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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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Please help thanks thanks thanks ty
Archy [21]

Answer:

104 degrees

Step-by-step explanation:

First let's start by finding Angle DGC. Since Angle FGD and DGC are a linear pair, Angle DGC = 180-90 = 90 degrees.

Next we need to find GDC

Angles in a triangle add up to 180 degrees therefore...

Angle GDC + DCG + DGC = 180

Plug in the values we found into the equation

Angle GDC + 37 + 90 = 180

Angle GDC + 127 = 180

Angle GDC = 53

Therefore Angle ADC = 53 + 51 = 104 degrees

Since ABCD is a parallelogram, then opposite angles are equal therefore...

Angle B = 104 degrees

3 0
2 years ago
A washer and a dryer cost $664 combined. The washer costs $86 less than the dryer. What is the cost of the dryer?
andreyandreev [35.5K]

Answer:

The dryer is 375 dollars

Step-by-step explanation:

The equation would be

664=(D)+(D-86) or

664=(375)+(375-86)

4 0
2 years ago
What is the value of the fourth term in the geometric sequence
ivanzaharov [21]

Answer:

a(4) = 15/4

Step-by-step explanation:

Here we're told that the first term is a(1) = 30 and that the common factor r = 1/2.

Thus, the geometric sequence formula specific to this case is

a(n) = 30(1/:2)^(n-1).

What is the fourth term?  Let n = 4,

a(4) = 30(1/2)^(4-1), or a(4) = 30(1/2)^(3), or  a(4) = 30(1/8) = 30/8, or, in reduced form,

a(4) = 15/4.

6 0
2 years ago
Without actual division prove that x4 +2x3 -2x2 +2x -3 is exactly divisible by<br> x2 +2x-3
Brut [27]

Answer:

Step-by-step explanation:                

\displaystyle\Large\boldsymbol{} x^4+2x^3-2x^2+2x-3= \\\\\\x^4+2x^2(x-1)+2x-\underbrace{2-1}_{-3}=  \\\\\\x^4-1+2x^2(x-1)+2x-2 = \\\\\\(x^2-1)(x^2+1)+2x^2(x-1)+2(x-1) = \\\\\\\underline{(x-1)}(x+1)(x^2+1)+2x^2\underline{(x-1)} +2\underline{(x-1)} =\\\\\\(x-1)((x+1)(x^2+1)+2x^2+2)=\\\\\\(x-1)(x^3+x^2+2x^2+x+2+1)=\\\\\\(x-1)(x^3+3x^2+x+3) =\\\\\\(x-1)( \underline{(x+3)}x^2+\underline{(x+3)})=(x^2+1)\underbrace{(x-1)(x+3)}_{x^2+2x-3}= \\\\\\(x^2+1)(x^2+2x-3) : (x^2+2x-3)=x^2+1

7 0
2 years ago
Can two different numbers have the same absolute value if your Give me Give an example if no explain why not
svlad2 [7]
Yes they can just think of numbers with opposite signs
I-5I=I+5I the absoulte value is 5

4 0
3 years ago
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