Inductive reasoning is when someone uses lots of data to make a conjecture

Determine an equation for the right bisector of the line segment with endpoints J(-5,3) and K(3,-2)

Norma-Jean [14]

Answer:

$y=1.6x+2.1$

Step-by-step explanation:

we know that

The right bisector of the line segment JK is a perpendicular line to the segment JK that pass through the midpoint of segment JK

step 1

Find the midpoint JK

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

$J(-5,3),K(3,-2)$

substitute the values

$M(\frac{-5+3}{2},\frac{3-2}{2})$

$M(\frac{-2}{2},\frac{1}{2})$

$M(-1,\frac{1}{2})$

step 2

Find the slope JK

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$J(-5,3),K(3,-2)$

substitute

$m=\frac{-2-3}{3+5}$

$m=\frac{-5}{8}$

$m=-\frac{5}{8}$

step 3

Find the slope of the line perpendicular to the segment JK

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{5}{8}$ ----> slope of segment JK

Find m_2

substitute

$(-\frac{5}{8})*m_2=-1$

$m_2=\frac{8}{5}$

step 4

Find the equation for the right bisector of the line segment JK

The equation in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=\frac{8}{5}$

$point\ M(-1,\frac{1}{2})$

substitute

$y-\frac{1}{2}=\frac{8}{5}(x+1)$

Convert to slope intercept form

isolate the variable y

$y-\frac{1}{2}=\frac{8}{5}x+\frac{8}{5}$

$y=\frac{8}{5}x+\frac{8}{5}+\frac{1}{2}$

$y=\frac{8}{5}x+\frac{21}{10}$

$y=1.6x+2.1$

7 0

3 years ago

By what power of 10 can the divisor be multiplied to make it a whole number?

nirvana33 [79]

Step-by-step explanation:

The number divisible by 10 need to be even and divisible by 5, because the prime factors of 10 are 5 and 2. So, it means that for the number to be divisible by 10, the last digit needs to be a zero.

4 0

2 years ago

A teacher needs 70 lengths of string cut to 40cm each. If balls of string are 10 m long, how many balls will be needed.

Genrish500 [490]

Answer:

3

Step-by-step explanation:

A ball is 10 meters. Since 100 centimeters are in a meter, each ball has 100*10 = 1000 centimeters.

The teacher needs 70 strings each 40 centimeters. The total amount they need is 70*40 = 2800 centimeters.

Since a ball has 1000 centimeters, 2800 centimeters will need 3 balls for a total of 3000 centimeters.

5 0

3 years ago

If f(x) = 2x - 1, find f'(x).

Kitty [74]

Answer:f(x)=3

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Разстоянието между селищата A и B е 410 км.От A за B пътува лека кола със скорост 90km/h, а 1 h по-късно от B за A тръгва камион

harkovskaia [24]

4,56 км / ч просто разделят ускорението и точката на среща.

4 0

3 years ago