Step-by-step explanation:
x² + y² − 8x + 10y − 8 = 0
Rearrange:
x² − 8x + y² + 10y = 8
To complete the square, take half of the x and y coefficients, square it, then add the result to both sides.
(-8/2)² = 16
(10/2)² = 25
x² − 8x + 16 + y² + 10y + 25 = 8 + 16 + 25
x² − 8x + 16 + y² + 10y + 25 = 49
Factor the squares:
(x − 4)² + (y + 5)² = 49
The center is (4, -5) and the radius is 7.
It took June 4 hours to get from Brookline to Brooklyn.
<h3><u>Time calculation</u></h3>
Given that June is driving from Brookline, Massachusetts to Brooklyn, New York, and the cities are 200 miles apart, and she can drive at a constant speed of 50mph the entire way, to determine the function that solves the time June takes to complete the route, the following calculation must be made:
- C / Constant speed = T
- 200 / 50 = T
- 4 = T
So it took June 4 hours to get from Brookline to Brooklyn.
Learn more about time calculation in brainly.com/question/26707195
Answer:
8.5 or 8½
Step-by-step explanation:
Arranged numbers in ascending order
2, 6, 8, 8, 9, 10, 12, 14
Median = middle number i. e 8 and 9
Therefore median = 8 + 9 divided by 2
= 17 divided 2
= 8.5
Answers = 8.5 or 8½
Answer:
$3000.
Step-by-step explanation:
Suppose the amount invested at 7% is $X and the amount invested at 10% is $Y (assuming that the college student invested all his/her income on the two schemes). Therefore:
X + Y = 8200 (The sum of investments is basically the total income).
0.07X + 0.1Y = 664 (The sum of the interest received from the invested amounts is actually the total return).
Now solving these 2 simultaneous equations:
x + y = 8200 (Equation 1)
7x + 10y = 66400 (Equation 2)
From (Equation 1):
x = 8200 - y (Equation 3)
Put (Equation 3) in (Equation 2):
7(8200 - y) + 10y = 66400.
57400 - 7y + 10y = 66400.
3y = 9000
y = 3000.
$Y is the amount invested at 10%, therefore the final answer is $3000!!!
