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2 years ago

Which pair of expressions are equivalent?

Mathematics

1 answer:

Zielflug [23.3K]2 years ago

4 0

Answer:

second one

Step-by-step explanation:

Because when you try to remove the brackets then you should multiply coefficient of x and coefficient of y by 2

So it will be 2x+18y

2*9=18

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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.

<u>Range:</u>

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

3 years ago

What missing angle of the figure

aniked [119]

Answer:

138

Step-by-step explanation:

152+125=277

277-135=142

around 138

4 0

3 years ago

Estimate the circumference of a circle that has a radius of 11 m.

tensa zangetsu [6.8K]

The answer would be <span>69.12m.</span>

3 0

3 years ago

12.

g100num [7]

Answer:

Step-by-step explanation:

$tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}$

7 0

3 years ago

If you multiplied 3x37, would the product be an even number or an odd number?

choli [55]

The answer would be an odd number, 111.

8 0

3 years ago