For this case we have a quadratic equation of the form:
![ax ^ 2 + bx + c = 0\\x ^ 2 + 11x-4 = 0](https://tex.z-dn.net/?f=ax%20%5E%202%20%2B%20bx%20%2B%20c%20%3D%200%5C%5Cx%20%5E%202%20%2B%2011x-4%20%3D%200)
Where:
![a = 1\\b = 11\\c = -4](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%2011%5C%5Cc%20%3D%20-4)
We find the roots:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-11 \pm \sqrt {11 ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {-11 \pm \sqrt {121 + 16}} {2}\\x = \frac {-11 \pm \sqrt {137}} {2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2%20%28a%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-11%20%5Cpm%20%5Csqrt%20%7B11%20%5E%202-4%20%281%29%20%28-%204%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-11%20%5Cpm%20%5Csqrt%20%7B121%20%2B%2016%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-11%20%5Cpm%20%5Csqrt%20%7B137%7D%7D%20%7B2%7D)
The roots are:
![x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%5Cfrac%20%7B-11%2B%20%5Csqrt%20%7B137%7D%7D%20%7B2%7D%5C%5Cx_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-11-%20%5Csqrt%20%7B137%7D%7D%20%7B2%7D)
Answer:
![x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%5Cfrac%20%7B-11%2B%20%5Csqrt%20%7B137%7D%7D%20%7B2%7D%5C%5Cx_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-11-%20%5Csqrt%20%7B137%7D%7D%20%7B2%7D)
Answer:
(a) ![\therefore C=\frac59(F-32)](https://tex.z-dn.net/?f=%5Ctherefore%20C%3D%5Cfrac59%28F-32%29)
(b)The boiling point of water in Celsius scale is 100°C.
(c)The setting in Celsius scale is 26.7°C.
Step-by-step explanation:
Given that,the formula is
......(1)
(a)
Given that,
![F=\frac95 C+32](https://tex.z-dn.net/?f=F%3D%5Cfrac95%20C%2B32)
[ subtracting 32 from both sides]
![\Rightarrow F-32=\frac95 C](https://tex.z-dn.net/?f=%5CRightarrow%20F-32%3D%5Cfrac95%20C)
![\Rightarrow \frac95 C=F-32](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac95%20C%3DF-32)
......(2) [Multiplying
]
![\therefore C=\frac59(F-32)](https://tex.z-dn.net/?f=%5Ctherefore%20C%3D%5Cfrac59%28F-32%29)
(b)
Given that, the boiling point of water is 212°F.
Putting F=212 in equation (2)
![\therefore C=\frac59(212-32)](https://tex.z-dn.net/?f=%5Ctherefore%20C%3D%5Cfrac59%28212-32%29)
![\Rightarrow C=\frac59\times 180](https://tex.z-dn.net/?f=%5CRightarrow%20C%3D%5Cfrac59%5Ctimes%20180)
![\Rightarrow C=5\times 20](https://tex.z-dn.net/?f=%5CRightarrow%20C%3D5%5Ctimes%2020)
![\Rightarrow C=100](https://tex.z-dn.net/?f=%5CRightarrow%20C%3D100)
The boiling point of water is 100°C.
(c)
Given that, a house thermostat is set at 80 degree.
Putting F=80 in equation (2)
![\therefore C=\frac59(80-32)](https://tex.z-dn.net/?f=%5Ctherefore%20C%3D%5Cfrac59%2880-32%29)
![\Rightarrow C=\frac59\times 48](https://tex.z-dn.net/?f=%5CRightarrow%20C%3D%5Cfrac59%5Ctimes%2048)
![\Rightarrow C\approx26.7](https://tex.z-dn.net/?f=%5CRightarrow%20C%5Capprox26.7)
The setting in Celsius scale is 26.7°C.
Answer:
1. 79.2 inches
2. 114
3. 55.2
4. 2599.992
5. 2350
Step-by-step explanation:
Yw
Answer:
7 hours
Step-by-step explanation:
12hrs=1116kms
1hr=1116÷12
1hr=93kms
Xhrs=651kms
Xhrs=(651÷93) ×1
=7×1
=7hrs