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3 years ago

write the inverse and converse for the following statement. If a number is divisible by 2 then it is an even number

Mathematics

1 answer:

rosijanka [135]3 years ago

7 0

If a statement has a hypothesis and a conclusion (i.e. it is in the form "if ... then ...")

The inverse is the statement built negating the hypothesis and the conclusion: "if A then B" becomes "if not A then not B"
The converse is the statement built exchanging hypothesis and conclusion: "if A then B" becomes "if B then A"

So, the inverse of your statement is "if a number is not divisible by 2, then it is an odd number"

The converse of your statement is "if a number is even, then it is divisible by 2".

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A rectangular field is 95 meters long and 65 meters wide. Give the length and width of another rectangular field that has the sa

Lena [83]

Answer:

There are a ton of answers. For instance, 1m by 159m.

Step-by-step explanation:

The formula for the area is $a=l*w$ , where $l$ and $w$ are constants.

The formula for perimeter is $p=2l+2w$

The question wants another rectangle that has the same perimeter, but a smaller area.

The perimeter of the two fields has to be:

$p=(2*95)+(2*65)\\p=190+130\\p=320$

Thankfully, the question never specified how much smaller the area has to be. So let's go to the logical extreme and make it 1 meter wide. To conserve the perimeter, we'd have to add the removed 64 meters to the original 95 meters of length, resulting in a rectangle with a width of 1m and a length of 159m. This results in an area of exactly 159 $m^{2}$ . The original rectangle had an area of 6175 $m^{2}$ . Mission accomplished!

But why stop there? Let's go even further down this rabbit hole!

Instead of 1, why don't we take it several steps further and use 0.0000001? At that point, the length would end up being 159.9999999m.

The area would be 0.00001599999999 $m^{2}$ .

Let's go further!!

Width: 0.00000000000000000001

Length: 159.99999999999999999999

Area: 0.00000000000000000001599999999999999999999 (approximate).

One more, for old time's sake.

Width: 0.00000000000000000000000000000000000000000000000001m

Length: 159.99999999999999999999999999999999999999999999999999m

Area: 0.00000000000000000000000000000000000000000000000015999999999999999999999999999999999999999999999999999 $m^{2}$

At that point, there's so little area in the plot of land that you could claim it has no area!

5 0

3 years ago

1. Your high school freshman class had a total of $1200 from fund-raisers during the year. To help

zysi [14]

Answer:

a is 67.20 and b is 1267.20

Step-by-step explanation:

first you have to multiply 1200 from 5.6% and you get 67.20 then you have to add 1200 to 67.20 and you get 1267.20

4 0

3 years ago

O. Find the distance between P (10,-7) and Q (7,- 10). Leave your answer in radical form.

mr Goodwill [35]

Answer:

$\sqrt{18}$ or $3\sqrt{2}$ units.

Step-by-step explanation:

To find the distance between two points, we can use the Distance Formula.

Distance Formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Given:

P (10, -7) ⇒ x₁ = 10, y₁ = -7

Q (7, -10) ⇒ x₂ = 7, y₂ = -10

Substitute the given values into the formula and simplify.

$\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}$