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4 years ago

the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?

Mathematics

2 answers:

Ratling [72]4 years ago

8 0

Answer:

Step-by-step explanation:

Zinaida [17]4 years ago

3 0

Answer:

x ≥ -5

Step-by-step explanation:

If we have a translation to left c units, we write " x + c " in the function, and

If we have a translation to right c units, we write " x - c" in the function

If we have vertical translation up b units, we "add b to the function", and

If we have vertical translation down b units, we "subtract b to the function"

The parent function is $f(x)=\sqrt{x}$

Since translation left 5 units and up 3 units, we can write:

$f(x)=\sqrt{x+5} + 3$

The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:

x + 5 ≥ 0

x ≥ -5

This is the domain.

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According to a recent survey, the salaries of entry-level positions at a large company have a mean of and a standard deviation o

saveliy_v [14]

The proportion of employees in entry-level positions at the company who earn at least $ 42,000 will be 0.48466.

<h3>What is a normal distribution?</h3>

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

According to a recent survey, the salaries of entry-level positions at a large company have a mean of $ 41,750 and a standard deviation of $ 6500.

Assuming that the salaries of these entry-level positions are normally distributed.

Then the proportion of employees in entry-level positions at the company who earn at least $ 42,000 will be

The z-score is given as

z = (x - μ) / σ

Then we have

z = (42000 - 41750) / 6500

z = 0.03846

Then we have

P(x ≥ 42000) = P(z ≥ 0.03846)

P(x ≥ 42000) = 1 - P(z < 0.03846)

P(x ≥ 42000) = 1 - 0.51534

P(x ≥ 42000) = 0.48466

More about the normal distribution link is given below.

brainly.com/question/12421652

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6 0

2 years ago

What is the area in square millimeters ?

navik [9.2K]

Ok the first I got was (1) but, the square meter I got was 0.00064516

7 0

3 years ago

Suppose Cotangent (theta) = StartFraction 5 Over 12 EndFraction, where Pi less-than theta less-than StartFraction 3 pi Over 2 En

Agata [3.3K]

Answer:

Sin theta = 12/13

Step-by-step explanation:

From the question;

Cot theta = 5/12

Kindly recall;

Cot theta = 1/ tan theta

Hence, tan theta = 12/5

Mathematically

tan theta= opposite/adjacent

to get hypotenuse, we will use Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides

let hypotenuse be h

h^2 = 12^2 + 5^2

h^2 = 144 + 25

h^2 = 169

h = √169

h = 13

But sine theta = opposite/ hypotenuse = 12/13

5 0

3 years ago

Tu’s family stayed at a hotel for 10 nights on their vacation. The hotel charged a 10% room tax, per night. How much did they pa

Papessa [141]

Answer:

$200

Step-by-step explanation:

$2000 total divided by 10 nights= $200 per night

10% of $200 is $20

so $20 in taxes for 10 nights is 10*20= 200 for taxes

hope this helped plz mark brainliest trying to rank up :PP

4 0

3 years ago

Find the equation of the line through the points (0, –3) and (4, 5)

vekshin1

Answer:

y=2x-3

Step-by-step explanation:

Hi there!

We are given the points (0, –3) and (4, 5)

We want to find the equation of the line between these points

There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

To write the equation of the line in this way, we need to first find the slope of the line
The slope can be found using the formula $\frac{y_2-y_1}{x_2-x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We already have 2 points, but let's label their values to avoid confusion and mistakes when calculating.

m= $\frac{y_2-y_1}{x_2-x_1}$

m= $\frac{5--3}{4-0}$

Simplify

m= $\frac{5+3}{4-0}$

m= $\frac{8}{4}$

Divide

m=2

We found the slope of the line.

Here is the equation of the line so far:

y=2x+b

Now let's find b

As stated before, b is the y intercept of the line, which is the point where the line passes through the y axis; the value of x at the y intercept is 0

One of the points we were given (0, -3) is actually the y intercept of the line!

The value of b is the value of y at the y intercept; in this case, b is equal to -3

Now substitute -3 as b in the equation.

y=2x-3

Hope this helps!

See more on this topic here: brainly.com/question/27172025

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2 years ago