tex]

Answer: There are 792 ways to pick 5 songs from 12 songs.

Peter makes $7,000 a month plus some extra commission he makes 6% of everything he sells if Peter sold $55,000 of jewelry this month what his salary this month

Answers

Comment
I'm taking this to mean that he does not have to sell above 7000 to start getting a commission. Furthermore, he makes 6% on the full 55000.

Formula
T = Base Salary +  6% Total Sales
T = Take home salary
Base Salary = 7000
Total Sales = 55000

Substitute and Solve
T = 7000 + 6% * 55000          Change the % to a decimal
T = 7000 + 6/100 * 55000
T = 7000 +  0.06 * 55000
T = 7000 + 3300
T = 10300 dollars.

Conclusion
His take home salary = 10300 dollars <<<< answer.

When ordering a student desk priced at $69.00, the shipping charges are 6%. What is the total cost of the desk?

Answers

Since the desk is $69.00 and the shipping charges are 6%

69*.06= 4.14

Your tax would be $4.14 so,

$4.14+$69.00= A total of $73.14
Shipping charges = 6% x $69 = 0.06 x 69 = $4.14

Total cost = $69 + $4.14 = $73.14

Answer: $73.14

Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.

Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?

Answers

The information you would need to create a two-variable equation is how much was her allowance and how much money did she have. Also you would need to know how many arcade games she played and how much each one cost and how many times she rode the Ferris wheel and how much each ride cost.

Hope this Helps!!

Answer:

To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.

Step-by-step explanation:

Please help with the question,

Answers

The correct answer is x^2-2x+2=0

 The explanation is shown below:

 1. To solve the problem shown in the figure above, you must apply the following proccedure:

 2. You have that the roots of the quadratic equation shown in the figure attached in the problem are:

  x=-1±i

 3.  Then, you know the quadratic formula to solve quadratic equations, which is:

 (-b±√(b^2-4ac))/2a

 4. You can see in the figure that a=1 and c=2; then, by analizing this, you can conclude that the coefficient b is:

 b=-2

 5. Therefore, you can conclude tha the quadratic equation is:

 x^2-2x+2=0

 6. If you want to verify it, apply the quadratic formula to the quadratic equation shown above and you will obtain the roots shown in the figure.

To form a quadratic equation, let α and β be the two roots.

Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).

According to the problem, roots of this equation are α and β.

Therefore,

α + β = - baba and αβ = caca.

Now, ax22 + bx + c = 0

⇒ x22 + babax + caca = 0 (Since, a ≠ 0)

⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]

⇒ x22 - (sum of the roots)x + product of the roots = 0

⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)

Formula (i) is used for the formation of a quadratic equation when its roots are given.

Given the roots: (-1+-i)

where; i=sqrt(-1)

Thus, the answer is (2x)

You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)

Hey can you please help me posted picture of question

Answers

A compound event is an event that consists of more than one simple event. The answer is option C. because option C. consists of two events, the rolling of one die followed by the rolling of another die. All other options are a single event.

Find the sum: (x5 - 3x4 + x2 - 4) + (5x4 + 3x2 + 2x + 1). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write as 4x^2.

Answers

For this case we have the following polynomials:
 (x5 - 3x4 + x2 - 4)
 (5x4 + 3x2 + 2x + 1)
 Adding we have:
 (x5 - 3x4 + x2 - 4) + (5x4 + 3x2 + 2x + 1)
 = x ^ 5 + x ^ 4 (-3 + 5) + x ^ 2 (1 + 3) + 2x + (-4 + 1)
 Rewriting we have:
 = x ^ 5 + 2x ^ 4 + 4x ^ 2 + 2x - 3
 Answer:
 The sum of the polynomials is:
 x ^ 5 + 2x ^ 4 + 4x ^ 2 + 2x - 3

Solve for e.

9e^2f=49

e=±√7f/3

e=±7√f/3

e=±7√f/3f

e=±√7f/3f

Answers

[tex]9e^{2}f=49[/tex]
Divide by the coefficient of e², multiply by f/f, then take the square root.
[tex]e^{2}=\dfrac{49}{9f}=\dfrac{49}{9f}\cdot \dfrac{f}{f}=\dfrac{49f}{9f^{2}}\\\\e=\pm \dfrac{\sqrt{7^{2}f}}{\sqrt{(3f)^{2}}}\\\\e=\pm \dfrac{7\sqrt{f}}{3f}[/tex]

The appropriate selection is ...
   e = ±7√f/(3f)

Use technology to determine an appropriate model of the data. (0,0), (1,3), (2,4), (3,3), (4,0)

f(x) = – x2 + 4x
f(x) = x2 - 4x
f(x) = - x2 + 4x - 1
f(x) = x2 - 4x + 1

Answers

A. 

Each of the ordered pairs satisfies the expression. 

