Answer:A is a quadratic function
Step-by-step explanation:
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. If you solve the function, y= 2x^2+x-6.
Answer:
D. ![\sqrt{65}](https://tex.z-dn.net/?f=%5Csqrt%7B65%7D)
Step-by-step explanation:
The computation of the length of a diagonal (AC or BD) of the rectangle is shown below:
As we know that
The Diagonal length of AC is
![= (x_2 - x_1)^2 + (y_2 - y_1)^2\\\\= (9 -2)^2 + (8 - 4)^2\\\\= (7)^2 + (4)^2](https://tex.z-dn.net/?f=%3D%20%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%5C%5C%5C%5C%3D%20%289%20-2%29%5E2%20%2B%20%288%20-%204%29%5E2%5C%5C%5C%5C%3D%20%287%29%5E2%20%2B%20%284%29%5E2)
![= \sqrt{49 + 16}\\\\= \sqrt{65}](https://tex.z-dn.net/?f=%3D%20%5Csqrt%7B49%20%2B%2016%7D%5C%5C%5C%5C%3D%20%5Csqrt%7B65%7D)
Therefore correct option is D.
Answer:
All potential roots are 3,3 and
.
Step-by-step explanation:
Potential roots of the polynomial is all possible roots of f(x).
![f(x)=3x^3-13x^2-3x+45](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3-13x%5E2-3x%2B45)
Using rational root theorem test. We will find all the possible or potential roots of the polynomial.
p=All the positive/negative factors of 45
q=All the positive/negative factors of 3
![p=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45](https://tex.z-dn.net/?f=p%3D%5Cpm%201%2C%5Cpm%203%2C%5Cpm%205%5Cpm%20%5Cpm%209%2C%5Cpm%2015%5Cpm%2045)
![q=\pm 1,\pm 3](https://tex.z-dn.net/?f=q%3D%5Cpm%201%2C%5Cpm%203)
All possible roots
![\frac{p}{q}=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45,\pm \frac{1}{3},\pm \frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7Bq%7D%3D%5Cpm%201%2C%5Cpm%203%2C%5Cpm%205%5Cpm%20%5Cpm%209%2C%5Cpm%2015%5Cpm%2045%2C%5Cpm%20%5Cfrac%7B1%7D%7B3%7D%2C%5Cpm%20%5Cfrac%7B5%7D%7B3%7D)
Now we check each rational root and see which are possible roots for given function.
![f(1)= 3\times 1^3-13\times 1^2-3\times 1+45\Rightarrow 32\neq 0](https://tex.z-dn.net/?f=f%281%29%3D%203%5Ctimes%201%5E3-13%5Ctimes%201%5E2-3%5Ctimes%201%2B45%5CRightarrow%2032%5Cneq%200)
![f(-1)= 3\times (-1)^3-13\times (-1)^2-3\times (-1)+45\Rightarrow \neq 32](https://tex.z-dn.net/?f=f%28-1%29%3D%203%5Ctimes%20%28-1%29%5E3-13%5Ctimes%20%28-1%29%5E2-3%5Ctimes%20%28-1%29%2B45%5CRightarrow%20%5Cneq%2032)
![f(-3)= 3\times (-3)^3-13\times (-3)^2-3\times (-3)+45\Rightarrow \neq -144](https://tex.z-dn.net/?f=f%28-3%29%3D%203%5Ctimes%20%28-3%29%5E3-13%5Ctimes%20%28-3%29%5E2-3%5Ctimes%20%28-3%29%2B45%5CRightarrow%20%5Cneq%20-144)
![f(3)= 3\times (3)^3-13\times (3)^2-3\times (3)+45\Rightarrow =0\\\\ \therefore x=3\text{ Potential roots of function}](https://tex.z-dn.net/?f=f%283%29%3D%203%5Ctimes%20%283%29%5E3-13%5Ctimes%20%283%29%5E2-3%5Ctimes%20%283%29%2B45%5CRightarrow%20%3D0%5C%5C%5C%5C%20%5Ctherefore%20x%3D3%5Ctext%7B%20Potential%20roots%20of%20function%7D)
Similarly, we will check for all value of p/q and we get
![f(-5/3)=0](https://tex.z-dn.net/?f=f%28-5%2F3%29%3D0)
Thus, All potential roots are 3,3 and
.
Answer:
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11
-4 + -7 = -11
-2 + -14 = -16
-1 + -28 = -29
1 + 28 = 29
2 + 14 = 16
4 + 7 = 11
7 + 4 = 11
14 + 2 = 16
28 + 1 = 29
Step-by-step explanation:
Answer:The answer is 24m-28
Step-by-step explanation:
Hope this helps