Please anwser fast and give an explanation step by step thank you

Describe the 2 transformations that occur when the graph of f(x) =x −−√ is transformed to the graph of g(x) = 2x√ +3 .

Flauer [41]

Answer:

Dilation followed by Translation.

Step-by-step explanation:

We have the function $f(x)=\sqrt{x}$ .

The new transformed function is $g(x)=2\sqrt{x}+3$

Now, the transformation applied to f(x) to obtain g(x) are:

1. Dilation - it is the transformation that changes the size/shape of the figure. It is generally of the form kf(x) where k is constant.

Since, we are dilating the given function by 2 units, the new dilated function becomes $2\sqrt{x}$ .

2. Translation - it is the transformation that shifts the figure in any direction. When the function is shifted vertically, the general form becomes f(x)+k.

As, we see that the new dilated function is shifted 3 units upwards, the final translated function becomes $g(x)=2\sqrt{x}+3$ .

Hence, the transformations applied to obtain g(x) from f(x) are Dilation followed by Translation.

5 0

3 years ago

(a)<br> Solve.<br> 3x – 4 = x + 5

exis [7]

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

3x - 4 = x +5 (1) subtract x

2x - 4 = 5 (2) subtract 5

2x + 1 (3) divide by 2

x = 1/2 or 0.5

4 0

3 years ago

what is the probability of seeing a sample mean for 21 observations less or equal to the sample mean that we observed

kramer

Answer:

$P(x \le 21) = 0.69146$

Step-by-step explanation:

The missing parameters are:

$n = 64$ --- population

$\mu = 20$ --- population mean

$\sigma = 16$ -- population standard deviation

Required

$P(x \le 21)$

First, calculate the sample standard deviation

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{16}{\sqrt {64}}$

$\sigma_x = \frac{16}{8}$

$\sigma_x = 2$

Next, calculate the sample mean $\bar_x$

$\bar x = \mu$

So:

$\bar x = 20$

So, we have:

$\sigma_x = 2$

$\bar x = 20$

$x = 21$

Calculate the z score

$x = \frac{x - \mu}{\sigma}$

$x = \frac{21 - 20}{2}$

$x = \frac{1}{2}$

$x = 0.50$

So, we have:

$P(x \le 21) = P(z \le 0.50)$

From the z table

$P(z \le 0.50) = 0.69146$

So:

$P(x \le 21) = 0.69146$

4 0

3 years ago

When y = 35,x = 2.5. If the value of y varies directly with x what is the value of y when the value of xis 3.25

leonid [27]

Answer:

The value of y would be 45.5

Step-by-step explanation:

To solve this problem, start with the base form of direct variation.

y = kx

Now we can use our original values to model the equation and find k.

35 = k(2.5)

14 = k

Now we can model the equation as:

y = 14x

Now to find y, when x = 3.25, simply put 3.25 into the equation.

y = 14(3.25)

y = 45.5

8 0

4 years ago

"3. When we have two sorted lists of numbers in non-descending order, and we need to merge them into one sorted list, we can sim

iren [92.7K]

Answer:

Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)

Step-by-step explanation:

To understand better how we arrived at the aforementioned algorithm, we take it step by step

a, Construct a min-heap of the minimum elements from each of "k" lists.

The creation of this min-heap will cost O (k) time.

b) Next we run delete Minimum and move the minimum element to the output array.

Each extraction takes O (log k) time.

c) Then insert into the heap the next element from the list from which the element was extracted.

Now, we note that since we extract n elements in total, the running time is

O (n log k+ k) = O (n log k).

So we can conclude that :

Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)

5 0

3 years ago