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3 years ago

Help me with this now before 1:05PM

Mathematics

1 answer:

Elodia [21]3 years ago

4 0

Then give her the answer ^^

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We say that an integer a is a type 0 integer if there exists an integer n such that a = 3n. An integer a is a type 1 integer if

Delicious77 [7]

Answer:

<em>Proof below</em>

Step-by-step explanation:

Let's assume a is a type 1 integer. By definition, it means we can find an integer n such that

a=3n+1

We need to prove $a^2$ is a type 1 integer

Expanding

$a^2=(3n+1)^2=9n^2+6n+1$

If $a^2$ is a type 1 integer, then we should be able to find an integer m such as

$a^2=3m+1$

Equating

$a^2=3m+1=9n^2+6n+1$

solving for m

$m=3n^2+2n$

Since we know n is an integer, then the expression of m gives an integer also. Having found the required integer m, the assumption is proven

5 0

3 years ago

Read 2 more answers

Can someone help me with this asap

a_sh-v [17]

Answer:

36.576

Step-by-step explanation:

3 0

3 years ago

Twenty toothpicks, each 6 cm long, form a figure consisting of six equilateral triangles and a rectangle as shown. What is the t

Roman55 [17]

The total area of the figure is 139.20 square centimeters

Areas

The area of a shape is the amount of space it occupies

<h3>Composite figure</h3>

The figure (see attachment) is a composite figure, and the total area is the sum of the areas of each shape that makes up the complete figure

The shape has 6 equilateral triangles, each of which has an area of:

$A_1 = \sqrt{\frac{3s^2}{4}}$

Where:

$s = 6$ --- the length of each toothpick

The area of the rectangle is then represented as:

$A_2 =3s \times s$

$A_2 =3s^2$

So, the total area of the figure is:

$Total = 6A_1 + A_2$

This gives

$Total =6 \times \sqrt{\frac{3s^2}{4}} + 3s^2$

Substitute 6 for s

$Total =6 \times \sqrt{\frac{3(6)^2}{4}} + 3(6)^2$

$Total =6 \times \sqrt{27} + 108$

$Total =6 \times 5.20+ 108$

$Total =139.20$

Hence, the total area of the figure is 139.20 square centimeters