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oksian1 [2.3K]
3 years ago
5

Harry needs to build a fence around his garden, but first he must figure out the dimensions of his garden. The length of his rec

tangular garden is 6 more than the width, and the area of the garden is 27 m units. Determine the dimensions of Harry’s garden.
Mathematics
1 answer:
navik [9.2K]3 years ago
3 0

Answer:

width=3m

length=9m

Step-by-step explanation:

-Let w be the width of the garden.

-Given that the length is 6 units more than the width, l=w+6

-We apply the area formula to solve for w:

A=lw\\\\27=w(w+6)\\\\w^2+6w-27=0\\\\\#Apply \ Complete \ Squares\\\\w^2-3w+9w-27=0\\\\w(w-3)+9(w-3)=0\\\\(w-3)(w+9)=0\\\\w=3 \ \ \or w=-9\\\\\therefore w=3m\\\\l=w+6=3+6=9m

Hence, the garden's width is 3 m and the length is 9 m

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Find numerical value if x=1 and y=5<br>4(x+y)​
Len [333]

Answer:

24

Step-by-step explanation:

4(x+y)

4(1+5)

4*6

24

6 0
2 years ago
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What is the value of the correlation coefficient r of the data set?
enyata [817]

The correct option will be:  C) 0.84

<u><em>Explanation</em></u>

Formula for Correlation coefficient :

r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

<em>(Please refer to the attached image for the table )</em>

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}\\ \\ r=\frac{7(1480)-(44)(183)}{\sqrt{[7(362)-(44)^2][7(6575)-(183)^2]}}\\ \\ r=\frac{10360-8052}{\sqrt{(598)(12536)}}\\ \\ r=\frac{2308}{\sqrt{7496528}}\\ \\ r=0.84

So, the value of the correlation coefficient is 0.84

4 0
3 years ago
Read 2 more answers
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=7
Rashid [163]
5x + 2y = 7....multiply by -3
-2x + 6y = 9
----------------
-15x - 6y = -21 (result of multiplying by -3)
-2x + 6y = 9
---------------add
-17x = - 12
x = 12/17 or 0.7

5x + 2y = 7
5(12/17) + 2y = 7
60/17 + 2y = 7
2y = 7 - 60/17
2y = 119/17 - 60/17
2y = 59/17
y = 59/17 * 1/2
y = 59/34 or 1.7 when rounded <====
4 0
3 years ago
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A game normally cost $53.00, but Isabel used a coupon and got the game for $37.10. The coupon was for what percent off.
Artist 52 [7]
We could use the numbers and the difference of the original cost - the end price in a equation.

53 × x/100 = 15.9

Cross multiply 100 × 15.9.

53x=1590

Divide both sides by 53.

x=30

The coupon was 30%
5 0
3 years ago
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The formula for the distance, d, an accelerating car can travel is d = 5.6t square. how many minutes, t, doe the car take to tra
Likurg_2 [28]
Your distance(d) is 1,814.4
1814.4 m = 5.6t square
then you square root 5.6t
\sqrt{1814.4} = \sqrt{ {5.6t}^{2} }
the square root eliminates the square
\sqrt{1814.4} = 5.6t
you square root 1,814.4 m
42.6 = 5.6t
(I rounded 42.6) then divide 42.6 by 5.6
7.6 = t
(I rounded 7.6)
6 0
2 years ago
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