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kolezko [41]
3 years ago
12

Consider the following statement. ∀a ∈ Z, (a − 1) a is not an integer. (a) Select the correct negation for this statement. For e

very integer a, a − 1 a is an integer. There is an integer a such that a − 1 a is not an integer. For every integer a, a − 1 a is not an integer. There is an integer a such that a − 1 a is an integer. (b) Is the given statement true or false? If the statement is true, enter TRUE; if the statement is false, enter a value of a that could be used as part of a counterexample that justifies its falseness.
Mathematics
1 answer:
Marta_Voda [28]3 years ago
8 0

Answer:

a) There is an integer a such that  \frac{a-1}{a} is  an integer

b) False

Step-by-step explanation:

Statement : ∀a ∈ Z,    (a − 1) a is not an integer

A) The correct negation will be :

There is an integer a such that  \frac{a-1}{a} is  an integer

B) The Given statement is FALSE because

when we assume the value of a = 1

( a - 1 ) / a = (1 - 1 ) / 1 = 0   ;  which is an integer

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How would 2.25 be represented as a percent? A. 225% B. 22.5% C. 2.25% D. 0.0225
ivolga24 [154]

Answer:

A

Step-by-step explanation:

move decimal two places to get percent

2.25 = 225%

6 0
3 years ago
What is the value of x in the equation -5/8x = -160?
Brut [27]

Answer:

Step-by-step explanation:

-5           -160

----      =  ------

8x            1

Cross multiply

-1280x = -5

Divide both sides of the equation by -152

x = 256

I hope it helps :)

3 0
3 years ago
Read 2 more answers
Find the inverse of ????−7 −2
Masja [62]

Answer:

A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

Step-by-step explanation:

A=\begin{bmatrix}-7 & -2\\ 4 & 1\end{bmatrix}

det\ A=-7\times 1-(-2)\times 4\\\Rightarrow det\ A=1

A^{-1}=\frac{1}{det\ A}\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A^{-1}=\frac{1}{1}\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

\therefore A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

A.A^{-1}=\begin{bmatrix}-7 & -2\\ 4 & 1\end{bmatrix}\times \begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A.A^{-1}=\begin{pmatrix}\left(-7\right)\cdot \:1+\left(-2\right)\left(-4\right)&\left(-7\right)\cdot \:2+\left(-2\right)\left(-7\right)\\ 4\cdot \:1+1\cdot \left(-4\right)&4\cdot \:2+1\cdot \left(-7\right)\end{pmatrix}\\\Rightarrow A.A^{-1}=\begin{pmatrix}1&0\\ 0&1\end{pmatrix}

Hence, confirmed

6 0
3 years ago
PLZ HLP I DONT KNOW
bekas [8.4K]
It’s 1 hope it helps
3 0
3 years ago
Read 2 more answers
Does anyone know the 4 answers
Naya [18.7K]
Yes, you can divide $5 by 2. There are 100 cense in a dollar, 500 in five dollars, if you divide 500 by 2 you get 250 cense, with each 100 cense equaling $1. You would have $2.50.

Also, you got number 5 wrong, it’s how far he’s gone, not how far he has left.
7 0
3 years ago
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