A. 2 teachers 26 students 8 teachers ?

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

I need information on rubix cubes and concentration

Angelina_Jolie [31]

Ubik's Cube is a 3 D combinations puzzle invented in 1974 by Hungarian sculptor and professors of architectures Ernő Rubyik. Originally called the Magic Cube,the puzzle was licensed by Rubik to be sold by Ideal Toy Corporation. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer,and won the German game of the year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide making it the world's top-selling puzzle game.It is widely considered to be the world's best-selling toy.

to play this game and to learn you need a lot of concentration and practice !

5 0

3 years ago

Can someone help me for once ?

hichkok12 [17]

Answer:

The answer is A)-4,6

Step-by-step explanation:

sorry if wrong

hope this helps

plz give brainliest

6 0

3 years ago

Plz.... I cant do my hone work its maths... plz some one help me it has photo

Rina8888 [55]

4)

variables d and w

5d +1(4d)=36

9d=36

d=4 w=4x4=16

difference of price $12

5)

E 5 comics

F= 10

G=20

e+ (e+5) + 2(e+5)=35

e+ e+5 + 2e +10 =35

4e +15=35

4e=20

e=5

Eugene = 5 comics

6)

Agnes and Billy had each 300 (after drinking it will be less water)

A 300-200 =100

B 300-100 =200

3 0

3 years ago

What is the average rate of change of the function f(x)=20(14)xf(x)=20(14)x from x = 1 to x = 2? Enter your answer, as a decimal

notsponge [240]

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= 20(14)^x \qquad 
\begin{cases}
x_1=1\\
x_2=2
\end{cases}\implies \cfrac{f(2)-f(1)}{2-1}
\\\\\\
\cfrac{[20(14)^2]~~-~~[20(14)^1]}{1}\implies \cfrac{20\cdot 196~~-~~20\cdot 14}{1}
\\\\\\
\cfrac{3920~~-~~280}{1}\implies \cfrac{3640}{1}\implies 3640$

4 0

3 years ago

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