It’s a Class of 24 students,5/6 are boys.<br> How many boys are in the class?

The cube root of 5 times the square root of 5 over the cube root of 5 to the 5th power

Fiesta28 [93]

(cube root of 5) * sqrt(5)
--------------------------------- = ?
(cube root of 5^5)

This becomes easier if we switch to fractional exponents:

5^(1/3) * 5^(1/2) 5^(1/3 + 1/2) 5^(5/6)
------------------------ = --------------------- = ------------- = 5^[5/6 - 5/3]
[ 5^5 ]^(1/3) 5^(5/3) 5^(5/3)

Note that 5/6 - 5/3 = 5/6 - 10/6 = -5/6.

1
Thus, 5^[5/6 - 5/3] = 5^(-5/6) = --------------
5^(5/6)

That's the correct answer. But if you want to remove the fractional exponent from the denominator, do this:

1 5^(1/6) 5^(1/6)
---------- * ------------- = -------------- (ANSWER)
5^(5/6) 5^(1/6) 5

7 0

3 years ago

Explain how to find the sum of 3/10 + 4/100

Neporo4naja [7]

Answer: 17/50

Step-by-step explanation:

First, to add fractions, we must find a common denominator, in this case, 100.

Then, we must make the fractions being added all have the common denominator.

So, we must multiply 3/10 * 10/10, which equals 30/100

30/100 + 4/100

Then, just add across the numerator to get 34/100, which can be simplified to 17/50

6 0

2 years ago

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Can someone help me please

yanalaym [24]

Answer:

Step-by-step explanation:

Alice in wonderland is about a 19 year old girl who visited wonderland when she was a young girl but as she hit her teen years she forgot all about wonderland, but when a white rabbit ruins her engagement party she is forced to remember what she forgot.

7 0

2 years ago

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Can you please belp me solve 100÷ 4,031.2

kolezko [41]

This might be wrong but I got .024806509

I don't know if you wanted it rounded but I hope this might have helped.

6 0

3 years ago

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Determine whether the lines given in each box are parallel, perpendicular, or neither

andrey2020 [161]

Answer/Step-by-sep explanation:

To determine whether the lines given in each box are parallel, perpendicular, or neither, take the following simple steps:

1. Ensure the equations for both lines being compared are in the slope-intercept form, y = mx + b. Where m is the slope.

2. If both lines have the same slope value, m, then both lines are parallel.

3. If the slope of one line is the negative reciprocal of the other, then both lines are perpendicular. That is, x = -1/x.

4. If the slope of both lines are not the same, nor the negative reciprocal of each other, then they are neither parallel nor perpendicular.

1. y = 3x - 7 and y = 3x + 1.

Both have the same slope value of 3. Therefore, they are parallel.

2. ⬜ $y = -\frac{2}{5}x + 3$ and $y = \frac{2}{5}x + 8$

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⅖ and the slope of the other is ⅖. Therefore, they are neither parallel nor perpendicular.⬜

3. $y = -\frac{1}{4}x$ and $y = 4x - 5$

The slope of the first line, ¼, is the negative reciprocal of the slope of the second line, 4.

Therefore, they are perdendicular.

4. 2x + 7y = 28 and 7x - 2y = 4.

Rewrite both equations in the slope-intercept form, y = mx + b.

2x + 7y = 28

7y = -2x + 28

y = -2x/7 + 28/7

y = -²/7 + 4

And

7x - 2y = 4

-2y = -7x + 4

y = -7x/-2 + 4/-2

y = ⁷/2x - 2

The slope of the first line, -²/7, is the negative reciprocal of the slope of the second line, ⁷/2.

Therefore, they are perdendicular.

5.⬜ y = -5x + 1 and x - 5y = 30.

Rewrite the second line equation in the slope-intercept form.

x - 5y = 30

-5y = -x + 30

y = -2x/-5 + 30/-5

y = ⅖x - 6

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -5 and the slope of the other is ⅖. therefore, they are neither parallel nor perpendicular.⬜

6.⬜ 3x + 2y = 8 and 2x + 3y = -12.

Rewrite both line equations in the slope-intercept form.

3x + 2y = 8

2y = -3x + 8

y = -3x/2 + 8/2

y = -³/2x + 4

And

2x + 3y = -12

3y = -2x -12

y = -2x/3 - 12/3

y = -⅔x - 4

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -³/2 and the slope of the other is -⅔ therefore, they are neither parallel nor perpendicular.⬜

7. y = -4x - 1 and 8x + 2y = 14.

Rewrite the equation of the second line in the slope-intercept form.

8x + 2y = 14

2y = -8x + 14

y = -8x/2 + 14/2

y = -4x + 7

Both have the same slope value of -4. Therefore, they are parallel.

8.⬜ x + y = 7 and x - y = 9.

Rewrite the equation of both lines in the slope-intercept form.

x + y = 7

y = -x + 7

And

x - y = 9

-y = -x + 9

y = -x/-1 + 9/-1

y = x - 9

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -1, and the slope of the other is 1, therefore, they are neither parallel nor perpendicular.⬜

9. y = ⅓x + 9 And x - 3y = 3

Rewrite the equation of the second line.

x - 3y = 3

-3y = -x + 3

y = -x/-3 + 3/-3

y = ⅓x - 1

Both have the same slope value of ⅓. Therefore, they are parallel.

10.⬜ 4x + 9y = 18 and y = 4x + 9

Rewrite the equation of the first line.

4x + 9y = 18

9y = -4x + 18

y = -4x/9 + 18/9

y = -⁴/9x + 2

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⁴/9, and the slope of the other is 4, therefore, they are neither parallel nor perpendicular.⬜

11.⬜ 5x - 10y = 20 and y = -2x + 6

Rewrite the equation of the first line.

5x - 10y = 20

-10y = -5x + 20

y = -5x/-10 + 20/-10

y = ²/5x - 2

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is ⅖, and the slope of the other is -2, therefore, they are neither parallel nor perpendicular.⬜

12. -9x + 12y = 24 and y = ¾x - 5

Rewrite the equation of the first line.

-9x + 12y = 24

12y = 9x + 24

y = 9x/12 + 24/12

y = ¾x + 2

Both have the same slope value of ¾. Therefore, they are parallel.

5 0

2 years ago

It’s a Class of 24 students,5/6 are boys. How many boys are in the class?