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Marrrta [24]
2 years ago
7

PLA

Mathematics
1 answer:
leva [86]2 years ago
7 0

Answer:

10

Step-by-step explanation:

1. 2(4.5)+1

2. 9+1

3. 10

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PLZ HELP I WILL MARK BRAINLEST IF CORRECT
Nataly_w [17]

they are equal or congruent because if you look at  it they both are right triangles

4 0
3 years ago
Need some help with this​
Katen [24]

Answer:

1/3

Step-by-step explanation:

Slope is rise over run

your rise is 1 (because you only go up one block each time)

your run is 3 ( because you go right three times)

so 1/3

3 0
2 years ago
10=a/2+7 will give Brainly
Finger [1]
10=a/2 + 7

First subtract 7 from both sides

3=a/2

Next multiple 2 on both sides, so that a is by itself

3(2)=a

A=6
8 0
3 years ago
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
Pls help! Due soon!!
bogdanovich [222]

Answer:

See below ~

Step-by-step explanation:

1. 3d + 2

2. John = Kelly - 6

3. y/4 - 3

4. Thomas = 2(Luis)

5. 8p + 6

6. x³ + 5

3 0
2 years ago
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