14.7 divided by 2.2=

Which of the following is a closed statement? Question 16 options: A) z is a positive number. B) x is an odd number. C) 30 is an

rusak2 [61]

Answer:

Step-by-step explanation:B) x es un número impar

3 0

3 years ago

A box of facial tissues is 22 cm by 10.5 cm by 8 cm how much cardboard is on the outside surface?

beks73 [17]

Dude y you even as its just the surface area you just use the formula

4 0

3 years ago

a regular hexagonal nut of side 1 cm and length 3 cm with a central hole of diameter 1 cm. 3 cm 1 cm 1 cm. Calculate the volume

Bogdan [553]

Answer:

5.44 cm³

Step-by-step explanation:

The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.

The area of a hexagon with side length s is given by ...

A = (3/2)√3·s²

For s=1 cm, the area is ...

A = (3/2)√3(1 cm)² = (3/2)√3 cm²

__

The area of a circle is given by ...

A = πr²

The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...

A = π(0.5 cm)² = 0.25π cm²

__

The volume is the face area multiplied by the length, so is ...

V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³

V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³

The volume of the metal is about 5.44 cm³.

5 0

2 years ago

the table shows the number of cars washed and the amount earned by the car wash over several days. circle the number or term tha

TEA [102]

The first 3 rows are proportional

because when you divide the earning by car washed they all have the same unit rate of 9.5/ to answer the second part you multiply 9.5 by 88. you'll get $836

5 0

3 years ago

Read 2 more answers

Use a proof by contradiction to show that the square root of 3 is national You may use the following fact: For any integer kirke

Ierofanga [76]

Answer:

1. Let us proof that √3 is an irrational number, using <em>reductio ad absurdum</em>. Assume that $\sqrt{3}=\frac{m}{n}$ where $m$ and $n$ are non negative integers, and the fraction $\frac{m}{n}$ is irreducible, i.e., the numbers $m$ and $n$ have no common factors.

Now, squaring the equality at the beginning we get that

$3=\frac{m^2}{n^2}$ (1)

which is equivalent to $3n^2=m^2$ . From this we can deduce that 3 divides the number $m^2$ , and necessarily 3 must divide $m$ . Thus, $m=3p$ , where $p$ is a non negative integer.

Substituting $m=3p$ into (1), we get

$3= \frac{9p^2}{n^2}$

which is equivalent to

$n^2=3p^2$ .

Thus, 3 divides $n^2$ and necessarily 3 must divide $n$ . Hence, $n=3q$ where $q$ is a non negative integer.

Notice that

$\frac{m}{n} = \frac{3p}{3q} = \frac{p}{q}$ .

The above equality means that the fraction $\frac{m}{n}$ is reducible, what contradicts our initial assumption. So, $\sqrt{3}$ is irrational.

2. Let us prove now that the multiplication of an integer and a rational number is a rational number. So, $r\in\mathbb{Q}$ , which is equivalent to say that $r=\frac{m}{n}$ where $m$ and $n$ are non negative integers. Also, assume that $k\in\mathbb{Z}$ . So, we want to prove that $k\cdot r\in\mathbb{Z}$ . Recall that an integer $k$ can be written as

$k=\frac{k}{1}$ .

Then,

$k\cdot r = \frac{k}{1}\frac{m}{n} = \frac{mk}{n}$ .

Notice that the product $mk$ is an integer. Thus, the fraction $\frac{mk}{n}$ is a rational number. Therefore, $k\cdot r\in\mathbb{Q}$ .

3. Let us prove by <em>reductio ad absurdum</em> that the sum of a rational number and an irrational number is an irrational number. So, we have $x$ is irrational and $p\in\mathbb{Q}$ .

Write $q=x+p$ and let us suppose that $q$ is a rational number. So, we get that

$x=q-p$ .

But the subtraction or addition of two rational numbers is rational too. Then, the number $x$ must be rational too, which is a clear contradiction with our hypothesis. Therefore, $x+p$ is irrational.

7 0

3 years ago