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3 years ago

6

Bernard typically runs x km/hour. While he was sick, he only ran 41.5 km/hour. What equation represents that the difference in h

is speeds is 13.5 km/hour?
x – 41.5 = 13.5
41.5 + x = 13.5
13.5 – x = 41.5
13.5 – 41.5 = x

2 answers:

Katyanochek1 [597]3 years ago

8 0

Answer: A) x-41.5=13.5

Step-by-step explanation: edge

poizon [28]3 years ago

3 0

Answer:

a is correct

Step-by-step explanation:

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3 years ago

Find the area of each figure, round to the nearest tenth if necessary.USE 3.14 for pi

Nina [5.8K]

Answer:

11 is 405, 12 is 107.5, 13 im not sure of

Step-by-step explanation:

First on 11 you can just do 21*21 (the big square) and subtract that by 36 (which is 6*6, the small square), you'll get 107.5.

Then on 12, it is made up of a large rectangle, a small triangle, and a flatter triangle. The top triangle's formula is 1/2(7*3) which = 10.5. The big rectangle is 13*7 = 91. The last triangle is 1/2(4*3) which = 6. It is 3 because 13-10. Add all those up and you should get 107.5.

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3 years ago

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dangina [55]

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3 years ago

Prove that if x is an positive real number such that x + x^-1 is an integer, then x^3 + x^-3 is an integer as well.

Shkiper50 [21]

Answer:

By closure property of multiplication and addition of integers,

If $x + \dfrac{1}{x}$ is an integer

∴ $\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot \left (x + \dfrac{1}{x} \right )$ is an integer

From which we have;

$x^3 + \dfrac{1}{x^3}$ is an integer

Step-by-step explanation:

The given expression for the positive integer is x + x⁻¹

The given expression can be written as follows;

$x + \dfrac{1}{x}$

By finding the given expression raised to the power 3, sing Wolfram Alpha online, we we have;

$\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot x + \dfrac{3}{x}$

By simplification of the cube of the given integer expressions, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot \left (x + \dfrac{1}{x} \right )$

Therefore, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )= x^3 + \dfrac{1}{x^3}$

By rearranging, we get;

$x^3 + \dfrac{1}{x^3} = \left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )$

Given that $x + \dfrac{1}{x}$ is an integer, from the closure property, the product of two integers is always an integer, we have;

$\left ( x + \dfrac{1}{x} \right) ^3$ is an integer and $3\cdot \left (x + \dfrac{1}{x} \right )$ is also an integer

Similarly the sum of two integers is always an integer, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 + \left(- 3\cdot \left (x + \dfrac{1}{x} \right ) \right )$ is an integer

$\therefore x^3 + \dfrac{1}{x^3} = \left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )= \left ( x + \dfrac{1}{x} \right) ^3 + \left(- 3\cdot \left (x + \dfrac{1}{x} \right ) \right )$ is an integer

From which we have;

$x^3 + \dfrac{1}{x^3}$ is an integer.

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3 years ago

Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round

dem82 [27]

Do the volume of a circle then multiply by the length of the cylinder
area of a circle = $\pi r^2$
diameter/2 = radius
so 4^2 = 16 16*3.14 = 50.24
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3 years ago

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