Answer:
x² + 2x + y² + 4y = 20
(x² + 2x + 1) - 1 + (y² + 4y + 4) - 4 = 20
(x + 2)² + (y + 4)² - 5 = 20
(x + 2)² + (y + 4)² = 25
Therefore, the center is (-2, -4) and the radius is √25 = 5.
Answer:
y=0
Step-by-step explanation:
(1) The value of x is 25
(2) The measure of ∠CBD is 60°
Explanation:
(1) The given two angles are vertical angles. Since, vertical angles are equal, we can add the two angles to determine the value of x.
Thus, we have,
![5x+15=6x-10](https://tex.z-dn.net/?f=5x%2B15%3D6x-10)
Subtracting 5x from both sides, we have
Adding 10 to both sides , we have,
![25=x](https://tex.z-dn.net/?f=25%3Dx)
Thus, the value of x is 25.
(2) It is given that the measure of ∠ABC = (x+7)° and ∠CBD = (2x+14)°
Since, these two angles are supplementary angles and supplementary angles add upto 90°
Thus, we have,
![2x+14+x+7=90](https://tex.z-dn.net/?f=2x%2B14%2Bx%2B7%3D90)
Simplifying, we get,
![3x+21=90](https://tex.z-dn.net/?f=3x%2B21%3D90)
![3x=69](https://tex.z-dn.net/?f=3x%3D69)
![x=23](https://tex.z-dn.net/?f=x%3D23)
Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.
![2x+14=2(23)+14=46+14=60](https://tex.z-dn.net/?f=2x%2B14%3D2%2823%29%2B14%3D46%2B14%3D60)
Thus, the measure of ∠CBD is 60°
Answer:
C
Step-by-step explanation:
Let the year represents x axis and consumption represents y axis.
Since 2010 is the initial year, x=0
and 2013 is third year , so x=3
Co-ordinates are (0,8.938)(3,10.480)
Exponential formula is ![y=ab^{x}](https://tex.z-dn.net/?f=y%3Dab%5E%7Bx%7D)
Putting the value of x in the above formula from 1st coordinate,
![8.938=ab^{0}](https://tex.z-dn.net/?f=8.938%3Dab%5E%7B0%7D)
As
= 1
this gives a= 8.938
Now using the 2nd coordinate
![10.480=ab^{3}](https://tex.z-dn.net/?f=10.480%3Dab%5E%7B3%7D)
putting the value of a in it we have
![10.480=8.938b^{3}](https://tex.z-dn.net/?f=10.480%3D8.938b%5E%7B3%7D)
taking cube roots on both sides we get
b= 1.05448
Now putting the values of a and b in the exponential formula-
![y=8.938(1.05448)^{x}](https://tex.z-dn.net/?f=y%3D8.938%281.05448%29%5E%7Bx%7D)
In the year 2028, x=28
so,
![y=8.938(1.05448)^{28}](https://tex.z-dn.net/?f=y%3D8.938%281.05448%29%5E%7B28%7D)
y= 39.474
Hence oil consumption per day in 2028 will be 39.474 million barrels.