Answer:
The answer is x2 - 3x - 8.
Step-by-step explanation:
The diagonal of the square creates two congruent right triangles, which you could see if you drew a picture. The diagonal is the hypotenuse of the triangle, and the sides of the square are the legs of the triangle. Again, a diagram might help.
The pythagorean theorem is (a^2)+(b^2)=(c^2), where c is the hypotenuse and a and b are the legs.
We know that c is 5 square root of 2, so:
(a^2)+(b^2)=((5 square root of 2)^2),
Now, distribute the square (exponent of 2) to both the 5 and the square root of 2. Squaring and the square root cancel each other out, leaving us with 2. 5^2 is 25. Then, both of those are multiplied together, so:
(a^2)+(b^2)=50
Since we are dealing with a square, both side lengths are the same, so a and b are the same number. So, we have two of the same term being added to each other. To eliminate any confusion, let x stand for the length of the sides of the triangle. This is equivalent to:
2(x^2)=50.
Then, we just solve for x.
(x^2)=25
x=5
All sides of the triangle are 5. So, the area is 5*5, or 25 inches.
Answer:
Step-by-step explanation:
Given that the random variable x represents the number of phone calls an author receives in a day
Poisson distribution is a discrete distribution with random variable countable.
Here no of calls cannot be in fraction or decimal.
Also given that X is Poisson with mean = 7.6
X is discrete since no of phone calls can take values as 1,2,3....
X can take any value from 0 to infinity.
x=3.2 is not possible since 3.2 calls does not exist.
The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
<h3>How to determine the vertex form of the quadratic equation?</h3>
The quadratic equation is given as:
y = -x^2 + 4x - 1
Differentiate the above quadratic equation.
This is done with respect to x by first derivative
So, we have:
y' = -2x + 4
Set the derivative to 0
-2x + 4 = 0
Subtract 4 from both sides of the equation
-2x + 4 - 4 = 0 - 4
Evaluate the difference in the above equation
-2x = -4
Divide both sides of the above equation by -2
x = 2
Rewrite as
h = 2
Substitute 2 for x in the equation y = -x^2 + 4x - 1
y = -2^2 + 4 *2 - 1
Evaluate the equation
y = 3
Rewrite as:
k = 3
A quadratic equation in vertex form is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x - 2)^2 + 3
In the equation y = -x^2 + 4x - 1, a = -1
So, we have:
y = -(x - 2)^2 + 3
Hence, the vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
Read more about vertex form at
brainly.com/question/18797214
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