Online school is not the move:( HELP PLEASE (40 points!!) (bottom right one says ✔️2 = 1.414213

What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

Range:

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

4 years ago

Mary gets an annual salary of $56,780. if she is paid semimonthly, what is the amount of her semimonthly gross pay?

Ulleksa [173]

There are 52 weeks in a year. Being paid biweekly means being paid every other week, or 26 times a year.

$567.20 * 26

There are 12 months in a year. If Mary is paid semimonthly, she is paid twice a month, or 24 times a year.

$56,780 / 24

3 0

3 years ago

Read 2 more answers

Find the sum of 5/8 + 3/10 *

Gnom [1K]

Answer:

37 / 40 or 0. 925

Step-by-step explanation:

5/ 8 + 3 / 10

= 37 / 40

= 0. 925

Mark brainliest pls

5 0

3 years ago

Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hu

dolphi86 [110]

Answer:

The monthly cost for 9 HCF is $38.54

Step-by-step explanation:

The graph is missing; however, the question can still be solved

Given

Slope = 1.55

When monthly cost = $47.84, Amount of water = 15 HCF

Required

Determine the monthly cost for 9 HCF

From the question, we understand that it is a linear function;

Linear functions are of the form

$y = mx + b$

Where y is the function of x and m is the slope

In this case; the function is the monthly water bill

and x is the amount of water

Solving for b

When monthly cost = $47.84, Amount of water = 15 HCF

The function is as follows;

$47.84 = 1.55 * 15 + b$

$47.84 = 23.25 + b$

Subtract 23.25 from both sides

$47.84 - 23.25= 23.25 - 23.25 + b$

$24.59 = b$

$b = 24.59$

Solving for the monthly cost for 9 HCF

Here, we have that

$x = Amount\ of\ water = 9$

$m = Slope = 1.55$

$b = 24.59$

Substitute these values in the linear function; $y = mx + b$

$y = 1.55 * 9 + 24.59$

$y = 13.95 + 24.59$

$y = 38.54$

Hence, the monthly cost for 9 HCF is $38.54

5 0

3 years ago

A 12 ft. rope is attached to the wall of a garage. A dog’s collar is attached to the end of the rope to allow him to safely stay

Zolol [24]

Since it's a wall, I'm guessing it will only have access to half the circle? Therefore:

Circle area formula: πr²

Radius: 12/2 = 6ft

Our case:

(π * 6²)/2 =

36π/2 =

18π = 56.55ft²

3 0

3 years ago