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3 years ago

Why is it preferable to measure a penny in millimeters?

Mathematics

1 answer:

White raven [17]3 years ago

5 0

When measuring a penny, using the millimeter measurement would be more accurate then using inches or centimeters.

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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

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

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

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

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

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

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

Referring to the Fig. in Question #40, find the unknown<br> length Y.

icang [17]

Answer:

tan30°=7/x

$\frac{1}{ \sqrt{3} } = \frac{7}{x } \\ x = 7 \sqrt{3}$

cos30°=x/y

$\frac{ \sqrt{3} }{2} = \frac{7 \sqrt{3} }{y} \\ \\ 7 \sqrt{3} \times 2 = \sqrt{3} \times y \\ \frac{7 \sqrt{3 } \times 2}{ \sqrt{3} } = y \\7 \times 2 = y \\ 14 = y$

tell me if it's wrong.

7 0

2 years ago

Read 2 more answers

Please Help here, i really need this joe

NNADVOKAT [17]

Answer:

The first answer choice, 4632.5

Step-by-step explanation:

At the rate of 85 feet per hour, after 5.5 hours the apprentice would have covered 467.5 square feet. Subtracting this from the total amount of 5,100 square feet, you get 4632.5, or the first answer choice. Hope this helps!

5 0

2 years ago

Read 2 more answers

Please help with this question!! Due soon

solmaris [256]

Answer:

$1,855

Step-by-step explanation:

Rent per year = $15.90 psf

Hence,

Rent per month = 15.90/12 psf = $1.325 psf

Rent of the store per month

= 1400 * $1.325 psf

= $1,855

6 0

3 years ago

Which verbal expression best describes the algebraic expression 2x ÷ 4?

Vlada [557]

Let's reason through the answers...

A) Do you see any sums? Any addition? Me neither... it's not A.

B) Well I see a product of 2 and "some number," but are we dividing by 2? Nope. Not B.

C) I see a quotient (2x) divided by 4, but the "some number" is not being multiplied by four. Not C.

D) Well this is the only one left, so it better be this one! We have a quotient, and we have two times some number (2x). The quotient (the division) is of 2x and four. This is it! It's D.

5 0

3 years ago