Answer:
Step-by-step explanation:
![a_n=-3n+50\\ \\ a_{15}=-3(15)+50\\ \\ a_{15}=-45+50\\ \\ a_{15}=5](https://tex.z-dn.net/?f=a_n%3D-3n%2B50%5C%5C%20%5C%5C%20a_%7B15%7D%3D-3%2815%29%2B50%5C%5C%20%5C%5C%20a_%7B15%7D%3D-45%2B50%5C%5C%20%5C%5C%20a_%7B15%7D%3D5)
keeping in mind that when the logarithm base is omitted, the base 10 is assumed.
![\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(x)=2\implies \log_{10}(x)=2\implies 10^2=x\implies 100=x](https://tex.z-dn.net/?f=%5Ctextit%7Bexponential%20form%20of%20a%20logarithm%7D%20%5C%5C%5C%5C%20%5Clog_a%28b%29%3Dy%20%5Cqquad%20%5Cimplies%20%5Cqquad%20a%5Ey%3D%20b%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Clog%28x%29%3D2%5Cimplies%20%5Clog_%7B10%7D%28x%29%3D2%5Cimplies%2010%5E2%3Dx%5Cimplies%20100%3Dx)
Answer:
5
Step-by-step explanation:
3-(-2) will become positive 5. so number line will go towards positive 5.
Answer:
(0,-5) and (-4,3)
Step-by-step explanation:
The given equations are
![\left \{ {{x^2+y^2=25} \atop {2x+y=-5}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%5E2%2By%5E2%3D25%7D%20%5Catop%20%7B2x%2By%3D-5%7D%7D%20%5Cright.)
Make y the subject in the second equation;
![y=-2x-5](https://tex.z-dn.net/?f=y%3D-2x-5)
Substitute into the first equation;
![x^2+(-2x-5)^2=25](https://tex.z-dn.net/?f=x%5E2%2B%28-2x-5%29%5E2%3D25)
Expand:
![x^2+4x^2+20x+25=25](https://tex.z-dn.net/?f=x%5E2%2B4x%5E2%2B20x%2B25%3D25)
![x^2+4x^2+20x+25-25=0](https://tex.z-dn.net/?f=x%5E2%2B4x%5E2%2B20x%2B25-25%3D0)
![5x^2+20x=0](https://tex.z-dn.net/?f=5x%5E2%2B20x%3D0)
![5x(x+4)=0](https://tex.z-dn.net/?f=5x%28x%2B4%29%3D0)
![\Rightarrow x=0,x=-4](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D0%2Cx%3D-4)
When x=0,
![y=-2(0)-5=-5](https://tex.z-dn.net/?f=y%3D-2%280%29-5%3D-5)
This gives; (0,-5)
When x=-4
![y=-2(-4)-5=3](https://tex.z-dn.net/?f=y%3D-2%28-4%29-5%3D3)
This gives (-4,3)
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.
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