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3 years ago

Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

7 0

5(3+n)=3(2n-1)
15+5n=6n-3
18=n

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Shania is planning a party at her home. She has made 126 chocolate truffles and 84 caramel truffles to give to her guests. If th

vodomira [7]

This turns out to be a division problem. To find how many each person can get, you must divide the amount of food by how many guests.
126 divided by 21 is 6
84 divided by 21 is 4
Each guest will get 6 chocolate truffles and 4 caramel truffles.

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IrinaVladis [17]

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2 years ago

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 $y>2$

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3 years ago

The bus arrived at 8:20. It left 30 minutes earlier. What time did the bus leave?

OlgaM077 [116]

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