Write the sentences below as a mathematical expression.

Prove: If n is a positiveinteger and n2 is<br> divisible by 3, then n is divisible by3.

notka56 [123]

Answer:

If $n^2$ is divisible by 3, the n is also divisible by 3.

Step-by-step explanation:

We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, $n^2$ is not divisible by 3.

Let n not be divisible by 3. Then $\frac{n}{3}$ can be written in the form of fraction $\frac{x}{y}$ , where x and y are co-prime to each other or in other words the fraction is in lowest form.

Now, squaring

$\frac{n^2}{9} = \frac{x^2}{y^2}$

Thus,

$n^2 = \frac{9x^2}{y^2}$

$\frac{n^2}{3} = \frac{3x^2}{y^2}$

It can be clearly seen that the fraction $\frac{3x^2}{y^2}$ is in lowest form.

Hence, $n^2$ is not divisible by 3.

Thus, by contrapositivity if $n^2$ is divisible by 3, the n is also divisible by 3.

5 0

4 years ago

Blake into her friends are going to an amusement park. The cost of admission to the park is $39.95 per person. Once they're in t

Sindrei [870]

Answer:

143.70 = 3(39.95) + x

where x is the additional fee spent to race the cars at the park

Step-by-step explanation:

Let’s write the complete question first before we solve;

Blake and two of her friends are going to an amusement park. The cost of admission to the park is $39.95 per person. Once they are in the park, Blake and her friends ride the race cars, which require an additional fee. The total amount spent by all three boys is $143.70. Write an equation that can be used to find the additional fee to ride the race cars.

solution;

we are trying to write an equation that could help determine the additional fee used to race cars at an amusement park by a group of friends.

we proceed as follows;

We identify that they are 3, with each spending an amount equal to $39.95 for admission.

now to find the additional fee, we simply multiply the admission fee by 3 and subtract from the total amount spent.

let’s say the additional fee is x

This means;

143.70 = 3(39.95) + x

To get x, we can then open the bracket then take the value to the other side to get x

3 0

3 years ago

The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only

sveta [45]

Answer:

its 72.50

Step-by-step explanation:

5 0

3 years ago

I NEED HELP WITH THIS ASAP!

horrorfan [7]

I think it’s the 1st one because it’s close too what it is when I work it out

7 0

3 years ago

a 20 foot ladder against a building that makes an angle of 72 with the ground.find to the nearest foot the distance between the

makvit [3.9K]

Hello from MrBillDoesMath

Answer: 6.2 feet

Discussion:

The ladder and the wall form a right triangle. The length of the ladder, 20 in this case, is the hypotenuse of the triangle. Let "x" be the distance between the foot of the ladder and the building. Then from trigonometry,

cos (@) = length of adjacent side/ hypotenuse

or in our case

cos(72) = x / 20 => (multiply both sides by 20)

20 * cos(72) = x.

Using a calculator this becomes

20 * ( .3090) = 6.18 feet (approx) or 6.2 feet , rounded to the nearest foot.

Thank you,

Mr. B

6 0

3 years ago