For the first one, remember that the parent function is y = x² for a parabola. The modifications made are the subtraction of five from the square of x, and the square of x is also being multiplied by two.
For the second one, look at the roots (Where the graph crosses the x - axis). From them, we can create a function with the following steps:
1.) Put the two roots into monomials:
(x - 1)(x - 3)
2.) Multiply them together with FOIL (First, Outside, Inside, Last):
x² - 3x - x + 3
x² - 4x + 3
3.) You have your answer!
x² - 4x + 3
Hope I was of help to you! Feel free to come back to Brainly for any other questions you might have :)
Answer:
![\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81](https://tex.z-dn.net/?f=%5Cleft%283%2Bx%5Cright%29%5E4%3A%5Cquad%20x%5E4%2B12x%5E3%2B54x%5E2%2B108x%2B81)
Step-by-step explanation:
Considering the expression
![\left(3+x\right)^4](https://tex.z-dn.net/?f=%5Cleft%283%2Bx%5Cright%29%5E4)
Lets determine the expansion of the expression
![\left(3+x\right)^4](https://tex.z-dn.net/?f=%5Cleft%283%2Bx%5Cright%29%5E4)
![\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Abinomial%5C%3Atheorem%7D%3A%5Cquad%20%5Cleft%28a%2Bb%5Cright%29%5En%3D%5Csum%20_%7Bi%3D0%7D%5En%5Cbinom%7Bn%7D%7Bi%7Da%5E%7B%5Cleft%28n-i%5Cright%29%7Db%5Ei)
![a=3,\:\:b=x](https://tex.z-dn.net/?f=a%3D3%2C%5C%3A%5C%3Ab%3Dx)
![=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i](https://tex.z-dn.net/?f=%3D%5Csum%20_%7Bi%3D0%7D%5E4%5Cbinom%7B4%7D%7Bi%7D%5Ccdot%20%5C%3A3%5E%7B%5Cleft%284-i%5Cright%29%7Dx%5Ei)
Expanding summation
![\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}](https://tex.z-dn.net/?f=%5Cbinom%7Bn%7D%7Bi%7D%3D%5Cfrac%7Bn%21%7D%7Bi%21%5Cleft%28n-i%5Cright%29%21%7D)
![i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0](https://tex.z-dn.net/?f=i%3D0%5Cquad%20%3A%5Cquad%20%5Cfrac%7B4%21%7D%7B0%21%5Cleft%284-0%5Cright%29%21%7D3%5E4x%5E0)
![i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1](https://tex.z-dn.net/?f=i%3D1%5Cquad%20%3A%5Cquad%20%5Cfrac%7B4%21%7D%7B1%21%5Cleft%284-1%5Cright%29%21%7D3%5E3x%5E1)
![i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2](https://tex.z-dn.net/?f=i%3D2%5Cquad%20%3A%5Cquad%20%5Cfrac%7B4%21%7D%7B2%21%5Cleft%284-2%5Cright%29%21%7D3%5E2x%5E2)
![i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3](https://tex.z-dn.net/?f=i%3D3%5Cquad%20%3A%5Cquad%20%5Cfrac%7B4%21%7D%7B3%21%5Cleft%284-3%5Cright%29%21%7D3%5E1x%5E3)
![i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4](https://tex.z-dn.net/?f=i%3D4%5Cquad%20%3A%5Cquad%20%5Cfrac%7B4%21%7D%7B4%21%5Cleft%284-4%5Cright%29%21%7D3%5E0x%5E4)
![=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%21%7D%7B0%21%5Cleft%284-0%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E4x%5E0%2B%5Cfrac%7B4%21%7D%7B1%21%5Cleft%284-1%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E3x%5E1%2B%5Cfrac%7B4%21%7D%7B2%21%5Cleft%284-2%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E2x%5E2%2B%5Cfrac%7B4%21%7D%7B3%21%5Cleft%284-3%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E1x%5E3%2B%5Cfrac%7B4%21%7D%7B4%21%5Cleft%284-4%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E0x%5E4)
