9514 1404 393
Answer:
b = √32
Step-by-step explanation:
The Pythagorean theorem tells you the relation between the side lengths is ...
2² + b² = 6²
b² = 36 -4 = 32
b = √32
_____
<em>Additional comment</em>
This radical can be simplified by removing a square from under the radical.
![b = \sqrt{32}=\sqrt{16\cdot2}=\sqrt{16}\cdot\sqrt{2}=4\sqrt{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B32%7D%3D%5Csqrt%7B16%5Ccdot2%7D%3D%5Csqrt%7B16%7D%5Ccdot%5Csqrt%7B2%7D%3D4%5Csqrt%7B2%7D)
Answer:
First number: -39
Second number: -37
Step-by-step explanation:
An odd number can be written as
where n is a whole number.
Let's call our first number 2n+1.
Our second, consecutive number will be 2 more than our first number, since it has to be odd. All numbers go: odd -> even -> odd -> even. If we have an odd number, and add 2, we'll get the next odd number.
First number: 2n+1
Second number: 2n+1+2 = 2n+3
The sum of these two numbers, 2n+1 and 2n+3 will be -76.
(2n+1) + (2n+3) = -76
2n + 2n + 1 + 3 = -76
4n + 4 = -76
4n = -80
n = -20
Since our first number is 2n+1:
2 * (-20) + 1 = -40 + 1 = -39
First number: -39
Our second number is 2n+3, or 2 more than our first number.
-39 + 2 = -37
Second number: -37
We can double check this:
-39 + (-37) = -39 - 37 = -76
There are two negative roots to the provided polynomial function
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
<h3>What is polynomial?</h3>
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
![\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n](https://tex.z-dn.net/?f=%5Crm%20a_1x%2Ba_2x%5E2%2Ba_3x%5E3%2Ba_4x%5E4..........a_nx%5En)
We have a polynomial function:
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
![\rm f(x) =\left(x+1\right)\left(x^6-x^5+x^4-3x^3+3x^2+4x-2\right)](https://tex.z-dn.net/?f=%5Crm%20f%28x%29%20%3D%5Cleft%28x%2B1%5Cright%29%5Cleft%28x%5E6-x%5E5%2Bx%5E4-3x%5E3%2B3x%5E2%2B4x-2%5Cright%29)
Using the zero product property:
![\rm \left x+1\right = 0 \ \ \ or \left x^6-x^5+x^4-3x^3+3x^2+4x-2\right = 0](https://tex.z-dn.net/?f=%5Crm%20%5Cleft%20x%2B1%5Cright%20%3D%200%20%5C%20%5C%20%5C%20or%20%5Cleft%20x%5E6-x%5E5%2Bx%5E4-3x%5E3%2B3x%5E2%2B4x-2%5Cright%20%3D%200)
After solving:
x = -1, x = -0.853, and x = 0.418 (using the graph method)
Thus, there are two negative roots to the provided polynomial function
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ1
Answer:
Option (4)
Step-by-step explanation:
Domain of a function is defined by the x-values or input values of the function.
Similarly, Range of a function is defined by the y-values of output values for the corresponding input values.
From the graph attached,
Domain is restricted to 0 ≤ x ≤ 8.
Therefore, Range will be 0 ≤ y ≤ 4.
Option (4) will be the answer.