There are 4 consecutive integers that have a sum of 18. What is the value of the least integer?

Mathematics

1 answer:

EleoNora [17]3 years ago

4 0

3,4,5,6

The lowest integer is 3

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3 years ago

30 POINTS! Consider the system of linear equations and the matrix equations below.

fiasKO [112]

Answer:

Option C is correct.

Step-by-step explanation:

-x+3y=2

4x-2y=22

In matrix form is represented as:

$\left[\begin{array}{cc}-1&3\\4&-2\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{c}2&22\end{array}\right]$

AX=B

$X = A^{-1}B$

$A^{-1} = |A|/Adj A$

|A| = (-1)(-2)-(3)(4)

|A| = 2-12

|A| = -10

Adj A = $\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right]$

A^-1 = -1/10 $\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right]$

A^-1 = 1/10 $\left[\begin{array}{cc}2&3\\4&1\end{array}\right]$

X= A^-1 B

X = 1/10 $\left[\begin{array}{cc}2&3\\4&1\end{array}\right]$ $\left[\begin{array}{c}2&22\end{array}\right]$

X=1/10 $X=1/10\left[\begin{array}{c}2*2+3*22\\4*2+1*22\end{array}\right]\\X=1/10\left[\begin{array}{c}4+66\\8+22\end{array}\right]\\X=1/10\left[\begin{array}{c}70\\30\end{array}\right]\\X=\left[\begin{array}{c}70/10\\30/10\end{array}\right]\\X=\left[\begin{array}{c}7\\3\end{array}\right]$