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Pie
3 years ago
14

Prove that 25^11−5^19 is divisible by 31.

Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
4 0

Answer:

Divisible by 3 is the answer

Step-by-step explanation:

First get everything to have the same base of 5

25^11 - 5^19

(5^2)^11 - 5^19

5^(2*11) - 5^19

5^22 - 5^19

Now factor out the GCF 5^19 to get

5^22 - 5^19

5^(19+3) - 5^(19+0)

5^19*5^3 - 5^19*5^0

5^19(5^3 - 5^0)

5^19(125 - 1)

5^19*(124)

At this point, we factor the 124 into 31*4 to end up with this full factorization: 5^19*31*4

Therefore, 25^11 - 5^19 is equivalent to 5^19*31*4

Since 31 is a factor of the original expression, this means the original expression is divisible by 31.

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The measure of the exterior angle of the triangle is what degree?
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Answer:

92°

Step-by-step explanation:

By exterior angle theorem:

(2x - 2) \degree = x \degree + 45 \degree \\  \\ (2x - 2 - x) \degree = 45 \degree \\  \\ (x - 2) \degree = 45 \degree \\  \\ (x - 2)  = 45 \\  \\ x = 45 + 2 \\  \\ x = 47 \\  \\ (2x - 2) \degree  = (2 \times 47 - 2)\degree  \\  \\ (2x - 2) \degree  = (94 - 2)\degree   \\  \\ (2x - 2) \degree  = 92\degree   \\  \\ measure  \: of  \: the  \: exterior \:  angle \\  = 92 \degree

4 0
3 years ago
If you take a number, times by 7 then subtract 1. You get the same as if you took the number multiply the number by 5 then subtr
Irina-Kira [14]

Answer:

-7/2 or -3.5

Step-by-step explanation:

Make the equation first

7x-1 = 5x-8

7 = -2x

-7/2 = x

4 0
2 years ago
Read 2 more answers
Find the ratio that is equivalent to 10:5.<br> OA) 15:5<br> OB) 5:10<br> OC) 2:1<br> OD 5:1
Vesnalui [34]

Answer:

OB) 2:1

Step-by-step explanation:

5 can go into 10 twice and 5 can go into itself once

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Answer:

180

Step-by-step explanation:

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two buildings stand 90 ft apart at their closest points, the angle of depression from the top of the taller building to the top
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<span>A new kind of temporary pavilion support for a square roof uses just two poles set at the diagonal corners of a square. The allowable distance between the poles is 18 feet. Find the area of the roof. The sides will have lengths of 18/sqrt(2). Since they are perpendicular, the area of the square will be (18^2)/2 = 81*4/2 = 162 square feet. 

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
8 0
3 years ago
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