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labwork [276]
2 years ago
12

The infinite sequence $T=\{t_0,t_1,t_2,\ldots\}$ is defined as $t_0=0,$ $t_1=1,$ and $t_n=t_{n-2}+t_{n-1}$ for all integers $n&g

t;1.$ If $a,$ $b,$ $c$ are fixed non-negative integers such that\begin{align*} a&\equiv 5\pmod {16}\\ b&\equiv 10\pmod {16}\\ c&\equiv 15\pmod {16}, \end{align*}then what is the remainder when $t_a+t_b+t_c$ is divided by $7?$ You can use a LaTeX renderer to see what this says.
Mathematics
1 answer:
katrin [286]2 years ago
6 0

t_n are the Fibonacci numbers,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Taken modulo 7, we get the sequence

0, 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6, 1, ...

that repeats with period 16 (this is known as the 7th Pisano period).

This is to say,

t_a\equiv t_{16n+5}\equiv t_5\equiv5\pmod7

t_b\equiv t_{16n+10}\equiv t_{10}\equiv6\pmod7

t_c\equiv t_{16n+15}\equiv t_{15}\equiv1\pmod7

so that

(t_a+t_b+t_c)\equiv(5+6+1)\equiv\boxed5\pmod7

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Transversal cuts parallel lines and at points X and Y respectively. The point nearest to C is X, and the point nearest to D is Y
hammer [34]

Answer:  The answer is (B) ∠SYD.


Step-by-step explanation: As mentioned in the question, two parallel lines PQ and RS are drawn in the attached figure. The transversal CD cut the lines PQ and RS at the points X and Y respectively.

We are given four angles, out of which one should be chosen which is congruent to ∠CXP.

The angles lying on opposite sides of the transversal and outside the two parallel lines are called alternate exterior angles.

For example, in the figure attached, ∠CXP, ∠SYD and ∠CXQ, ∠RYD are pairs of alternate exterior angles.

Now, the theorem of alternate exterior angles states that if the two lines are parallel having a transversal, then alternate exterior angles are congruent to each other.

Thus, we have

∠CXP ≅ ∠SYD.

So, option (B) is correct.

5 0
2 years ago
Of the 100 entries in a costume contest, 39 entrants were dressed as heroes and 45 entrants were wearing a mask. If 21 entrants
ehidna [41]

Correct question with correct options has been attached

Answer:

37

Step-by-step explanation:

Let C represent those dressed as heroes and let B represent those wearing mask

Thus;

n(C) = 39

n(D) = 45

We are told that 21 entrants were dressed as heroes wearing a mask.

Thus; n(C n D) = 21

We are also told that there were a total of 100 entries.

Thus, n(T) = 100

Now, number of entrants neither dressed as heroes nor wearing a mask is given by;

n(T) - n(C u D)

n(C u D) = n(C) + n(D) - n(C n D)

n(C u D) = 39 + 45 - 21

n(C u D) = 63

Thus;number of entrants neither dressed as heroes nor wearing a mask is: 100 - 63 = 37

3 0
3 years ago
Find the difference of 8xand twice the sum of x and 7.
Anna11 [10]

Answer -

8x - (sum of x and 7)

= 8x - (x + 7)

= 8x - x - 7

= 7x - 7

= 7(x - 1)

3 0
2 years ago
Please help please I don’t know :( explain please
Bas_tet [7]

Answer:

t = 5

Step-by-step explanation:

It's asking what t needs to equal for the equation to be equivalent to -44.

-10t + 6 = -44

-10t = -50

t = 5

check

-10(5) + 6 = -44

-50 + 6 = -44

-44 = -44

3 0
3 years ago
Read 2 more answers
Factorise 49x^2-121 what’s the answer
asambeis [7]

Answer:

( 7x + 11  )( 7x-  11 )

Step-by-step explanation:

( 7x + 11  )( 7x-  11 )

Because 7*7 is 49

-11*11= -121

7*11=77

-7*11= -77

77-77=0

so the answer is 49x^2-121

8 0
3 years ago
Read 2 more answers
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