All categories

3 years ago

N - 89 > 171. what inequality below true. 1. n=82. 2. n=105. 3. n=268. 4. n=300. 5. n=312

Mathematics

1 answer:

Maru [420]3 years ago

7 0

Answer:

1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.

Square the equality √2 + √3 = r − √5 to obtain 5 + 2

√6 = r2 + 5 − 2r

√5. It follows

that 2√6 + 2r

√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r

√30

is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is

irrational can now be applied to show that this is not true. Write √30 = m

n in lowest

terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because

2( m

2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest

terms, a contradiction. We conclude that the initial assumption was false, and therefore

√2 + √3 + √5 is irrational.

Step-by-step explanation:

You might be interested in

Can someone please help meee

valentinak56 [21]

Answer:

with a line accross the points

4 0

2 years ago

Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus. use the distance formula

riadik2000 [5.3K]

In order to prove this, we have to put the trapezoid to the coordinate system. In the attached photo you can see how it has to be put. The coordinates for the vertices of trapezoid written according to the midpoint principle. By using the distance between two points formula, we can find the coordinates for the vertices of the rhombus.
$D_{x} = \frac{-2b-2a}{2}=-b-a$ and $D_{y}= \frac{2c+0}{2}=c$ . The coordinates of D is $(-b-a, c)$
$E_{x} = \frac{-2b+2b}{2}=0$ and $E_{y}= \frac{2c+2c}{2}=2c$ . The coordinates of E is $(0,2c)$
Since we have the reflection in this graph, the coordinates of F is $(b+a, c)$
And the coordinates of G is (0,0).

Using the distance formula, we can find that
$DE= \sqrt{(-b-a)^{2}+ c^{2}}=\sqrt{(b+a)^{2} + c^{2}}$
$EF= \sqrt{(b+a)^{2} + c^{2} }$
$GF= \sqrt{(b+a )^{2} + c^{2} }$
$DG= \sqrt{(b+a)^{2}+ c^{2}$

Since all the sides are equal this completes our proof. Additionally, we can find the distances of EG and DF in order to show that the diagonals of this rhombus are not equal. So that it is not a square, but rhombus.

6 0

3 years ago

Read 2 more answers

A university law school accepts 7 out of every 12 applicants. If the school accepted 686 students, find how many applications th

jeyben [28]

Answer:

1176 applications

Step-by-step explanation:

7:12 accepted:applied

686 = 7

686 / 7 = 98

98 x 12 = 1176

4 0

3 years ago

One-half of a number y is more than 22

Anit [1.1K]

Given that,

$\frac{1}{2}y \ \textgreater \ 22$

$\frac{y}{2} \ \textgreater \ 22$

$y \ \textgreater \ 22*2$

$y \ \textgreater \ 44$

Hence, y is any number greater than 44.

4 0

3 years ago

Read 2 more answers

Select the proper inverse operation to check the answer to 14 + 17 = 31. A. 31 × 14 = 17 B. 31 ÷ 17 = 14 C. 31 − 17 = 14 D. 14 −

timama [110]

The solution is c ...

4 0

3 years ago

N - 89 > 171. what inequality below true. 1. n=82. 2. n=105. 3. n=268. 4. n=300. 5. n=312​

N - 89 > 171. what inequality below true. 1. n=82. 2. n=105. 3. n=268. 4. n=300. 5. n=312