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Wewaii [24]
3 years ago
10

Number 15. Find the equation of the line that passes through (3,-1) and is perpendicular to the line that passes through (-5, 2)

and (-1, 7)

Mathematics
1 answer:
MArishka [77]3 years ago
3 0
For lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

So we first need to find the slope of the reference line.

m=(y2-y1)/(x2-x1)=(7-2)/(-1--5)=5/4

So the perpendicular line will have a slope of:

5m/4=-1

m=-4/5

So our perpendicular line so far is:

y=-4x/5+b, now we can use point (3,-1) to solve for the y-intercept, "b"

-1=-4(3)/5+b

-1=-12/5+b

-5/5+12/5=b

7/5=b

So the line is:

y=-4x/5+7/5 or more neatly

y=(-4x+7)/5

y=-0.8x+1.4
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Answer:

Step-by-step explanation:

In order to make a specific shade of green paint, a painter mixes 1 1/2 quarts of blue paint. Converting 1.5 quarts to cup,

1 quart = 4 cups

1.5 quarts = 1.5 × 4 = 6 cups

She also used 1/2 gallon of white paint. Converting 0.5 gallons to cup,

0.0625 gallons = 1 cup

0.5 gallons = 0.5/0.0625 = 8 cups

This means that the ratio of cups of blue paint to green paint to white paint is 6: 2 :8

Total ratio = 6 +2 + 8 = 16

To make 100 cups of this shade of green,

Cups of blue paint needed = 6/16 × 100 = 37.5 cups

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3 years ago
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Answer:

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A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as it is wide. Both the banner and the po
Svetradugi [14.3K]

The length and width of poster are 9 inches and 3 inches respectively and length and width of banner are 10 inches and 2 inches respectively

<u> Solution:</u>

Given, A rectangular poster is 3 times as long as it is wide.  

Rectangular banner is 5 times as long as it is wide.  

Both the banner and the poster have perimeters of 24 inches

Let, the width of poster be p, then its length will be 3p

And, the width of banner be b, then its length will be 5b

Now, according to given information,

Perimeter of poster = 24 inches and perimeter of banner = 24 inches

2(length of poster + width of poster) = 24

2(3p + p) = 24

2(4p) = 24

8p = 24

p = 3

And 2(length of banner + width of banner) = 24

2(5b + b) = 24

2(6b) = 24

12b = 24

b = 2

So, width of poster is 3 inches, then length of poster is 3p = 3 x 3 = 9 inches

And, width of banner is 2 inches, then length of banner is 5b = 5 x 2 = 10 inches

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