Answer:

Option A.

Step-by-step explanation:

To determine an appropriate model of the data each data should satisfy the expression.

For function 1. f(x) = -x² + 4x

Now for each point

f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0

therefore the given points lie on the function.

For option 2

f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0

Therefore points do not lie on the function.

For Option 3.

f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1

Therefore the points do not satisfy the expression.

For option 4.

f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1

Therefore, the points do not satisfy the expression.

Option A. is the correct option.

Graph the quadratic function
F(x)=3x^2+6x-24

Answers

For this case we have the following function:
 F (x) = 3x ^ 2 + 6x-24
 We observe that it is a quadratic equation.
 The graph is therefore a parabola.
 Its cut points are:
 (-4, 0)
 (2, 0)
 Answer:
 See attached image to see graph of the function

1¼ gallons equals how many pints?

Answers

Answer:

10 pints

Step-by-step explanation:

There are 8 pints in a gallon, so ...

(1.25 gal) × (8 pt/gal) = 10 pt

When a number is decreased by 24% of itself the result is 171. What is the number?

Answers

let
x----------> original number

we know that
if a number is decreased by 24% of itself the result is 
x*(100%-24%)/100%------> x*0.76
171=0.76*x
x=171/0.76---------> 225

the answer is
the number is 225

Find the area of a rectangle with a length of (4x^2) and a width of (x+6)

Answers

Substitute the given values into the formula for area of a rectangle.
  area = length*width
  area = (4x^2)*(x +6)
Use the distributive property to eliminate parentheses.
  area = 4x^3 +24x^2

QM Q6.) Write the​ slope-intercept equation of the function f whose graph satisifies the given conditions.

Answers

Greetings!

The equation of a line in slope-intercept form is:

y = mx + b

m is the slope
b is the y- intercept

What we need to do is to re-arrange 2x - 9y - 18 = 0. We wanna make it looks like y = mx + b

So, the equation is:

2x - 9y - 18 = 0

Subtract 2x - 18 from both sides

→ -9y = -2x + 18

Since we want y, we need to divide both sides by -9

[tex] \frac{-9y}{-9} = \frac{-2x + 18}{-9} [/tex]

Thus,

y = 2/9 x - 2 which is in the slope intercept form

Slope m = 2/9 and the y-intercept is = - 2

Given a line with slope m then the slope of a line perpendicular is:

[tex] m_{perpendicular} = - \frac{1}{m} [/tex]

[tex] m_{perpendicular} = - \frac{1}{2/9 } [/tex]  = - 9/2

Thus,

The equation of the function is:

[tex]y = - \frac{9}{2} x - 2 [/tex]

Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!

The base of a triangular prism is an equilateral triangle with a perimeter of 15in. If the height of the prism is 4in, find the surface area.

Answers

we know that
surface area=2*[area of the base]+perimeter of the base*height 
find the area of the base

is an equilateral triangle
b=15/3----> 5 in
applying the law of sines to find the area
Area=(1/2)*b²*sin 60°------> area=(1/2)*5²*sin 60°----> 10.8253 in²

alternative method to find the area of the equilateral triangle
find the h value
applying the Pythagoras theorem
h²=5²-2.5²-----> h=√18.75-----> h=4.33 in
area=b*h/2----> area=5*4.33/2----> 10.8253 in²

surface area=2*[10.8253]+15*4----->  81.65 in²

the answer is
81.65 in²

A jogger goes 1.2 mi west then turns south. If the jogger finishes 1.3 mi from the starting point, how far south did the jogger go?

Answers

0.1 mi because the jogger has a 0.1 mi difference from west to south.

0.5 miles

The jogger's movement can be represented as a right-angled triangle, where the legs of the triangle represent the distances traveled west and south, and the hypotenuse is the direct distance from the starting point to the finishing point. To solve for the distance the jogger traveled south, we need to use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as c2 = a2 + b2.

Using the Pythagorean theorem:

1.32 = 1.22 + b2

Therefore:

b2 = 1.32 - 1.22

b2 = 1.69 - 1.44

b2 = 0.25

b = [tex]\sqrt{0.25}[/tex]

b = 0.5 mi

So, the jogger traveled 0.5 miles south.

The music teacher has a list if 128 students who have signed up for music classes. The music teacher can register 6 students in each class. What is the LEAST number of classes needed for all the students to be registered in a class?

Answers

The least number of classes needed for all the students to be registered in a class is 21 classes. 
128 divided by 6 is 21.3 so you will need at least 22 classes.

i need help with this

Answers

8. The mean of the grades (74) is substantially below the median (88), so the distribution is not symmetrical. Of course, half the grades are below the median, just as half are above the median. However, the mean being 88-74 = 14 points below the median means that the lower half of the grades will have an average at least twice that much, or 28 points, below the median. The distribution of grades must extend quite a bit further to the left of the median than it does to the right. Hence ...
  B. The distribution is skewed left.

