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3 years ago

5

Two of the Boy Scouts (exercise 19), Tom and Jerry, are weightlifters. They carry 50 lb. per trip. How many trips will each scou

t have to make?

1 answer:

steposvetlana [31]3 years ago

3 0

Answer:

is the the whole question ?

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A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:

Dima020 [189]

Answer:

Part A) $y=\frac{3}{4}x-\frac{1}{4}$

Part B) $y=\frac{2}{7}x-\frac{5}{7}$

Part C) $y=\frac{2}{7}x+\frac{8}{7}$

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment NM

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

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

we have

N(3, 2) and M(-1,-1)

substitute the values

$m=\frac{-1-2}{-1-3}$

$m=\frac{-3}{-4}$

$m=\frac{3}{4}$

step 3

Find the equation of the line in point slope form

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

we have

$m=\frac{3}{4}$

$point\ N(3, 2)$

substitute

$y-2=\frac{3}{4}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{3}{4}x-\frac{9}{4}$

$y=\frac{3}{4}x-\frac{9}{4}+2$

$y=\frac{3}{4}x-\frac{1}{4}$

Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 3

Find the slope of the perpendicular line to segment LP

Remember that

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

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

so

$m_2=\frac{2}{7}$

step 4

Find the equation of the line in point slope form

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

we have

$m=\frac{2}{7}$

$point\ M(-1,-1)$ ----> midpoint LP

substitute

$y+1=\frac{2}{7}(x+1)$

step 5

Convert to slope intercept form

Isolate the variable y

$y+1=\frac{2}{7}x+\frac{2}{7}$

$y=\frac{2}{7}x+\frac{2}{7}-1$

$y=\frac{2}{7}x-\frac{5}{7}$

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 2

Find the slope of the perpendicular line to segment LP

Remember that

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

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

so

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

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

we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

7 0

3 years ago

Write an recursive formula for An, the nth term of the sequence<br> 5, -2, -9,

oksian1 [2.3K]

Given:

The given sequence is:

$5,-2,-9,...$

To find:

The recursive formula for $a_n$ , the nth term of the sequence.

Solution:

We have,

$5,-2,-9,...$

Here, the first term is 5.

$-2-5=-7$

$-9-(-2)=-9+2$

$-9-(-2)=-7$

The common difference is -7.

The recursive formula for the nth term of the sequence is

$a_n=a_{n-1}+d$

Where, $d$ is the common difference.

Putting $d=-7$ in the above formula, we get

$a_n=a_{n-1}+(-7)$

$a_n=a_{n-1}-7$

Therefore, the recursive formula for the nth term of the sequence is $a_n=a_{n-1}-7$ .

3 0

2 years ago

1. The value of 20 x 5º =............

photoshop1234 [79]

Answer: salt

Step-by-step explanation:

4 0

3 years ago

What is the slope in y-6=-2 (x-7)

amid [387]

<span>y-6=-2 (x-7)

Start by distributing..

y - 6 = - 2x + 14

Add 6 to both sides...

y = - 2x + 20

Slope of this equation is -2</span>

5 0

3 years ago

Read 2 more answers

To make a salad dressing you mix vinegar and olive oil in the ratio 2:5 how much olive oil is needed with 20 ml of vinegar

eduard

Answer:

Step-by-step explanation:

Set this up as a proportion with the ratios being

$\frac{vinegar}{oil}$ If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:

$\frac{v}{o}:\frac{2}{5}$ and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:

$\frac{v}{o}:\frac{2}{5}=\frac{20}{x}$ and cross multiply.

2x = 100 so

x = 50 ml of oil

3 0

3 years ago