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jekas [21]
3 years ago
14

Which of the following conjectures is false?Please give a counterexample!Thank youuu

Mathematics
1 answer:
MakcuM [25]3 years ago
6 0

Which of the following conjectures is false?

Solution: The false conjecture is:

J. The sum of two odd numbers is odd

Explanation:

F. The product of two even numbers is even.

For example: Let us take two even numbers 4 and 6.

The product of two even numbers is:

4 \times 6 = 24

Therefore, the product is also even number. Hence the conjecture is true.

G. The sum of two even numbers is even.

For example: Let us take two even numbers 4 and 6.

The sum of two even numbers is:

4+6 = 10

Therefore, the sum is also even number. Hence the conjecture is true.

H. The product of two odd numbers is odd.

For example: Let us take two odd numbers 3 and 5.

The product of two odd numbers is:

3\times5 = 15

Therefore, the product is also odd number. Hence the conjecture is true.

J. The sum of two odd numbers is odd.

For example: Let us take two odd numbers 3 and 5.

The sum of two odd numbers is:

3+5= 8

Therefore, the sum is not an odd number. Hence the conjecture is false.

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Let u,v,wu,v,w be three linearly independent vectors in R7R7. Determine a value of kk, k=k= , so that the set S={u−3v,v−2w,w−ku}
11Alexandr11 [23.1K]

Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

6 0
2 years ago
The perimeter of a rectangle is 154 feet. The length of the rectangle is 55 feet. What is the width of the rectangle?
alisha [4.7K]
Hi there! Okay well to find out the width when you all ready have the perimeter and length just add up both sides of the length, 55+55=110 okay now just subtract 110 from 154, 154-110=44 now since there are to sides for width in a rectangle divide 44 by 2, 44÷2=22 so your width is 22 now to check add up all your side's: 55+22+55+22=154 ANSWER: width = 22ft
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3 years ago
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Igoryamba

Answer:

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Step-by-step explanation:

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2 years ago
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Answer: 77°

Step-by-step explanation:

First we are going to find x and then insert it in 18x +5 to be able to get our <WZX

But to find x, we will have to apply the the exterior angle theorem

The exterior angle theorem state that : the exterior angle is equal to the sum of the two opposite interior anges

Using this theorem, then from the diagram above ;

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we collect like term

18x - 8x = 48-3-5

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