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irina [24]
2 years ago
12

How do you solve this problem (5x+10)=(2-7x)

Mathematics
1 answer:
SVETLANKA909090 [29]2 years ago
6 0

Answer:

x=-2/3

Step-by-step explanation:

(5x+10)=(2-7x)

5x+10=2-7x

5x+7x=2-10

12x=-8

x=-8/12

x=-2/3

You might be interested in
Use Gaussian Elimination to find an equation of a polynomial that passes through points A(-5,-3), B(-2,3). C(3,3), D(6,19). Indi
Marrrta [24]

Answer:

The polynomial equation that passes through the points is 2-\frac{2}{3}x+\frac{1}{12}x^{2}+\frac{1}{12}x^{3}

Step-by-step explanation:

Suppose you have a function y = f(x) which goes through these points

A(-5,-3), B(-2,3). C(3,3), D(6,19)

there is a polynomial P(x) of degree 3 which goes through these point.

We use the fact that <em>four distinct points will determine a cubic function.</em>

P(x) is the degree 3 polynomial through the 4 points, a standard way to write it is

P(x) = a+bx+cx^2+dx^3

Next replace the given points one by one, which leads to a system of 4 equations and 4 variables (namely a,b,c,d)

-3=a+b\cdot-5+c\cdot -5^2+d\cdot -5^3\\3=a+b\cdot-2+c\cdot -2^2+d\cdot -2^3\\3=a+b\cdot 3+c\cdot 3^2+d\cdot 3^3\\19=a+b\cdot 6+c\cdot 6^2+d\cdot 6^3

We can rewrite this system as follows:

-3=a-5\cdot b+25\cdot c-125\cdot d\\3=a-2\cdot b+4\cdot c-8\cdot d\\3=a+3\cdot b+9\cdot c+27\cdot d\\19=a+6\cdot b+36\cdot c+216\cdot d

To use the Gaussian Elimination we need to express the system of linear equations in matrix form (<em>the matrix equation Ax=b</em>).

The coefficient matrix (A) for the above system is

\left[\begin{array}{cccc}1&-5&25&-125\\1&-2&4&-8\\1&3&9&27\\1&6&36&216\end{array}\right]

the variable matrix (x) is

\left[\begin{array}{c}a&b&c&d\end{array}\right]

and the constant matrix (b) is

\left[\begin{array}{c}-3&3&3&19\end{array}\right]

We also need the augmented matrix, it is obtained by appending the columns of the coefficient matrix and the constant matrix.

\left[\begin{array}{cccc|c}1&-5&25&-125&-3\\1&-2&4&-8&3\\1&3&9&27&3\\1&6&36&216&19\end{array}\right]

To transform the augmented matrix to the reduced row echelon form we need to follow these steps:

  • Subtract row 1 from row 2 \left(R_2=R_2-R_1\right)

\left[\begin{array}{cccc|c}1&-5&25&-125&-3\\0&3&-21&117&6\\1&3&9&27&3\\1&6&36&216&19\end{array}\right]

  • Subtract row 1 from row 3 \left(R_3=R_3-R_1\right)

\left[\begin{array}{cccc|c}1&-5&25&-125&-3\\0&3&-21&117&6\\0&8&-16&152&6\\1&6&36&216&19\end{array}\right]

  • Subtract row 1 from row 4 \left(R_4=R_4-R_1\right)

\left[\begin{array}{cccc|c}1&-5&25&-125&-3\\0&3&-21&117&6\\0&8&-16&152&6\\0&11&11&341&22\end{array}\right]

  • Divide row 2 by 3 \left(R_2=\frac{R_2}{3}\right)

\left[\begin{array}{cccc|c}1&-5&25&-125&-3\\0&1&-7&39&2\\0&8&-16&152&6\\0&11&11&341&22\end{array}\right]

  • Add row 2 multiplied by 5 to row 1 \left(R_1=R_1+\left(5\right)R_2\right)

\left[\begin{array}{cccc|c}1&0&-10&-70&7\\0&1&-7&39&2\\0&8&-16&152&6\\0&11&11&341&22\end{array}\right]

  • Subtract row 2 multiplied by 8 from row 3 \left(R_3=R_3-\left(8\right)R_2\right)

\left[\begin{array}{cccc|c}1&0&-10&-70&7\\0&1&-7&39&2\\0&0&40&-160&-10\\0&11&11&341&22\end{array}\right]

