Answer:
Hulian's age is 7.
Thomas's age is 22.
Step-by-step explanation:
Let Hulian = h
Let Thomas = t
Set the system of equation:
h = t - 15
h + t = 29
Plug in t - 15 for h in the second equation:
(t - 15) + t = 29
Simplify. Combine like terms:
2t - 15 = 29
Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 15 to both sides:
2t - 15 (+15) = 29 (+15)
2t = 44
Divide 2 from both sides:
(2t)/2 = (44)2
t = 44/2
t = 22
Plug in 22 for t in one of the equations:
h = t - 15
h = 22 - 15
h = 7
Hulian's age is 7.
Thomas's age is 22.
~
Answer:
The correct answer would be chart A.
Step-by-step explanation:
Answer:
![\large \boxed{\sf \ \ \ p=-11 \ \ \ }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Csf%20%5C%20%5C%20%5C%20p%3D-11%20%5C%20%5C%20%5C%20%7D)
Step-by-step explanation:
Hello,
![\alpha \text{ and } \beta \text{ are the roots of the following equation}](https://tex.z-dn.net/?f=%5Calpha%20%5Ctext%7B%20and%20%7D%20%5Cbeta%20%5Ctext%7B%20are%20the%20roots%20of%20the%20following%20equation%7D)
![2x^2+6x-7=p](https://tex.z-dn.net/?f=2x%5E2%2B6x-7%3Dp)
It means that
![2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\](https://tex.z-dn.net/?f=2%5Calpha%5E2%2B6%5Calpha-7%3Dp%20%5C%5C%5C%5C2%5Cbeta%20%5E2%2B6%5Cbeta%20-7%3Dp%20%5C%5C%5C%5C)
And we know that
![\alpha= 2\cdot \beta](https://tex.z-dn.net/?f=%5Calpha%3D%202%5Ccdot%20%5Cbeta)
So we got two equations
![2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\6\beta^2+6\beta =0\\\\\beta(\beta+1)=0\\\\ \beta =0 \ or \ \beta=-1](https://tex.z-dn.net/?f=2%282%5Cbeta%29%5E2%2B6%5Ccdot%202%20%5Ccdot%20%5Cbeta%20-7%3Dp%20%5C%5C%5C%5C%3C%3D%3E8%5Cbeta%5E2%2B12%5Cbeta%20-7%3Dp%5C%5C%5C%5C%20and%20%5C%202%5Cbeta%20%5E2%2B6%5Cbeta%20-7%3Dp%20%5C%20So%20%5C%5C%5C%5C%5C%5C8%5Cbeta%5E2%2B12%5Cbeta%20-7%20%3D%202%5Cbeta%20%5E2%2B6%5Cbeta%20-7%5C%5C%5C%5C%3C%3D%3E6%5Cbeta%5E2%2B6%5Cbeta%20%3D0%5C%5C%5C%5C%3C%3D%3E%5Cbeta%28%5Cbeta%2B1%29%3D0%5C%5C%5C%5C%3C%3D%3E%20%5Cbeta%20%3D0%20%5C%20or%20%5C%20%5Cbeta%3D-1)
For ![\beta =0, \ \ \alpha =0, \ \ p = -7](https://tex.z-dn.net/?f=%5Cbeta%20%3D0%2C%20%5C%20%5C%20%5Calpha%20%3D0%2C%20%5C%20%5C%20p%20%3D%20-7)
For ![\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11](https://tex.z-dn.net/?f=%5Cbeta%20%3D-1%2C%20%5C%20%5C%20%5Calpha%20%3D-2%2C%20%5C%20%5C%20p%3D%202-6-7%3D-11%2C%20%5C%20p%3D2%2A4-12-7%3D-11)
I assume that we are after two different roots so the solution for p is p=-11
b) ![\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1](https://tex.z-dn.net/?f=%5Calpha%20%2B2%20%3D-2%2B2%3D0%20%5C%20and%20%5C%20%5Cbeta%2B2%3D-1%2B2%3D1)
So a quadratic equation with the expected roots is
![x(x-1)=x^2-x](https://tex.z-dn.net/?f=x%28x-1%29%3Dx%5E2-x)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
81
Step-by-step explanation:
93-12=81
Answer: 296 degrees
Step-by-step explanation:
Arc PRT is just the entire circumference - arc PT.
Since the 64 degree angle is a central angle, arc PT measures 64 degrees.
So arc PRT = 360 degree - 64 degree = 296 degrees.