Answer: Choice B) (24,10)
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Work Shown:
2x - 4y = 8
2( x ) - 4y = 8
2( 3y-6 ) - 4y = 8 ... notice x has been replaced with 3y-6
2(3y)+2(-6) - 4y = 8
6y-12 - 4y = 8
2y-12 = 8
2y-12+12 = 8+12 ... add 12 to both sides
2y = 20
2y/2 = 20/2 ... divide both sides by 2
y = 10
If y = 10, then
x = 3y-6
x = 3*10-6 ... replace y with 10
x = 30-6
x = 24
Put together, the solution is (x,y) = (24,10)
which is why the answer is choice B
As a check, we can plug (x,y) = (24,10) into each equation
x = 3y-6
24 = 3*10 - 6
24 = 30 - 6
24 = 24 ... true equation
and similarly for the second equation as well
2x-4y = 8
2*24 - 4*10 = 8
48 - 40 = 8
8 = 8 ... true equation
Both equations are true when (x,y) = (24,10) so the solution is confirmed
The correct answer is A because if you add 200 and 85 together to get the amount of money he has to have, and then divide that by 45, you get 13 weeks
Answer:
<u>After July, Ana's monthly salary was $1920</u>
Step-by-step explanation:
In May, Ana's monthly salary was $2000. During the next month, the salary increased by 20%, or (0.2)(2000)
![2000+(0.2)(2000)=2000+400=2400](https://tex.z-dn.net/?f=2000%2B%280.2%29%282000%29%3D2000%2B400%3D2400)
So, in June, Ana's monthly salary was $2400. During the next month, the salary decreased by 20%, or (0.2)(2000)
![2400-(0.2)(2400)=2400-480=1920](https://tex.z-dn.net/?f=2400-%280.2%29%282400%29%3D2400-480%3D1920)
Therefore, after the two changes, Ana's monthly salary was <u>$1920</u>
Answer:
The y-coordinate of point A is
.
Step-by-step explanation:
The equation of the circle is represented by the following expression:
(1)
Where:
- Independent variable.
- Dependent variable.
,
- Coordinates of the center of the circle.
- Radius of the circle.
If we know that
,
and
, then the equation of the circle is:
(1b)
Then, we clear
within (1b):
![y^{2} = 4 - x^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D%20%3D%204%20-%20x%5E%7B2%7D)
(2)
If we know that
, then the y-coordinate of point A is:
![y = \sqrt{4-1^{2}}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7B4-1%5E%7B2%7D%7D)
![y = \sqrt{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7B3%7D)
The y-coordinate of point A is
.
Answer:
2:7
Step-by-step explanation: