You construct lines p, q, r, and s such that p || q, r ⊥ p, and s ⊥ q. Which of the following must be true?

Mathematics

1 answer:

jolli1 [7]3 years ago

4 0

Answer:

r ll s

Step-by-step explanation:

The easiest way to solve thi is to draw a picture .

P and Q are parallel, so draw those as two opposite seides of a square.

R and P are perpendictular so draw that as the top line of the square. Since it is perpendicular to P, R has to be perpendictular to Q.

Draw line S as the bottom line of the square and the same rules apply, so R is parallel to S

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PLEASE HELP! Calculate $40^{13} \pmod{85}.$

SVEN [57.7K]

In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

Notice

40*40*40=64,000

so we check how many time does 85 fit into 64,000:

64,000/85=752.94

85*753=64,005; 64000-64,005=-5

this means that

$40^{3} =-5\pmod{85}$

thus

$40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}$

Answer: 10 (mod85)

Remark, the set of all solutions is:

{......-75, 10, 95, .....}, that is 85k +10

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The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number

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Let the smaller number be x.

Given, the larger number is 7 times the smaller number.

So, the larger number = 7x.