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3 years ago

Use the venn diagram to complete 96 is not the answer help

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

4 0

Answer:

52 students

Step-by-step explanation:

Let's assume A represents number of students in the library means A=86,

B represents number of student in student union means B = 78

U represents total students surveyed means U = 136

section II represents number of students in library and student union means

II = 34

Now from figure we can see

number of students only in library is represented by section I .

and section I can be written as

I = A - II

I = 86-34 = 52

only in Union represents III

III = B - II

III = 78-34 = 44

not in library or not in union = U - (I + II + III)

= 136 - (52+ 34+ 44)

= 136 - 130 = 6

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The smallest possible number for the third side would be 15

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Find the exact value of: sin13pi/8

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Sin(13π/8) , is in quadrant IV so the angle will be negative, find the reference angle.

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4 years ago

Read 2 more answers

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timurjin [86]

Answer:

(a) $x_1=-2,x_2=1$

(b) $x_1=\frac{3}{4} ,x_2=-\frac{1}{2} ,x_3=\frac{1}{4}$

Step-by-step explanation:

(a) For using Cramer's rule you need to find matrix $A$ and the matrix $B_j$ for each variable. The matrix $A$ is formed with the coefficients of the variables in the system. The first step is to accommodate the equations, one under the other, to get $A$ more easily.

$2x_1+5x_2=1\\x_1+4x_2=2$

$\therefore A=\left[\begin{array}{cc}2&5\\1&4\end{array}\right]$

To get $B_1$ , replace in the matrix A the 1st column with the results of the equations:

$B_1=\left[\begin{array}{cc}1&5\\2&4\end{array}\right]$

To get $B_2$ , replace in the matrix A the 2nd column with the results of the equations:

$B_2=\left[\begin{array}{cc}2&1\\1&2\end{array}\right]$

Apply the rule to solve $x_1$ :

$x_1=\frac{det\left(\begin{array}{cc}1&5\\2&4\end{array}\right)}{det\left(\begin{array}{cc}2&5\\1&4\end{array}\right)} =\frac{(1)(4)-(2)(5)}{(2)(4)-(1)(5)} =\frac{4-10}{8-5}=\frac{-6}{3}=-2\\x_1=-2$

In the case of B2, the determinant is going to be zero. Instead of using the rule, substitute the values of the variable $x_1$ in one of the equations and solve for $x_2$ :

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$2x_1+x_2 =1\\x_1+2x_2+x_3=0\\x_2+2x_3=0$

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$B_2=\left[\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right]$

$B_3=\left[\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right]$

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$x_2=\frac{det\left(\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{(2)(0)(2)+(1)(0)(0)+(0)(1)(1)-(2)(0)(1)-(1)(1)(2)-(0)(0)(0)}{4} \\x_2=\frac{0+0+0-0-2-0}{4}=\frac{-2}{4}=-\frac{1}{2}\\x_2=-\frac{1}{2}$

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Answer:

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