The degree of a polynomial is the highest power of the polynomial.
The polynomial is ![\mathbf{P(x) = (x + 3)^4}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28x%29%20%3D%20%28x%20%2B%203%29%5E4%7D)
The degree is given as:
![\mathbf{n = 4}](https://tex.z-dn.net/?f=%5Cmathbf%7Bn%20%3D%204%7D)
The zero is given as:
![\mathbf{x = -3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%3D%20-3%7D)
Add 3 to both sides
![\mathbf{x + 3= 0}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%20%2B%203%3D%200%7D)
From the question, we understand that the polynomial has a single zero.
So, the polynomial is:
![\mathbf{P(x) = (x + 3)^n}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28x%29%20%3D%20%28x%20%2B%203%29%5En%7D)
Substitute 4 for n
![\mathbf{P(x) = (x + 3)^4}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28x%29%20%3D%20%28x%20%2B%203%29%5E4%7D)
Hence, the polynomial is ![\mathbf{P(x) = (x + 3)^4}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28x%29%20%3D%20%28x%20%2B%203%29%5E4%7D)
Read more about polynomials at:
brainly.com/question/11536910
Answer:
the leaf is 8 meters away from the tree
Step-by-step explanation:
we can think of this problem as a right triangle where height represents a leg, and what flew the bird represents the hypotenuse
then we would have to find the other leg
for this we can use Pythagoras
h = hypotenuse = 17 meters
l1 = leg1 = 15 meters
l2 = leg2 = ?
h² = l1² + l2²
17² = 15² + l2²
17² - 15² = l2²
289 - 225 = l2²
64 = l2²
√64 = l2
8 = l2
the leaf is 8 meters away from the tree
Answer:
x= 45
Step-by-step explanation:
90-45=x
Answer:
38 or 36 if there's options
Step-by-step explanation:
Answer:
There are at least two runners whose times are less than 9 seconds apart.
Step-by-step explanation:
Let's assume that Tₙ is the time of the n-th runner, we know that:
6 min < Tₙ < 7 min
knowing that:
1 min = 60 s
We can rewrite this as:
6*60 s < Tₙ < 7*60 s
360 s < Tₙ < 420 s
We know that there are 7 runners, and we want to see if we can conclude that there are two runners whose times are less than nine seconds.
So, the smallest time allowed in seconds is 361 seconds (the first value larger than 360 seg) while the largest time allowed is 419 seconds (the largest time allowed smallest than 420 seconds).
Now, let's assume that the first runner has the smallest time:
then:
T₁ = 361 s
Now let's add 9 seconds to the time of each runner (here we want to check that we can have all the runners with exactly 9 seconds apart in their times, so we will prove that the statement is false), then:
T₂ = 361s + 9s = 370s
T₃ = 370s + 9s = 379s
T₄ = 379s + 9s = 388s
T₄ = 388s + 9s = 397s
T₅ = 397s + 9s = 406s
T₆ = 406s + 9s = 415s
T₇ = 415s + 9s = 424s
But 424s > 420s
So this is not allowed (as the maximum time allowed was 419 s), so at least two of the runners must have times that are less than 9 seconds apart.
Then; Can you conclude that there are two runners whose times are less than nine seconds apart? Yes.