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3 years ago

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

Mathematics

1 answer:

Stells [14]3 years ago

7 0

Answer:

See below

Step-by-step explanation:

25¹¹ - 5¹⁹

Convert to base 5 = (5²)¹¹ - 5¹⁹

= 5²² - 5¹⁹

Factor out the GCF = 5¹⁹(5³ - 1)

= 5¹⁹(125 - 1)

= 5¹⁹ × 124

= 5¹⁹ × 4 × 31

31 is a factor of 25¹¹ - 5¹⁹, so the expression is divisible by 31.

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4 years ago

Homework due at 12:00 I Need Help

Leya [2.2K]

Answer:

k = - 7.5

Step-by-step explanation:

Slope "m" of a line through points

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

is m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Slopes of perpendicular lines are opposite reciprocal: $m_{1}$ $m_{2}$ = - 1

~~~~~~~~~~~~~~~

The slope of a line through points (0, 7) and (2, 10)

$m_{1}$ = $\frac{10-7}{2-0}$ = $\frac{3}{2}$

Slope of perpendicular line through points (3, 5) and (k, 12) is $m_{2}$ = $-\frac{2}{3}$

or $m_{2}$ = $\frac{12-5}{k-3}$

$\frac{7}{k-3}$ = $-\frac{2}{3}$

2(k - 3) = - 21

k - 3 = - 10.5

k = - 7.5

6 0

3 years ago

A force of 61 N is applied to an area of 750 cm2. Calculate the pressure in N/m2. Give your answer to the nearest integer

Dafna11 [192]

Answer:

813 N/m²

Step-by-step explanation:

The units of pressure tell you it is found by dividing force by area. Here, we need to convert the units of the given area so we can express the pressure appropriately.

pressure = force / area

pressure = (61 N)/(750 cm² × ((1 m)/(100 cm))²) = (61 N)/(0.0750 m²)

pressure ≈ 813 N/m²

6 0

3 years ago

The coordinates of the vertices of triangle ABC are A(3,6), B(6, 3), and C(9, 9). If triangle ABC Is dilated by 1/3x and 1/3y to

katovenus [111]

Answer:

$A' = (1,2)$

$B'=(2,1)$

$C' =(3,3)$

Step-by-step explanation:

Given

$A = (3,6)$

$B = (6,3)$

$C = (9,9)$

$Scale = \frac{1}{3}$

Required

Determine the vertices of ABC

If truly the question asks for the vertices of ABC, then the vertices are:

$A = (3,6)$ $B = (6,3)$ $C = (9,9)$

However, I'm quite sure that's not the requirement of the question. So, I'll solve for A'B'C'

To do this, we simply multiply the vertices of ABC by the scale of dilation.

$(A'B'C') = Scale\ Factor * (ABC)$

$A' = \frac{1}{3} * A$

$A' = \frac{1}{3} * (3,6)$

$A' = (\frac{3}{3},\frac{6}{3})$

$A' = (1,2)$

$B' = \frac{1}{3} * B$

$B' = \frac{1}{3} * (6,3)$

$B' = (\frac{6}{3},\frac{3}{3})$

$B'=(2,1)$

$C' = \frac{1}{3} * C$

$C' = \frac{1}{3} * (9,9)$

$C' = (\frac{9}{3},\frac{9}{3})$

$C' =(3,3)$

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3 years ago

Select the equation that represents the function given in the table below.

masya89 [10]

Answer:

Step-by-step explanation:

The answer is D

y=1/2x-8

Take x=-6

Y=1/2(-6)-8=-11

Take X=-2

Y=1/2(-2)-8=-9

Take X=4

Y=1/2(4)-8=-6

Take X=8

Y=1/2(8)-8=-4

7 0

3 years ago