9. It seems likely the distribution has a number of low grades pulling the average down. There certainly exists the possibility that at least one of them qualifies as an outlier by being more than 1.5 times the IQR below the first quartile. That rule, however, only applies when the distribution is relatively symmetrical, which this one is not. There does not appear to be any recommended way to describe an outlier when the distribution is skewed and has a long tail.*
  TRUE: The distribution likely has an outlier.

_____
* Math instruction these days rarely recognizes such subtleties. Since it is probable that at least one value is well below the bottom quartile, I've shown my guess at the expected answer as TRUE. In a real set of grades, I expect the tail of the distribution to have enough low grades that they cannot be considered to be outliers.

Identify the problem with the following poll.

A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.


correlation and causality


loaded questions


nonresponse


self interest

Answers

It is Nonresponse. We can infer that the entire population cannot be made.

The price of a dozen roses in the united states is $30. if $0.3472 can purchase 1.00 turkish lira, how much does the same dozen roses cost in turkey if purchasing power parity holds

Answers

For this case we can make the following rule of three:
 0.3472 $ -----> 1.00 turkish lira
 $ 30 -----------> x
 Clearing x we have:
 x = (30 / 0.3472) * (1)
 x = 86.40552995 turkish lira
 Answer:
 the same dozen roses costs:
 x = 86.40552995 turkish lira

well $30 is 185.02 in turkish lira.

Using the graph below, what are the common ratio and the general term equation, an, of the geometric sequence?

Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.

Answers

Given that the geometric series is given by:
an=a1(r)^(n-1)
where:
a1= first term
r=common ratio
n=number of terms:
from the graph, our sequence is:
-32,-24,-18,...
where:
a1=-32
a2=-24
a3=-18
thus
common ratio, r=-24/-32=3/4

thus the general form will be:
an=-32(3/4)^(n-1)

Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x + x + 0.5x + y + y – 2. Who is correct? Explain.

Answers

Gabriel and his sister are in apparent agreement. There is insufficient information to tell whether they are correct or not.

Gabriel's representation is a more compact form of his sister's representation, but they mean the same thing.*

_____
* In some computer applications, one gets a different result from computing 2.5x than from computing x + x + 0.5x. This has to do with the way numbers are represented in the computer and the way they are rounded during multiplication and/or addition. For the purposes of algebra, the expressions mean the same thing.

Gabriel and his sister's expression mean the same; However, the information available is not sufficient to determine if they are correct or not.

According to the question;

Gabriel representation is; 2.5x + 2y – 2.His sister's expression is; x + x + 0.5x + y + y – 2.

Upon computation; we find out that the expressions supplied by Gabriel and his sister are the same.

However, we must note that the information available is not sufficient to determine if both parties are correct or not.

Ultimately, if Gabriel is correct, then his sister is too and if otherwise, she is not correct too.

Read more:

https://brainly.com/question/9253705

A 12 pack of soda is roughly $3.75. What is the cost per can of soda?

Answers

So you just need to divide the cost of 12 pack of soda by 12 pack of soda.

That would be $3.75 / 12 = $0.3125

So answer is $0.3125 per can of soda or you can round it to approximately $0.31 per can of soda.

Hope this helps.

write (-5,2) and (-5,6) in standard form [if you can describe how to do this for the future]

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& 2~) % (c,d) &&(~ -5 &,& 6~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-2}{-5-(-5)}\implies \cfrac{6-2}{-5+5}\implies \stackrel{und efined}{\cfrac{4}{0}}[/tex]

now, an undefined slope, simply means a vertical line, check the picture below.

Mr zucco baked a total of 270 cupcakes and muffins. After ue sold 1/3 of the cupcakes and baked 18 more miffins, he had twice as many cupcakes as muffins. How many cupcakes and muffins did mr. Zucco bake to begin with?

Answers

Let:

c = cupcakes
m = muffins

total  = 270

c/3 = 2m 
c + m = 270

solving for the variables with 2 eqs 2 unknowns

m = 38.57 = 39
c = 231.43 = 231

less 18 muffins initially

21 muffins
231 cupcakes

In a right triangle, if the measures of the other two angles are 2x – 5 and 3x + 10, what are the measures of these two angles?

A. 30° & 60°

B. 29° & 61°

C. 50° & 40°

D. 51° & 39°

Answers

Sum of angles in a triangle = 180

2x – 5 + 3x + 10 + 90 = 180
5x + 95 = 180
5x = 85
x = 17

2x – 5 = 2(17)  - 5 = 29
3x + 10 = 3(17) + 10 = 61

Answer: 29° and 61° (Answer B)


Answer: B. 29° & 61°

Step-by-step explanation:

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