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Rzqust [24]
2 years ago
6

What is the ratio for 4, 8, 12, 14 (r)

Mathematics
1 answer:
olasank [31]2 years ago
7 0

answer for this question is 2 is to 4 is to6 is to 7

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This is Matrix for pre calc
gavmur [86]

The given system of equations in augmented matrix form is

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\-6&1&2&4&-12\\1&-3&-3&5&-20\\-2&5&6&0&12\end{array}\right]

If you need to solve this, first get the matrix in RREF:

  • Add 2(row 1) to row 2, row 1 to -3(row 3), and 2(row 1) to 3(row 4):

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&11&5&-13&37\\0&19&10&4&-10\end{array}\right]

  • Add 11(row 2) to -5(row 3), and 19(row 1) to -5(row 4):

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&-164&132&-1052\end{array}\right]

  • Add 164(row 3) to -91(row 4):

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&13080&-39240\end{array}\right]

  • Multiply row 4 by 1/13080:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&1&-3\end{array}\right]

  • Add -153(row 4) to row 3:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&0&-364\\0&0&0&1&-3\end{array}\right]

  • Multiply row 3 by -1/91:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Add 6(row 3) and -8(row 4) to row 2:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&0&0&-10\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Multiply row 2 by 1/5:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Add -2(row 2), 4(row 3), and -2(row 4) to row 1:

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

  • Multiply row 1 by 1/3:

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

So the solution to this system is (w,x,y,z)=(1,-2,4,-3).

6 0
3 years ago
When a pair of six sided dice is rolled , each with faces numbered 1 to 6,is rolled once,what is the probability that the result
77julia77 [94]
In probability, there are hint clues that you must be vigilant of. When it tells you to find the probability of event 1 'or' event 2, you must ADD their individual probabilities. When it tells you to find the probability of event 1 'and' event 2, you must MULTIPLY their individual probabilities. 

Now, you have two dices. You are asked to find the probability of getting a face of 3, 4 or 5. The probability of each face of a dice is 1/6, because there are a total of 6 faces. When you use two dices, it becomes 2/12 or still 1/6. So, the total probability of getting either 3, 4 or 5 is: 1/6 + 1/6 + 1/6 = 1/2. However, you still have to multiply this with the total probability of getting a prime numbers which are 1, 2, 3 and 5. Thus, 1/6 + 1/6 + 1/6 + 1/6 = 2/3

Hence, the total probability would be 1/2 * 2/3 = 1/3 or 33%
5 0
2 years ago
Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).
vivado [14]

The equation of the line is y=\frac{1}{4}x-\frac{29}{7}

Explanation:

The equation of the line is perpendicular to y=-14 x-8

The equation is of the form y=mx+b where m=-14

<u>Slope:</u>

The slope of the perpendicular line can be determined using the formula,

m_1 \cdot m_2=-1

-14 \cdot m_2=-1

       m_2=\frac{1}{14}

Thus, the slope of the line is m=\frac{1}{14}

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

Substituting the slope m=\frac{1}{14} and the point (2,-4), we get,

y+4=\frac{1}{14}(x-2)

Simplifying, we get,

y+4=\frac{1}{14}x-\frac{1}{7}

     y=\frac{1}{14}x-\frac{1}{7}-4

     y=\frac{1}{4}x-\frac{29}{7}

Thus, the equation of the line is y=\frac{1}{4}x-\frac{29}{7}

3 0
3 years ago
What's the answer to my answer answer right ok thanks
Anika [276]
Feel free to ask any questions as to what I did

6 0
3 years ago
Find two consecutive integers whose sum is 35
4vir4ik [10]
Two consecutive integers are 17+18 
6 0
3 years ago
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