Answer:
B) Isolate the variable through inverse operations
Step-by-step explanation:
In order to get the value of y, we need to get y by itself. Since y is being multiplied by the coefficient 7, dividing both sides by 7 gets us y=10, so B is the right choice.
Answer:
The center is -1,5 and the radius is 2
Step-by-step explanation:
Subtract 22 from both sides of the equation. x 2 + y 2 + 2 x − 10 y = − 22 Complete the square for x 2 + 2 x . ( x + 1 ) 2 − 1 Substitute ( x + 1 ) 2 − 1 for x 2 + 2 x in the equation x 2 + y 2 + 2 x − 10 y = − 22 . ( x + 1 ) 2 − 1 + y 2 − 10 y = − 22 Move − 1 to the right side of the equation by adding 1 to both sides. ( x + 1 ) 2 + y 2 − 10 y = − 22 + 1 Complete the square for y 2 − 10 y . ( y − 5 ) 2 − 25 Substitute ( y − 5 ) 2 − 25 for y 2 − 10 y in the equation x 2 + y 2 + 2 x − 10 y = − 22 . ( x + 1 ) 2 + ( y − 5 ) 2 − 25 = − 22 + 1 Move − 25 to the right side of the equation by adding 25 to both sides. ( x + 1 ) 2 + ( y − 5 ) 2 = − 22 + 1 + 25 Simplify − 22 + 1 + 25 . ( x + 1 ) 2 + ( y − 5 ) 2 = 4 This is the form of a circle. Use this form to determine the center and radius of the circle. ( x − h ) 2 + ( y − k ) 2 = r 2 Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin. r = 2 h = − 1 k = 5 The center of the circle is found at ( h , k ) . Center: ( − 1 , 5 ) These values represent the important values for graphing and analyzing a circle.
Answer: There is a strong association between age and weight.
Step-by-step explanation:
The correlation coefficient (r) is used to describe the relationship between two variables.
If r lies between -1 to -0.5 or 0.5 to 1, then there is strong association between them.
Here, Variables: Age and weight.
correlation coefficient = 0.512
That means, there is a strong association between age and weight.
The answer is 12.8 cm³
<span>The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p):
v = k/p
p * v = k (k - constant)
p1v1 = k
p2v2 = k
So, p1v1 = p2v2
v1 = 24 cm</span>³
p1 = 16 lb
v2 = ?
p2 = 30 lb
24 * 16 = x * 30
384 = x * 30
x = 384 / 30
x = 12.8 cm³
Answer:
B 840cm^2
Step-by-step explanation:
20x10 = 200
20x13 = 260
1/2(10)(12) = 60
200+260+260+60+60= 840
