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asambeis [7]
3 years ago
5

Line m passes through the points (5, 1) and (8, 6) while line n passes through the points (-4, 3) and (-1, 8). Which statement a

ccurately describes the relationship between the two lines? A. Lines m and n have the same slope so they are perpendicular. B. Lines m and n have opposite reciprocal slopes so they are perpendicular. C. Lines m and n have opposite reciprocal slopes so they are parallel. D. Lines m and n have the same slope so they are parallel.
Mathematics
1 answer:
Anna [14]3 years ago
8 0
Find the equations of the lines...

First find the slope...(y2-y1)/(x2-x1)=m

m=(6-1)/(8-5)=5/3 and it passes through (5,1) so

y=mx+b becomes:

y=5x/3+b and using (5,1)

1=5(5)/3+b

1=25/3+b

3/3-25/3=b

b=-22/3 so 

y1=(5x-22)/3

.... now y2...

m=(8-3)/(-1--4)=5/3 (note it has the same slope as y1...

y=5x/3+b and using the point (-1,8)

8=5(-1)/3+b

8=-5/3+b

24/3+5/3=b

b=29/3, now note that the y-intercept is different...

y2=(5x+29)/3

Since these lines have the same slope but different y-intercepts, they are parallel to each other. (and will never intersect.)
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A family tree business removes overgrown trees for 3 months in the summer. In June, they removed 1/3 the number of trees as they
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Answer: 299

Step-by-step explanation:

Given

Family removes one-third of tress in June as much as they dd in July

They remove twice the number of July in august

Suppose they removed x trees in July

for June it is, \frac{x}{3}

for August, it is 2x

If they removed less than 1000 tress in 3 months

\Rightarrow \dfrac{x}{3}+x+2x

So, maximum number of tress removed in July is 299

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3 years ago
How do i find the sum or difference of this fraction
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7 0
3 years ago
Uma secretária possui 6 camisas, 4 saias, e 3 pares de sapatos. Qual o número de maneiras distintas com que a secretária poderá
juin [17]

Answer:

72 maneiras

Step-by-step explanation:

O que acontecerá aqui é que um de cada tipo de roupa será selecionado.

Das 6 camisas, 1 será selecionada O número de maneiras pelas quais podemos fazer isso é 6C1 = 6

Das saias também, ela estará selecionando uma O número de maneiras que isso pode ser feito é 4C1 = 4

O terceiro é selecionar um par de sapatos de 3 e isso seria 3C1 = 3

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6 0
3 years ago
Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bott
SpyIntel [72]

Answer:

<em>Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2</em>

<em></em>

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = \frac{1}{2}bh

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  \frac{1}{2}*4*2.24 = 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = <em>8.96 ft^2</em>

For the rectangular sections of the roof, area is

A = lh

where l is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = <em>30 ft^2</em>

<em></em>

For the bottom face, area is

A = lw

where l is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = <em>20 ft^2</em>

<em></em>

Surface area of the roof of the dog kennel is

<em>8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2</em>

4 0
2 years ago
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