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Hoochie [10]
2 years ago
13

Given the system of equations presented here: 3x + 5y = 29 x + 4y = 16 Which of the following actions creates an equivalent syst

em such that, when combined with the other equation, one of the variables is eliminated? (5 points) Select one: a. Multiply the second equation by −1 to get −x − 4y = −16 b. Multiply the second equation by −3 to get −3x − 12y = −48 c. Multiply the first equation by −1 to get −3x − 5y = −29 d. Multiply the first equation by −3 to get −9x − 15y = −87
And pls show work
Mathematics
1 answer:
lesantik [10]2 years ago
3 0
It would be b. If you combine -3x-5y and 3x+5y, the x's cancel out. That would be the variable.
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How do I find the integral<br> ∫10(x−1)(x2+9)dxint10/((x-1)(x^2+9))dx ?
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\int\frac{10}{(x-1)(x^2+9)}\ dx=(*)\\\\\frac{10}{(x-1)(x^2+9)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+9}=\frac{A(x^2+9)+(Bx+C)(x-1)}{(x-1)(x^2+9)}\\\\=\frac{Ax^2+9A+Bx^2-Bx+Cx-C}{(x-1)(x^2+9)}=\frac{(A+B)x^2+(-B+C)x+(9A-C)}{(x-1)(x^2+9)}\\\Updownarrow\\10=(A+B)x^2+(-B+C)x+(9A-C)\\\Updownarrow\\A+B=0\ and\ -B+C=0\ and\ 9A-C=10\\A=-B\ and\ C=B\to9(-B)-B=10\to-10B=10\to B=-1\\A=-(-1)=1\ and\ C=-1

(*)=\int\left(\frac{1}{x-1}+\frac{-x-1}{x^2+9}\right)\ dx=\int\left(\frac{1}{x-1}-\frac{x+1}{x^2+9}\right)\ dx\\\\=\int\frac{1}{x-1}\ dx-\int\frac{x+1}{x^2+9}\ dx=\int\frac{1}{x-1}-\int\frac{x}{x^2+9}\ dx-\int\frac{1}{x^2+9}\ dx=(**)\\\\\#1\ \int\frac{1}{x-1}\ dx\Rightarrow\left|\begin{array}{ccc}x-1=t\\dx=dt\end{array}\right|\Rightarrow\int\frac{1}{t}\ dt=lnt+C_1=ln(x-1)+C_1

\#2\ \int\frac{x}{x^2+9}\ dx\Rightarrow  \left|\begin{array}{ccc}x^2+9=u\\2x\ dx=du\\x\ dx=\frac{1}{2}\ du\end{array}\right|\Rightarrow\int\left(\frac{1}{2}\cdot\frac{1}{u}\right)\ du=\frac{1}{2}\int\frac{1}{u}\ du\\\\\\=\frac{1}{2}ln(u)+C_2=\frac{1}{2}ln(x^2+9)+C_2

\#3\ \int\frac{1}{x^2+9}\ dx=\int\frac{1}{x^2+3^2}\ dx=\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3\\\\therefore:\\\\\#1;\ \#2;\ \#3\Rightarrow(**)=ln(x-1)+C_1-\frac{1}{2}ln(x^2+9)+C_2-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3

\boxed{=ln(x-1)-\frac{1}{2}ln(x^2+9)-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C}



4 0
3 years ago
What is the length of a in this triangle? A=x B=35 C=37 find C
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B. 12 assuming that it is a right triangle :)
7 0
2 years ago
I have no idea what the answer is , plz help
natima [27]
1/3 of 1/4 is the same as 2/6 of 2/8 
(easier for me this way)
2/6 is 0.33 
2/8 is 0.25 so you are in essence finding roughly 0.8333
that would be equal to the diagram at the bottom right
The other question is (i believe) 1/5 of 5/6
1/5 is 0.2, 5/6 is 0.833
another way to do it is to divide 833 by 5 is 166.6 so it would be 0.166
that would (i think) be the top right
3 0
3 years ago
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