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2 years ago

Prove that if n is an even integer, then n + 1 is odd. Give a proof by contraposition of this theorem.

Mathematics

1 answer:

S_A_V [24]2 years ago

7 0

Answer:

Proved below

Step-by-step explanation:

If we assume that n + 1 even when n is even, it means that;

n + 1 = 2x

Where x is an integer

Then;

n = 2x - 1

This means that n is odd because 2x - 1 is odd.

But we know that n is even, thus, our assumption is wrong.

Therefore, n + 1 is odd when n is even.

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Please answer question 18 using the information above.

Zolol [24]

Answer:

Third and forth.

Step-by-step explanation:

Marks up mean increasing the price.

8 0

3 years ago

What is the surface area of this composite solid?______________ square feet 242 319 363 517

jeka57 [31]

Answer:

<h2>The right answer is 415.4 cubic feet.</h2>

Step-by-step explanation:

As you can observe in the image attached, the composite figure is formed by a square prism and a pyramid on top.

We need to find the volum of each part separately.

<h3> Square prism.</h3>

$V_{prims}=11 \times 11 \times 2=242 \ ft^{3}$

<h3>Square pyramid.</h3>

First, we need to find the height of the pyramid. We already know the height of each triangular face of the pyramid, which divides equally the side.

Let's use Pythagorean's Theorem to find the height of the pyramid.

$7^{2}=h^{2} +(5.5)^{2}\\ 49-30.25=h^{2}\\ h=\sqrt{18.75} \approx 4.3$

The height is 4.3 feet, approximately.

Now, we find the volume of the pyramid

$V_{pyramid}=\frac{1}{3}(11 \times 11 \times 4.3) \approx 173.4ft^{3}$

The sum of both figures represents the total volume of the composite figure

$V_{total}=242+173.4=415.4ft^{3}$

Therefore, the right answer is 415.4 cubic feet.

3 0

3 years ago

Read 2 more answers

2. If AB = 4x + 9. BC = 5x + 2, and AC = 56, then find the value for . AB, BC.<br> A<br> B

inysia [295]

Answer:

AB=29; BC=27

Step-by-step explanation:

So they told us AB=4x+9 and that BC=5x+2, and AC=56 , now to help with the question you can draw this information on a number line. Now on a number you can see that basically AC=AB+BC.

So you would write it as such,,

4x+9+5x+2=56

Combine like terms

9x+11=56

Now you have to isolate the x by itself but first get rid of the 11.

9x+11-11=56-11

You would get

9x=45

Here you can divide 9 by both sides to isolate x.

9x/9=45/9

{x=5}

Now to find the value for both substitue x in the equations for both

1. AB=4x+9 where x is 5

4(5)+9 =AB

20+9 =AB

29=AB

You would do the same with BC

2. BC= 5x+2 where x is 5

5(5)+2= BC

25+2= BC

27=BC

If you want to check your answers you can just substitute x for 5 in the first equation we did where AC=AB+BC

6 0

3 years ago

An office spends $375.00 per month on office supplies.

podryga [215]

Answer:

$51 saved.

Step-by-step explanation:

Well 12% of $425 is found by multiplying

(.12)(425) = $51 saved.

8 0

3 years ago

Find exact volume of a sphere with a radius of 10in

Elodia [21]

To find the volume of a sphere, we can apply the following formula:

/3)πr^3

We know the radius is 10, so we can plug that value in.

(4/3) * pi * 10^3

The question says "exact" volume, so I've included all of the digits in the tenths and beyond place, without rounding.

3 0

3 years ago