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Usimov [2.4K]
3 years ago
12

If the area of Bianca’s rectangular backyard patio is represented by the expression x2−18x + 81, and the length of the patio is

represented by the expression x-9, what is the expression for the width of the patio and what special rectangular shape is the patio? Explain and show all work when factoring.
Mathematics
1 answer:
frosja888 [35]3 years ago
4 0

Answer:

a square backyard with width (x - 9)

Step-by-step explanation:

x²−18x + 81 = x² - (2 x 9) x + 9² = (x - 9)²

width = area / length = (x - 9)² / (x - 9) = x - 9

Length = width

This is a square backyard

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Find the ratio of the area inside the square but outside the circle to the area of the square in the picture
Eduardwww [97]

Answer:

0.2146

Step-by-step explanation:

From the picture:

The radius of the circle = r. This means that the area of the circle = πr²

Also For the square, the length of the square = 2r, Therefore the area of the square = Length × length = 2r × 2r = 4r²

The area inside the square but outside the circle = Area of square - Area of circle = 4r² - πr² = r²(4 - π) = 0.8584r²

The ratio of the area inside the square but outside the circle to the area of the square =  r²(4 - π) / 4r² = (4 - π) / 4 = 1 - π/4 = 0.2146

5 0
3 years ago
Compare the line passing through the points (−3, −11) and (6, 4) to the line given by the equation y=35x−6.
Aleks04 [339]
Let
<span>A------> (−3, −11)
B------>  (6, 4)

step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> </span>m=(4+11)/(6+3)----> m=15/9---> 5/3

step 2
with m=5/3 and point B (6, 4)  find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6

case <span>a. they have the same slope------> is not correct
because
</span><span>y=35x−6------> the slope m=35
</span>y=(5/3)x-6---> the slope m =5/3

case <span>b. they have the same x-intercept.----> is not correct
because
</span>the x-intercept is for y=0

y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)

y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)

case <span>c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because

if two lines are perpendicular
m1*m2=-1-------> </span><span>this condition is not satisfied
</span>
the y intercept is for x=0

y=35x−6-------> y=-6
the y intercept is the point (0,-6)

y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)

 they have the same y-intercept but the two lines are not perpendicular

see the attached figure

7 0
3 years ago
It would be amazing if you can help me with this !
denis23 [38]

Answer:

Step-by-step explanation:

Blank 1 = " x "

Blank 2 = " 3 "

4 0
3 years ago
Light travels at approximately 2.998*10^5 kilometers per second. There are 6.048*10^5 seconds in one week. About how many kilome
BartSMP [9]

Answer:

okay, you have pay special attention to time.i.e 60secs = 1 minute, 60 minutes = 1 hour, 24 hours in one day, and 7 days in one week. No. of seconds in one week we are told is 6.1048 x 10 ^5 seconds.  

Step-by-step explanation:

s = d/t [ speed = distance/time]

therefor, rearranging, we get d = s x t

Since speed = 2.998*10^5 Km/s and time = 6.048^10^5

d = (2.998 x 10^5) x (6.048 x10^5) = (2.998 x 6.048) x 10 ^(5+5)

d = 18.131904 X 10^10 km

d = approximately 18.132 x 10^10 km (to 3 decimal places)

6 0
3 years ago
What is the slope of the line through (2,-1) and (-2,-3)
Ipatiy [6.2K]

Answer:

y=1/2x-2

Step-by-step explanation:

1. Find slop by subtracting y values over subtracting x values, which will get you the m value

-1+3 / 2+2 = 1/2

3 0
3 years ago
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