Answer:
9(n + 22) ≤ -15
Step-by-step explanation:
9 times the sum of a number and 22 is at most −15
Let n = number
Times = multiplication
Sum = Addition
9 * n + 22
We must add parenthesis on the end on 22 and before n
We must do this because it says 9 times the sum of a number and 22 which means that 9 is being multiplied by both n and 22
We would have 9(n + 22)
9(n + 22) is at most -15
At most meaning that -15 is the highest number that 9(n + 22) can equal
Because it says at most 9(n + 22) can equal -15 or anything less than -15
So at most can be replaced with ≤
9(n + 22) ≤ -15
To complete the square:
we take the coefficient ox "x" (which in this problem is -20)
we divide it by 2
square that number
then add it to both sides of the equation
-20 / 2 = -10
-10^2 = 100
then we add 100 to both sides of the equation:
x^2 -20x
x^2 -20x +100 = 100
******************************************************
To get the roots of the equation, we take the square root of both sides:
(x -10) * (x-10) = 10
(x-10) = square root (10)
x-10 =
<span>
<span>
<span>
3.1622776602
</span>
</span>
</span>
x1 =
<span>
<span>
<span>
13.1622776602
</span>
and don't forget that square root of 10 also equals </span></span><span><span><span> -3.1622776602
</span>
</span>
</span>
x2 = 10
-<span>
<span>
<span>
3.1622776602
x2 = </span></span></span>
<span>
<span>
<span>
6.8377223398
</span>
</span>
</span>
Basically, it is not a function because 1 domain (in this case, 5) can not be connected to two different ranges(1 and -2). Each domain must only connect to one range.
Answer:
Center = (5, -2) and radius = √33
Step-by-step explanation:
The equation of a circle is given by the formula;
(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius of the circle.
In this case;
2x² - 20x + 2y² + 8y =40 ;
Dividing both sides of the equation by 2 we get;
x² - 10x + y² + 4y = 20
we can then use the completing the square on both x and y terms.
x² - 10x + y² + 4y = 20
x² + 2(-5)x + 25 + y² + 2(2) y + 4 = 20 +9 + 4
In standard form we get;
(x-5)² + (y+2)² = 33
Therefore;
Center = (5, -2) and radius = √33
Step-by-step explanation:
k/4=33/20
k=33/20×4
k=33/5
