What is the simplified form of the expression 2b^-6·b^12?

Tìm m để phương trình có 1 nghiệm duy nhất x+2y-2z=2 3x+7y-z=5 2x+4y+mz=7

RSB [31]

Rewrite the system of equations in matrix form.

$\begin{bmatrix}1&2&-2\\3&7&-1\\2&4&m\end{bmatrix} \mathbf x = \mathbf b$

This system has a unique solution $\mathbf x = \mathbf A^{-1}\mathbf b$ so long as the inverse of the coefficient matrix $\mathbf A$ exists. This is the case if the determinant is not zero.

We have

$\det(\mathbf A) = m+4$

so the inverse, and hence a unique solution to the system of equations, exists as long as m ≠ -4.

4 0

2 years ago

Choose the graph which matches the function. (2 points) f(x) = 3x-4

vovangra [49]

The last image is the graph of $y = 3^x$

In fact, it is an increasing exponential function, and it passes through the points $(0,1)$ , which reflects the fact that $3^0=1$ and $(1,3)$ , which reflects the fact that $3^1=3$ .

Now, $y = 3^{x-4}$ is a child of the parent function we just described. Precisely, it is the result of the transformation $f(x) \to f(x-4)$

In general, every time you perform a transformation like $f(x) \to f(x+k)$ , you translate the graph horizontall, k units to the left if k is positive, and k units to the right if k in negative.

Since in this case $k = - 4$ , we have a horizontal translation of 4 units to the right.

So, the correct option is the third one, because:

The first graph is the parent function translated 4 units to the left
The second graph is the parent function translated 4 units down
The third graph is the parent function translated 4 units to the right
The fourth graph is the parent function

5 0

2 years ago

Kraig deposited money into a money market account. It has an interest of 12% and is compounded annually. Kraig thought 3% would

Klio2033 [76]

Answer:

If the amount is P, with the interest rate of 12%, the interest over the year is:

P*(1.12) - P = 0.12P

In this case the quarterly interest rate is:

0.12P/4 = 0.03P

With the same amount and 3% quarterly rate, the yearly interest would be:

P*(1.03)^4 - P = 0.1255P

The quarterly interest rate in this case is:

0.1255P/4 = 0.031375P

If the quarterly interest rate is r, it should be little less than 3% to yield a 12% yearly rate.

So Kraig is wrong.

7 0

3 years ago

Solve Systems by Substitution 2x+5y=-3 x+8y=4 and 2x+y=7 x-2y=-14

ASHA 777 [7]

2x + 5y = -3 ⇒ 2x + 5y = -3
1x + 8y = 4 ⇒ 2x + 16y = 8
 -11y = -11 
 -11 -11
 y = 1
 2x + 5(1) = -3
 2x + 5 = -3
 -5 -5
 2x = -8
 2 2
 x = -4
 (x, y) = (-4, 1)

2x + 1y = 7 ⇒ 2x + 1y = 7
1x - 2y = -14 ⇒ 2x - 4y = -28
 5y = 35
 5 5
 y = 7
 2x + 7 = 7
 -7 -7
 2x = 0
 2 2
 x = 0
 (x, y) = (0, 7)

4 0

3 years ago

Find the value of x when 6-3x= 5x-10x+20

icang [17]

Answer:

7

Step-by-step explanation:

5 0

2 years ago