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Yuki888 [10]
3 years ago
6

For all integers n, if n2 is odd, then n is odd. Use a proof by contraposition, as in Lemma 1.1. Let n be an integer. Suppose th

at n is even, i.e., n =
Mathematics
1 answer:
Reil [10]3 years ago
8 0
Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"

Suppose n is even. That means n = 2k where k is any integer.

Square both sides

n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)

The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even. 

So this contradicts the initial statement which forces n to be odd. 
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dezoksy [38]
For every multivitamin tablet you take, you get 0.14 grams of vitamin C.

0.14 * 30 = 4.2

The question wants the answer in milligrams.

One milligram = 0.001 gram

4.2 / 0.001 = 42000
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So, 42000 is the answer.</span>
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3 years ago
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A triangle has sides with lengths of 8 inches, 15 inches, and 17 inches. Is it a right triangle?
In-s [12.5K]

Answer:

Yes

Step-by-step explanation:

A square plus b square equal c square

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Y=2 Enter the solution (x, y) to the system of equations shown 7y+3x=5
AnnyKZ [126]

Answer:

(x, y) = (-3, 2)

Step-by-step explanation:

Put the given value of y into the equation and solve for x.

... 7·2 +3x = 5

... 3x = -9 . . . . . . subtract 14

... x = -3 . . . . . . . divide by the x-coefficient

The solution (x, y) is (-3, 2).

6 0
3 years ago
Connor is stuck in a traffic jam on a single-lane road. The traffic report tells him the traffic jam stretches for 5.5 miles. If
dedylja [7]

Answer:

2323

Step-by-step explanation:

According to the questions above, the report from the traffic jam says the traffics jam stretches for 5.5 miles

As Connor assumes that each car is about 12.5 long

The next step is to convert 5.5 miles into feet.

Since 1 mile = 5280

To convert 5.5 miles, 5.5 x 5280 = 29040 feet  

To find the numbers of cars struck in traffic, we will have to divide 29040 by 12.5

29040/12.5 = 2323.3 ≅ 2323    

5 0
3 years ago
Can anyone help me?pls
Mama L [17]

Answer/Step-by-step explanation:

Given:

C = right angle = 90°

BC = a = ?

AB = c = 12

AC = b = 9

Required:

a, <A, and <B

Solution:

✔️Find a using Pythagorean Theorem:

a = √(c² - b²)

a = √12² - 9²) = √63

a = 7.93725393 = 8 (nearest whole number)

✔️Find A by applying trigonometric ratio:

Thus,

Reference angle = A

Hypotenuse = 12

Adjacent = 9

Therefore,

cos(A) = \frac{adj}{hyp} = \frac{9}{12}

cos(A) = 0.75

A = cos^{-1}(0.75)

m<A = 41° (nearest whole number)

✔️Find B:

m<B = 180 - (90 + 41) (sum of interior angles of triangle)

m<B = 49°

8 0
3 years ago
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