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2 years ago

Proving the Converse of the Parallelogram Side Theorem

Mathematics

1 answer:

butalik [34]2 years ago

7 0

Answer:

statement

the sum of two adjacent angle of a triangle is 180° . prove that sides are parallel.

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Find the simplified product where x>=0

irinina [24]

Answer:

The last one

Step-by-step explanation:

in the second part, x2 could to pull out as x

6 0

2 years ago

Read 2 more answers

If the atomic number of an element is 7 and its mass number is 16, how many neutrons are in the atom's nucleus

Margaret [11]

Number of Neutrons = Atomic mass - Atomic number
= 16 - 7 = 9

In short, Your Answer would be 9

Hope this helps!

7 0

3 years ago

Prove that u(n) is a group under the operation of multiplication modulo n.

katrin2010 [14]

Answer:

The answer is the proof so it is long.

The question doesn't define u(n), but it's not hard to guess.

Group G with operation ∘

For all a and b and c in G:

1) identity: e ∈ G, e∘a = a∘e = a,

2) inverse: a' ∈ G, a∘a' = a'∘a = e,

3) closed: a∘b ∈ G,

4) associative: (a∘b)∘c = a∘(b∘c),

5) (optional) commutative: a∘b = b∘a.

Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.

If n isn't prime, we exclude from the group all integers which share factors with n.

Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).

Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).

Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.

Associative and Commutative:

(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)

a∘b = b∘a because ab = ba.

5 0

2 years ago

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Find the area of the shaded sector of the circle. Leave your answer in terms of pi.

pentagon [3]

We know that
area of circle =pi*r²
for r=4 ft
area=pi*4²------> 16*pi ft²

<span>the shaded sector of the circle represent 3/4 of the total area
so
3/4*16*pi-----> 12*pi ft</span>²

the answer is
12*pi ft²

3 0

2 years ago

Read 2 more answers

How many students were surveyed about their mode of transportation to school?

AlekseyPX

Answer:

Total number of students surveyed about their mode of transportation to school is 400.

Step-by-step explanation:

Here, given student who uses car as their mode of transport = 120 students

We have to find the total number of students who are surveyed.

Also, since complete circle represents 100% of data,

Total students who uses at least one mode of transport out of foot, bicycle, bus or car let it be x students.