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3 years ago

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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How do you translate the graph of f(x) = x3 left 4 units and down 2 units? Identify the equation of the graph

Marina CMI [18]

Answer:

The correct option is B.

Step-by-step explanation:

The given function is

$f(x)=x^3$

The translation of a function is defined as

$g(x)=f(x+a)+b$

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3 years ago

Read 2 more answers

Find the number whose arithmetic square root is 0.6

slavikrds [6]

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Step-by-step explanation:

6/10 x 6.10= 36/100

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3 years ago

What is the equation of the function shown in the graph provided? y= _ x + _

Mkey [24]

Answer:

y = -3x - 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step-by-step explanation:

Step 1: Define

Find points from graph.

x-intercept (-2, 0)

y-intercept (0, -6)

Step 2: Find slope m

Substitute: $m=\frac{-6-0}{0+2}$
Subtract/Add: $m=\frac{-6}{2}$
Divide: $m=-3$

Step 3: Redefine

Slope m = -3

y-intercept b = -6

Step 4: Write linear equation

Slope-Intercept Form: y = -3x - 6

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3 years ago