![=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%21%7D%7B0%21%5Cleft%284-0%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E4x%5E0%2B%5Cfrac%7B4%21%7D%7B1%21%5Cleft%284-1%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E3x%5E1%2B%5Cfrac%7B4%21%7D%7B2%21%5Cleft%284-2%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E2x%5E2%2B%5Cfrac%7B4%21%7D%7B3%21%5Cleft%284-3%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E1x%5E3%2B%5Cfrac%7B4%21%7D%7B4%21%5Cleft%284-4%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E0x%5E4)
as
![\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81](https://tex.z-dn.net/?f=%5Cfrac%7B4%21%7D%7B0%21%5Cleft%284-0%5Cright%29%21%7D%5Ccdot%20%5C%3A%5C%3A3%5E4x%5E0%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A81)
![\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x](https://tex.z-dn.net/?f=%5Cfrac%7B4%21%7D%7B1%21%5Cleft%284-1%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E3x%5E1%3A%5Cquad%20108x)
![\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2](https://tex.z-dn.net/?f=%5Cfrac%7B4%21%7D%7B2%21%5Cleft%284-2%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E2x%5E2%3A%5Cquad%2054x%5E2)
![\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3](https://tex.z-dn.net/?f=%5Cfrac%7B4%21%7D%7B3%21%5Cleft%284-3%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E1x%5E3%3A%5Cquad%2012x%5E3)
![\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4](https://tex.z-dn.net/?f=%5Cfrac%7B4%21%7D%7B4%21%5Cleft%284-4%5Cright%29%21%7D%5Ccdot%20%5C%3A3%5E0x%5E4%3A%5Cquad%20x%5E4)
so equation becomes
![=81+108x+54x^2+12x^3+x^4](https://tex.z-dn.net/?f=%3D81%2B108x%2B54x%5E2%2B12x%5E3%2Bx%5E4)
![=x^4+12x^3+54x^2+108x+81](https://tex.z-dn.net/?f=%3Dx%5E4%2B12x%5E3%2B54x%5E2%2B108x%2B81)
Therefore,
Answer:
The measure of x=![11.35^{\circ}](https://tex.z-dn.net/?f=11.35%5E%7B%5Ccirc%7D)
Step-by-step explanation:
We are given that
Height of tower=200ft
Distance between two boats=250 ft
From given figure
![\frac{perpendicular\;side}{base}=tan\theta](https://tex.z-dn.net/?f=%5Cfrac%7Bperpendicular%5C%3Bside%7D%7Bbase%7D%3Dtan%5Ctheta)
![\frac{200}{base}=tan15^{\circ}](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7Bbase%7D%3Dtan15%5E%7B%5Ccirc%7D)
![base=\frac{200}{tan15^{\circ}}=746.55 ft](https://tex.z-dn.net/?f=base%3D%5Cfrac%7B200%7D%7Btan15%5E%7B%5Ccirc%7D%7D%3D746.55%20ft)
Again ,
![\frac{200}{746.55+250}=tan x](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B746.55%2B250%7D%3Dtan%20x)
![\frac{200}{996.55}=tan x](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B996.55%7D%3Dtan%20x)
![x=tan^{-1}(0.20069)=11.35^{\circ}](https://tex.z-dn.net/?f=x%3Dtan%5E%7B-1%7D%280.20069%29%3D11.35%5E%7B%5Ccirc%7D)
Hence, the measure of x=![11.35^{\circ}](https://tex.z-dn.net/?f=11.35%5E%7B%5Ccirc%7D)
Answer:
{x|√5 ≥ x ≥ -√5}
Step-by-step explanation:
Simply take the ±√5 then square it to get rid of the radical [5].
I am joyous to assist you anytime.
First, you have to find which two numbers go into 24 when multiplied.
24=
6×4
2×12
24×1
-6×4
-2×12
-24×1
Then you add each set of numbers together.
6+4=10
2+12=14
24+1=25
-6+4=-2
-2+12=10
-24+1=-23
6+(-4)=1
2+(-12)=-10
24+(-1)=23
Then you find which set when added makes 4. Since none of these are 4, it is no solution.