Someone answer please, its a test. will give brainliest to the fastest.

Which of the following are based on the diagram below? (select all answers that are true)

andreev551 [17]

It’s the first one.

6 0

3 years ago

If f(x)=1/6x+12, then f^-1(x)=<br> PLEASE HELP

Finger [1]

$f(x)=\dfrac{1}{6}x+12\to y=\dfrac{1}{6}x+12$

Change x to y, and y to x.

$x=\dfrac{1}{6}y+12$

solve for y:

$\dfrac{1}{6}y+12=x\ \ \ |-12\\\\\dfrac{1}{6}y=x-12\ \ \ \ |\cdot6\\\\y=6x-72$

Your answer is:

$f^{-1}(x)=6x-72$

5 0

3 years ago

Rewrite the following system of linear equations in matrix equation form and in vector equation form. Solve the system.

alisha [4.7K]

Answer:

The set of solutions is $\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}$

Step-by-step explanation:

The matrix associated to the problem is $A=\left[\begin{array}{ccccc}1&-1&2&-8&1\\2&-1&-4&1&-2\\-4&1&4&-3&-1\end{array}\right]$ and the vector of independent terms is (3,1,-1)^t. Then the matrix equation form of the system is Ax=b.

The vector equation form is $a\left[\begin{array}{c}1\\2\\-4\end{array}\right]+b\left[\begin{array}{c}-1\\-1\\1\end{array}\right] + x\left[\begin{array}{c}2\\-4\\4\end{array}\right]+y\left[\begin{array}{c}-8\\1\\-3\end{array}\right] + z\left[\begin{array}{c}1\\-2\\-1\end{array}\right]=\left[\begin{array}{c}3\\1\\-1\end{array}\right]$ .

Now we solve the system.

The aumented matrix of the system is $\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\2&-1&-4&1&-2&1\\-4&1&4&-3&-1&-1\end{array}\right]$ .

Applying rows operations we obtain a echelon form of the matrix, that is $\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\0&1&-8&-15&-4&-5\\0&0&1&-80&-9&-4\end{array}\right]$

Now we solve for the unknown variables:

x-80y-90z=-4 then x=-4+80y+90z
b-8x-15y-4z=-5, b-8(-4+80y+90z)-15y-4z=-5 then b=-37+655y+724z.
a-b+2x-8y+z=3, a-(-37+655y+724z)+2(-4+80y+90z)-8y+z=3, then a=-26+503y+543z

Since the system has two free variables then has infinite solutions.

The set of solutions is $\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}$

5 0

3 years ago

What equations have m=5 as the solution

sergeinik [125]

Is there a picture ??

3 0

3 years ago

Read 2 more answers

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Goryan [66]

................................................i dont know

6 0

3 years ago