1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anettt [7]
3 years ago
15

A clockwise rotation of 90 degrees is equivalent to a counter clockwise rotation of how many degrees?

Mathematics
2 answers:
Veseljchak [2.6K]3 years ago
7 0
If it's two full rotations its 360 degrees
WARRIOR [948]3 years ago
5 0
Equivalent to 180 degrees. 90 degrees clockwise +90 degrees
You might be interested in
I'll give 20 p to whoever answers 10-16 :D
BartSMP [9]
This is so easy. You should try before posting a question on this site. No offense. 

Having said that im still here to help :)

10. 4,2  -3,5
11. Sorry dont know this one
12. Plot a point at -3,-4 label is Resturant
13. Plot a point at 0,-3 label it Beth

I will only post these ones, The others are extremely simple. 

6 0
3 years ago
PLZ HELP MEEEE!!!
LiRa [457]

Answer:

D

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Prove that if n is a perfect square then n + 2 is not a perfect square
notka56 [123]

Answer:

This statement can be proven by contradiction for n \in \mathbb{N} (including the case where n = 0.)

\text{Let $n \in \mathbb{N}$ be a perfect square}.

\textbf{Case 1.} ~ \text{n = 0}:

\text{$n + 2 = 2$, which isn't a perfect square}.

\text{Claim verified for $n = 0$}.

\textbf{Case 2.} ~ \text{$n \in \mathbb{N}$ and $n \ne 0$. Hence $n \ge 1$}.

\text{Assume that $n$ is a perfect square}.

\text{$\iff$ $\exists$ $a \in \mathbb{N}$ s.t. $a^2 = n$}.

\text{Assume $\textit{by contradiction}$ that $(n + 2)$ is a perfect square}.

\text{$\iff$ $\exists$ $b \in \mathbb{N}$ s.t. $b^2 = n + 2$}.

\text{$n + 2 > n > 0$ $\implies$ $b = \sqrt{n + 2} > \sqrt{n} = a$}.

\text{$a,\, b \in \mathbb{N} \subset \mathbb{Z}$ $\implies b - a = b + (- a) \in \mathbb{Z}$}.

\text{$b > a \implies b - a > 0$. Therefore, $b - a \ge 1$}.

\text{$\implies b \ge a + 1$}.

\text{$\implies n+ 2 = b^2 \ge (a + 1)^2= a^2 + 2\, a + 1 = n + 2\, a + 1$}.

\text{$\iff 1 \ge 2\,a $}.

\text{$\displaystyle \iff a \le \frac{1}{2}$}.

\text{Contradiction (with the assumption that $a \ge 1$)}.

\text{Hence the original claim is verified for $n \in \mathbb{N}\backslash\{0\}$}.

\text{Hence the claim is true for all $n \in \mathbb{N}$}.

Step-by-step explanation:

Assume that the natural number n \in \mathbb{N} is a perfect square. Then, (by the definition of perfect squares) there should exist a natural number a (a \in \mathbb{N}) such that a^2 = n.

Assume by contradiction that n + 2 is indeed a perfect square. Then there should exist another natural number b \in \mathbb{N} such that b^2 = (n + 2).

Note, that since (n + 2) > n \ge 0, \sqrt{n + 2} > \sqrt{n}. Since b = \sqrt{n + 2} while a = \sqrt{n}, one can conclude that b > a.

Keep in mind that both a and b are natural numbers. The minimum separation between two natural numbers is 1. In other words, if b > a, then it must be true that b \ge a + 1.

Take the square of both sides, and the inequality should still be true. (To do so, start by multiplying both sides by (a + 1) and use the fact that b \ge a + 1 to make the left-hand side b^2.)

b^2 \ge (a + 1)^2.

Expand the right-hand side using the binomial theorem:

(a + 1)^2 = a^2 + 2\,a + 1.

b^2 \ge a^2 + 2\,a + 1.

However, recall that it was assumed that a^2 = n and b^2 = n + 2. Therefore,

\underbrace{b^2}_{=n + 2)} \ge \underbrace{a^2}_{=n} + 2\,a + 1.

n + 2 \ge n + 2\, a + 1.

Subtract n + 1 from both sides of the inequality:

1 \ge 2\, a.

\displaystyle a \le \frac{1}{2} = 0.5.

Recall that a was assumed to be a natural number. In other words, a \ge 0 and a must be an integer. Hence, the only possible value of a would be 0.

Since a could be equal 0, there's not yet a valid contradiction. To produce the contradiction and complete the proof, it would be necessary to show that a = 0 just won't work as in the assumption.

If indeed a = 0, then n = a^2 = 0. n + 2 = 2, which isn't a perfect square. That contradicts the assumption that if n = 0 is a perfect square, n + 2 = 2 would be a perfect square. Hence, by contradiction, one can conclude that

\text{if $n$ is a perfect square, then $n + 2$ is not a perfect square.}.

Note that to produce a more well-rounded proof, it would likely be helpful to go back to the beginning of the proof, and show that n \ne 0. Then one can assume without loss of generality that n \ne 0. In that case, the fact that \displaystyle a \le \frac{1}{2} is good enough to count as a contradiction.

7 0
3 years ago
Why wuld 8/4 be considerd a whole number
kumpel [21]

Answer:

because 8/4=2

Step-by-step explanation:

4/4=1

8/4=2

it's because the numerator is bigger if it were 6/4 it would be a mixed number but the eight goes in to 4 directly 2 time so therefore it's 2.

3 0
3 years ago
how to wrok out a rate of 15 orders every 5 hours. At this rate, how many hours will it take to ship 156 orders
VLD [36.1K]

Answer:

52 hours

Step-by-step explanation:

Given that it takes 15 orders every 5 hours.

With that we can find that it takes 3 orders every hour. Using that we can find that in 52 they would have shipped 156 orders

With that we find that the answer is 52 hours

4 0
3 years ago
Other questions:
  • One number is 8 a first number . A third number is 100 more than the first number . If the sum of three numbers is 750, find the
    5·1 answer
  • Find the product 14,560 × 10
    15·2 answers
  • In a survey, 600 adults in a certain country were asked how many hours they worked in the
    13·1 answer
  • Given the function ƒ(x) = 5x2 − 9x + 18, find ƒ(3).
    14·1 answer
  • Here are the LETTERS that goes with the file<br> <br> A=3<br> B=4<br> C=6<br> D=2
    14·1 answer
  • What's 42/66 in simplest form
    7·2 answers
  • What is the TOTAL area of a square with sides that are 67 cm and a rectangle with sides that are 47cm long and 27cm wide?
    11·2 answers
  • Can someone solve 2x+3=5x-2<br> step by step
    15·2 answers
  • Mk pls somebodyyyy help :)
    11·1 answer
  • Gumawa ng bilog na grap (pie graph) na nagpa
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!