The given circles are given in standard form:
(x - xc)² + (y - yc)² = r²
The second quadrant is the one that has negative x coordinates and positive y coordinates.
This said, let's see all your options:
A) (x - 5)² + (y - 6)² = 25
xc = -(-5) = +5
yc = -(-6) = +6
C (5 , 6) is in the first quadrant.
B) (x + 1)² + (y - 7)² = 16
xc = -(+1) = -1
yc = -(-7) = +7
C (-1 , 7) is in the second quadrant.
C) (x - 4)² + (y + 3)² = 32
xc = -(-4) = +4
yc = -(+3) = -3
C (4, -3) is in the fourth quadrant.
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D) (x + 2)² + (y - 5)²= 9</span>
xc = -(+2) = -2
yc = -(-5) = +5
C (-2 , +5) is in the second quadrant.
Therefore, the correct answers are B and D.
Answer:
-5
Step-by-step explanation:
The y coordinate of the vertex is -5.
Answer:
Step-by-step explanation:
a. 3-4x=-7-4x
3=-7. no solution
b. 15 - 2x = -7x
15 = -5x
x=-3. one solution
c. 7y-21=6y-21
y=0
1. -3x+4=-3x+7
4=7
2. 10+2x = 5x+2
8=3x
x=3/8
3. x+5=x+5
The answer is: x = 7 - √53 or x = 7 + √53
The general quadratic equation is: ax² + bx + c =
0.
But, by completing the square we turn it into: a(x + d)² + e = 0, where:<span>
d = b/2a
e = c - b²/4a
Our quadratic equation is x² - 14x -4 = 0, which is
after rearrangement:
So, a = 1, b = -14, c = -4
Let's first calculate d and e:
d = b/2a = -14/2*1 = -14/2 = -7
e = c - b²/4a = -4 - (-14)</span>²/4*1 = -4 - 196/4 = -4 - 49 = -53<span>
By completing the square we have:
a(x + d)² + e = 0
1(x + (-7))</span>² + (-53) = 0
(x - 7)² - 53 = 0
(x - 7)² = 53
x - 7 = +/-√53
x = 7 +/- √53
Therefore, the solutions are:
x = 7 - √53
or
x = 7 + √53
So for every 6 people with a car, there are another 5 that own an SUV, or expressed the other way around, for every 5 SUVs, there's one extra car. If there are 200 extra cars, that means there are 5 × 200 SUVs = 1000 SUVs, and 1200 cars.
Now let's just quickly test if the math is correct, and if the ratio of cars to SUVs is still 6:5:
1200 : 1000 << get rid of the 00
12 : 10 << divide by two
6:5
Yep, math is correct.
Answer: There are 1200 people who own cars, and 1000 people who own SUVs.
