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Katyanochek1 [597]
3 years ago
9

Consider the following statement: ∀ integers n, if n2 is even then n is even. Which of the following are equivalent ways of expr

essing this statement? a. All integers have even squares and are even. b. Given any integer whose square is even, that integer is itself even. c. For all integers, there are some whose square is even. d. Any integer with an even square is even. e. If the square of an integer is even, then that integer is even. f. All even integers have even squares
Mathematics
1 answer:
Leni [432]3 years ago
6 0

Answer:

B, D, E, F.

Step-by-step explanation:

In the statement, the square of an even integer is even. From the options provided, we have to select the ones that provide similar ways of expressing this.

Options B, D, E, F provided with the question and reproduced below convey the same statement in different ways:

B: Given any integer whose square is even, that integer is itself even.;

D: Any integer with an even square is even.;

E: If the square of an integer is even, then that integer is even and  

F: All even integers have even squares.

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What is1/12+7/9. I need help.
Katarina [22]
You have to make them have their least common denominator to add or subtract, in this case 36.
Multiply 1/12 by 3, to get the denominator 36: 3/36.
Multiply 7/9 by 4, to get the denominator 36: 28/36.
Now add the numerators: 3+28=31, 31/36 is as simplified as possible so your answer is 31/36 :) I hope this helps :)
7 0
3 years ago
Consider the following function. f(x) = 16 − x2/3 Find f(−64) and f(64). f(−64) = f(64) = Find all values c in (−64, 64) such th
VARVARA [1.3K]

Answer:

This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−64, 64).

Step-by-step explanation:

The given function is

f(x)=16-\frac{x^2}{3}

To find f(-64), we substitute x=-64 into the function.

f(-64)=16-\frac{(-64)^2}{3}

f(-64)=16-\frac{4096}{3}

f(-64)=-\frac{4048}{3}

To find f(64), we substitute x=64 into the function.

f(64)=16-\frac{(64)^2}{3}

f(64)=16-\frac{4096}{3}

f(64)=-\frac{4048}{3}

To find f'(c), we must first find f'(x).

f'(x)=-\frac{2x}{3}

This implies that;

f'(c)=-\frac{2c}{3}

f'(c)=0

\Rightarrow -\frac{2c}{3}=0

\Rightarrow -\frac{2c}{3}\times -\frac{3}{2}=0\times -\frac{3}{2}

c=0

For this function to satisfy the Rolle's Theorem;

It must be continuous on [-64,64].

It must be differentiable  on (-64,64).

and

f(-64)=f(64).

All the hypotheses are met, hence this does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−64, 64) is the correct choice.

6 0
3 years ago
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If the 10 is being multiplied it’s 90
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The variable, y, varies directly with x. if y = 20 when x = 25, what is y when x = 43? Also please explain so I can understand t
Gwar [14]

Answer:

25

Step-by-step explanation:

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2 years ago
If the frequency of hba homozygotes is 0.1 what is the value of p2
Angelina_Jolie [31]

we know that

p^2 is the the frequency of hba homozygote

we are given

frequency of hba homozygotes is 0.1

so,

p^2 =frequency of hba homozygotes

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and we get

p^2=0.1..............Answer

3 0
3 years ago
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