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kipiarov [429]
3 years ago
12

The area of a rectangle is 27m and the length of the rectangle is 3m less then twice the width. Find the dimensions of the recta

ngle
Mathematics
1 answer:
Zielflug [23.3K]3 years ago
5 0

Answer:

w = 4 1/2

l = 6

Step-by-step explanation:

w = width

2w-3 = length

A = lw

27 = w(2w-3)

27 = 2w² - 3w

subtract 27 from each side:

2w² - 3w - 27 = 0

factor:

(2w-9)(w+3) = 0

solve each for 'w':

w = 9/2

w = -3  (This answer can be discounted because a length cannot be negative)

width = 9/2

length = 2(9/2) - 3 which is 6

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Find an equation for the line perpendicular to 4x+12y=72 and goes through the point (-9,6)
il63 [147K]

Answer:

Step-by-step explanation:

Given the equation

4x+12y=72

The equation of a line can written as

y=mx+c

Where m is the slope

And c is the intercept on y axis

Then, we need to write the equation given in the form of equation of a line (y=mx+c), by making y subject of the formula

4x+12y=72

12y=-4x+72

Divide through by 12

y=-4x/12 + 72/12

y=-⅓x+6

Then, comparing with equation of a line shows that

m=-⅓ and c=6

So we need to get another linen that is perpendicular to this line and passes through the point (-9,6)

The slope of the line perpendicular to another line is given as

m1=-1/m2

Then, m1=-1÷-⅓

Then, the slope of the perpendicular line is 3

Then, m=3

So apply this to equation of the line

y=mx+c

Then, y=3x+c

So to know c, we will insert the point given(-9,6), x=-9 and y=6

y=3x+c

6=3(-9)+c

6=-27+c

Then, c=6+27

c=33

Then, the equation of line becomes

y=3x+33

7 0
3 years ago
What is the sum of the geometric series
lbvjy [14]
If S denotes the sum of the first n terms of a geometric series with first term a and common ratio r, then

S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}
rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n
\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n
\implies (1-r)S=a(1-r^n)
\implies S=a=\dfrac{1-r^n}{1-r}

Using summation notation, you have

S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}

In this case, you have a=2, r=\dfrac12, and n=16. So the value of the sum is

\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67

Rounded to the nearest whole number, the answer would be 3.
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Answer:

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shtirl [24]

Answer:

About 23.9 in

Step-by-step explanation:

We are given ;

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we are required to determine the circumference

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Therefore, the circumference of the figure is about 23.9 in

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