Answer:
ADB and ABC are similar
x = 8
Step-by-step explanation:
hypotenuse in ADB = 
since two triangles are similar,
solving for x, x=8
The equation we are looking at would have to be divided by 2 first.
x²-6x+3
When looking at that, I can tell that 1 may be the possible answer since you would have to subtract 6 from both sides. That would leave a 3. Let's check.
(x-3)(x-3)
x²-6x+9=6
Now subtract 6 from both sides.
x²-6x+3=0
So, 1- (x-3)²=6 would be used.
Answer: The answer is 8.
Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;
Y^2 - 40.
Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,
Y^2 - 40 = 3Y
If we move all expressions to one side of the equation, what we would have is,
Y^2 - 3Y -40 = 0
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
We now have a quadratic equation
Y^2 -3Y - 40 = 0
By factorizing we now have
(Y -8) (Y + 5) = 0
Therefore Y - 8 = 0 or
Y + 5 = 0
Hence, Y = 8 or Y = -5
Since we are asked to calculate the positive solution, Y = 8
Answer:
Step-by-step explanation:
The equation of a circle in standard form:
(h, k) - center
r - radius
1. We have the equation:
<h2 />
2. We have the center (-4, 3) and the radius r = 6. Substitute:
3. We have the endpoints of the diameter: (-1, 6) and (5, -4).
Midpoint of diameter is a center of a circle.
The formula of a midpoint:
Substitute:
The center is in (2, 1).
The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.
The formula of a distance between two points:
Substitute the coordinates of the points (2, 1) and (5, -4):
Finally we have:
Answer:
vertex = (4, - 8 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x - 4)² - 8 ← is in vertex form
with (h, k ) = (4, - 8 ) ← coordinates of vertex
