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4 years ago

N and p are integers greater than 1;

Mathematics

1 answer:

yan [13]4 years ago

5 0

Answer: 14

Step-by-step explanation:

We want the smallest value so:

we know 5n is the square of a number, so

n = 5a^2, so a > 1

we know 75np is the cube of a number, so

p= 3^2a = 9a

Now, n+p = 5a^2 + 9a = a [5a+9]

The smallest value would be when a=1

Therefore when you plug it in , n+p = 5+9 = 14

Hopefully that helped :)

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Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.

ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m= $\frac{-1}{4}$

Step-by-step explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m= $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

$m = \frac{0-(-4)}{0-(-1)} =4$

Two non-vertical lines are parallel if and only if their slopes are parallel

$m_{1} = m_{2}$

Therefore the slope of the line that is parallel to the another line

$m_{1} =m_{2} =4$

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

$m_{2} =\frac{-1}{4}$

Therefore the slope of the line is perpendicular to the another line is

$m=\frac{-1}{4}$

3 0

3 years ago

Read 2 more answers

Georgina works on the 30 floor she took an elevator to the 7 floor how many floors did she travel

svlad2 [7]

Georgina walk 23 floor
30 - 7 = 23

8 0

3 years ago

Help! this is urgent i need it rn ty in advance

olganol [36]

Answer:

The graph shows a steady declining plot as the aveage traffic volume increases. Since y axis is speed the correct answer is that as traffic volume increases the average vehicle speed decreases.

Step-by-step explanation:

4 0

2 years ago

cynthia and amy are customer service representives cynthia earns $13 per hour and amy earns $1.50 more per hour than cynthia. Am

Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

Let h bet the # of hours worked

If Cynthia earns $13 per hour then her equation would be:

C = $13h

If Amy makes $1.5 more per hour then her equation would be:

A = $14.5x

Now lets plug in some numbers:)

A = $14.5(43.5)

A = $630.75

7 0

3 years ago

Write an equation to represent each situation.

mina [271]

Answer:

18 years

Step-by-step explanation:

2(8+x) = 34+x

16+2x = 34+x

-18 = -x

4 0

3 years ago