Answer:
Length of rectangle = 36 yd and width of rectangle = 9 yd
Step-by-step explanation:
Let width of rectangle = w
Length of rectangle = 4w (four times the width)
Perimeter of rectangle = 90 yd
We need to find length and width of rectangle.
The formula used will be: ![Perimeter \ of \ rectangle=2(l+w)](https://tex.z-dn.net/?f=Perimeter%20%5C%20of%20%5C%20rectangle%3D2%28l%2Bw%29)
Where l is length and w is width
Putting values and finding length and width of rectangle
![Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9](https://tex.z-dn.net/?f=Perimeter%20%5C%20of%20%5C%20rectangle%3D2%28l%2Bw%29%5C%5C90%3D2%284w%2Bw%29%5C%5C90%3D2%285w%29%5C%5C90%3D10w%5C%5Cw%3D%5Cfrac%7B90%7D%7B10%7D%5C%5Cw%3D9)
So,width (w) of rectangle is w= 9 yd
Finding length of rectangle = 4w = 4*9 = 36 yd
So, length of rectangle = 36 yd and width of rectangle = 9 yd
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
Let us say that:
V1 = initial gallons in first container
V2 = initial gallons in second container
From the problem statement, we can create the equations:
V1 = 2 V2
V1 – 3 = 4.5 (V2 – 2)
Combining the two:
2 V2 – 3 = 4.5 (V2 – 2)
2 V2 – 3 = 4.5 V2 – 9
2.5 V2 = 6
V2 = 2.4 gallons
V1 = 2 V2 = 4.8 gallons
So there are 4.8 gallons in the 1st container
while 2.4 gallons in the 2nd container.
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Answer:
![- 13 - \frac{2}{x - 2}](https://tex.z-dn.net/?f=%20-%2013%20%20-%20%5Cfrac%7B2%7D%7Bx%20-%202%7D%20)
Step-by-step explanation:
<h3>
![\frac{ - 3x - 10x + 24}{x - 2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%203x%20-%2010x%20%2B%2024%7D%7Bx%20-%202%7D%20)
</h3><h3>
![\frac{ - 13x + 24}{x - 2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%2013x%20%2B%2024%7D%7Bx%20-%202%7D%20)
</h3>
![- 13 - \frac{2}{x - 2}](https://tex.z-dn.net/?f=%20-%2013%20%20-%20%5Cfrac%7B2%7D%7Bx%20-%202%7D%20)
<h3>Hope it is helpful...</h3>