  • Subtract row 2 multiplied by 11 from row 4 \left(R_4=R_4-\left(11\right)R_2\right)

\left[\begin{array}{cccc|c}1&0&-10&-70&7\\0&1&-7&39&2\\0&0&40&-160&-10\\0&0&88&-88&0\end{array}\right]

  • Divide row 3 by 40 \left(R_3=\frac{R_3}{40}\right)

\left[\begin{array}{cccc|c}1&0&-10&-70&7\\0&1&-7&39&2\\0&0&1&-4&-1/4\\0&0&88&-88&0\end{array}\right]

  • Add row 3 multiplied by 10 to row 1 \left(R_1=R_1+\left(10\right)R_3\right)

\left[\begin{array}{cccc|c}1&0&0&30&9/2\\0&1&-7&39&2\\0&0&1&-4&-1/4\\0&0&88&-88&0\end{array}\right]

  • Add row 3 multiplied by 7 to row 2 \left(R_2=R_2+\left(7\right)R_3\right)

\left[\begin{array}{cccc|c}1&0&0&30&9/2\\0&1&0&11&1/4\\0&0&1&-4&-1/4\\0&0&88&-88&0\end{array}\right]

  • Subtract row 3 multiplied by 88 from row 4 \left(R_4=R_4-\left(88\right)R_3\right)

\left[\begin{array}{cccc|c}1&0&0&30&9/2\\0&1&0&11&1/4\\0&0&1&-4&-1/4\\0&0&0&264&22\end{array}\right]

  • Divide row 4 by 264 \left(R_4=\frac{R_4}{264}\right)

\left[\begin{array}{cccc|c}1&0&0&30&9/2\\0&1&0&11&1/4\\0&0&1&-4&-1/4\\0&0&0&1&1/12\end{array}\right]

  • Subtract row 4 multiplied by 30 from row 1 \left(R_1=R_1-\left(30\right)R_4\right)

\left[\begin{array}{cccc|c}1&0&0&0&2\\0&1&0&11&1/4\\0&0&1&-4&-1/4\\0&0&0&1&1/12\end{array}\right]

  • Subtract row 4 multiplied by 11 from row 2 \left(R_2=R_2-\left(11\right)R_4\right)

\left[\begin{array}{cccc|c}1&0&0&0&2\\0&1&0&0&-2/3\\0&0&1&-4&-1/4\\0&0&0&1&1/12\end{array}\right]

  • Add row 4 multiplied by 4 to row 3 \left(R_3=R_3+\left(4\right)R_4\right)

\left[\begin{array}{cccc|c}1&0&0&0&2\\0&1&0&0&-2/3\\0&0&1&0&1/12\\0&0&0&1&1/12\end{array}\right]

From the reduced row-echelon form the solutions are:

\left[\begin{array}{c}a=2&b=-2/3&c=1/12&d=1/12\end{array}\right]

The polynomial P(x) is:

2-\frac{2}{3}x+\frac{1}{12}x^{2}+\frac{1}{12}x^{3}

We can check our solution plotting the polynomial and checking that it passes through the points.

3 0
2 years ago
Solve using the substitution method. What is the y coordinate of the solution?
Slav-nsk [51]
If this is solve using system of equations it would be 2,0 for substitution
3 0
3 years ago
How did brianly choose the best answer
ladessa [460]

Answer:

➢ Unfortunately, Brainly appears more to be a place to get quick answers so that students can finish homework faster. The answers, even if they're correct, often offer little to no elaboration or depth on the topic, and there's no guarantee that given answers will be correct.

#CarryOnLearning

5 0
2 years ago
HELP ME AGAIN PLSSSSS
Greeley [361]

Answer:

16

Step-by-step explanation:

4^2 = 16

4×4=16 thats the answer

5 0
2 years ago
Read 2 more answers
HELP! WILL GIVE BRAINLIEST AND 100 POINTS
sertanlavr [38]

Answer:

tyce is correct because the sides they were given were sides a and c if they were either side of the right angle since c is always the hypotenuse which is opposite the right angle. he followed the steps through correctly and got the right answer. cade used the wrong sides so the answer was wrong.

Step-by-step explanation:

hope thats right!

<3 ;)

4 0
3 years ago
Read 2 more answers
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